Armington elasticities for Brazil

Abstract

In this article we estimate substitution elasticities for goods distinguished by place of production, specifying whether they are imported or produced domestically. These are known as the Armington (1969) elasticities and are widely used to assess the impact on the domestic economy of policy changes in countries’ tariff structures; and, in particular, to evaluate the costs and benefits of signing free trade agreements. The sample period
for our study is 1986-2002, and the estimation is done separately for each of the 28 industrial sectors specified in the Brazilian input-output table. Special consideration is given to the fact that the data is affected by import restrictions for part of that period, and that foreign trade liberalization occurred in Brazil in 1990. The estimation procedure is automated and takes into consideration the stochastic dynamic properties of the quantity and price series, using the appropriate estimation approach in each case. The Armington elasticities we estimate have the correct sign, and are
significant at the 5% level for 20 sectors, at 10% for two sectors, and at 20% for two others. In one sector the estimated value is significant, but has the incorrect sign (negative). For three sectors the estimated elasticity is not significantly different from zero; but these represent only 12% of the average value of total import value in the period 1997-2002. The point estimate of the elasticity of substitution, for the sectors where it is positive and statistically different from zero, varies from 0.16 to 3.6; and its weighted average value is 0.93.

Full text

Modeling Public Policies in Latin America and the Caribbean 285
Chapter IX
Armington elasticities for Brazil1
Octávio Augusto Fontes Tourinho2
Honorio Kume3
Ana Cristina de Souza Pedroso4
In this article we estimate substitution elasticities for goods distinguished
by place of production, specifying whether they are imported or produced
domestically. These are known as the Armington (1969) elasticities and
are widely used to assess the impact on the domestic economy of policy
changes in countries’ tariff structures; and, in particular, to evaluate the
costs and benefits of signing free trade agreements. The sample period
for our study is 1986-2002, and the estimation is done separately for each
of the 28 industrial sectors specified in the Brazilian input-output table.
Special consideration is given to the fact that the data is affected by import
restrictions for part of that period, and that foreign trade liberalization
1 This is an English language version of Tourinho, Kume and Pedroso (2007). The authors
would like to thank participants in the seminar “Encuentro Regional sobre Modelos
de Equilíbrio General Computable: sus aportes em la Formulacipón de La Política
Econômica em America Latina”, sponsored by ECLAC and IDB, held in Santiago, Chile,
in April 2007, for their comments and suggestions.
2 Brazilian Development Bank (BNDES) and University of the State of Rio de Janeiro
(UERJ). E-mail: touri@bndes.gov.br
3 Institute of Applied Economic Research (IPEA) and University of the State of do Rio de
Janeiro (UERJ). E-mail: kume@ipea.gov.br
4 Institute of Applied Economic Research (IPEA), when involved in the research reported
in this paper. E-mail: anapedroso@globo.com

286 ECLAC – IDB
occurred in Brazil in 1990. The estimation procedure is automated and
takes into consideration the stochastic dynamic properties of the quantity
and price series, using the appropriate estimation approach in each case.
The Armington elasticities we estimate have the correct sign, and are
significant at the 5% level for 20 sectors, at 10% for two sectors, and at
20% for two others. In one sector the estimated value is significant, but
has the incorrect sign (negative). For three sectors the estimated elasticity
is not significantly different from zero; but these represent only 12%
of the average value of total import value in the period 1997-2002. The
point estimate of the elasticity of substitution, for the sectors where it is
positive and statistically different from zero, varies from 0.16 to 3.6; and
its weighted average value is 0.93.
A. Introduction
Regional free trade agreements are hard to evaluate economically
because they affect multiple productive sectors in several different
ways, and they impact the performance of the national economy in
a complex manner.5 Nonetheless, it is possible to assess their main
consequences using either a partial-equilibrium approach or, more
broadly, computable general equilibrium models (CGEs). In either
case, the agreement is represented by the tariff reductions it imposes
on the countries signing it. These, in turn, alter the domestic price
of the imported good relative to the domestically produced good,
and this change affects the proportion of domestic demand that is
supplied by imports. To analyse this effect and attempt to forecast its
intensity, requires estimating the elasticity of substitution between
goods distinguished by place of origin. These are known as Armington
elasticities, in honour of the economist who first drew attention to their
importance. Moreover, as the substitutability between imports and
domestic production varies widely from one product to another, these
estimates are needed at a disaggregated product level.
Estimates of Armington elasticities by sector are not readily
available for most countries, despite their crucial importance for
evaluating the impact of changes in trade policy on foreign trade flows.
To deal with this lack of empirical data, studies in this area often make
use of elasticity values obtained for other countries, in many cases
completely disregarding important differences that may exist between
5 Brazil is engaged in the negotiation of several trade agreements, of varying scope:
multilateral – the World Trade Organization (WTO); free trade agreements with the
countries of MERCOSUR and the European Union (UE); and bilateral agreements, with
South Africa and India, among others.

Modeling Public Policies in Latin America and the Caribbean 287
the production and consumption structures of different countries.6 As
these elasticity values are also not available for Brazil, the aim of this
study is to estimate them for our country, using the longest data series
available, which runs from 1986 to 2002. We have adopted the same level
of aggregation as in the Brazilian input-output matrix, to make it easy to
use the estimates in empirical studies of the country’s import basket.
The approach proposed here makes a methodological innovation
with respect to the literature in this area, by advocating extensive use
of the time-series properties of the series in question, to select the
most suitable estimation method and the corresponding equation.
Depending on the order of integration of the relative-price and quantity
series, we employ one of four approaches: simple regression of the
levels of variables, regression of first differences, linear model of mixed
equations, or a vector error correction model (VEC).7 We also consider
the possibility of a structural break occurring in the data series caused
by the foreign-trade liberalization which began in Brazil in 1990, together
with the possibility of seasonal factors and a time trend. This is done
both in the tests to determine the order of integration of the series, and
in the estimation itself. Lastly, we also consider the possibility that the
demand for imports is affected not only by the level of the relative price
of imported goods, but also by its uncertainty .
This painstaking approach to model specification and estimation
has clear empirical advantages in the case of Brazil for the period
considered, since an attempt to employ simpler methods had led to poor
or incorrect estimates. We believe that the approach proposed here will
also prove useful in the case of other countries, especially if the sample
period includes a trade liberalization episode.
This paper is divided into five sections including the introduction.
In section B we briefly review the concept of elasticity of substitution,
and introduce the approach used to deal with the impact on the observed
data of the foreign-trade liberalization initiative that began in 1990 and
lasted through 1993. Section C discusses the tests used to determine the
existence of unit roots in the price and quantity series, and the models
used in the estimation process. Section D reports the estimates obtained
for the 28 industrial sectors of the Brazilian input-output table; and
section E summarizes the main conclusions.
6 For example, Sánchez (2001) evaluates the costs and benefits for Mercosur of joining
FTAA using the applied general equilibrium model of the Global Trade Analysis Project
(GETAP), but it arbitrarily multiplies the original elasticities by six. Harrison et al (2002)
analyse the impacts of regional and multilateral trade agreements for Brazil while using
elasticities estimated for Hong-Kong.
7 We believe this is a pioneering application of the methods developed by Johansen (1988)
to the problem of estimating the Armington elasticity.

288 ECLAC – IDB
B. Armington elasticity and Brazilian trade
liberalization of 1990
The approach proposed by Armington (1969) to evaluate impacts
of changes in trade policy on the volume of imports has been widely
used, both in its original partial equilibrium formulation and in general
equilibrium models.8 The approach assumes that goods are differentiated
by country of origin, and that domestic demand for each sector is
supplied by a composite good which is a CES (Constant Elasticity of
Substitution) aggregation of domestically produced and imported goods.
This is represented in equation (1), for sector i.
where Qi , Mi and Di represent the quantity index of the aggregate good,
the imported good, and the domestically produced good, respectively.
The scale parameter is Qi , and ρi δi are the substitution and the
distribution parameters, respectively. The first of these indicates
the degree of substitutability between domestically produced and
imported goods, and determines the shape of the indifference curve
that represents the smooth transition between these two goods in the
preferences of the representative consumer. Its role can be clearly seen
by noting that, for ρi = -1, the composite good is a linear combination of
Mi and Di and the indifference curve is linear. The second parameter
indicates the shares of imported and domestically produced goods in
the composite good.
The solution to the problem of minimizing the cost of supplying
total demand, given expenditure and the prices of the imported and
domestically produced goods, gives the optimal mix of these two goods
in the composite good Qi , and is represented by equation (2). This shows
that the proportions of the domestic and the imported good depend on
the elasticity of substitution σi = 1/(1+ρi) and on the ratio of their prices,
represented by
d
i
P
and
m
i
P
.
8 A good example is Dervis, Melo and Robinson (1982) which uses the Armington
specification in a computable general equilibrium (CGE) model, which has become
a standard model for policy analysis. See also Melo and Robinson (1989) for a more
detailed discussion of its use in CGEs. For examples of its use in a partial equilibrium
framework, see the series of studies to measure the social cost of protection in several
countries, started by Hufbauer and Elliot (1994) and sponsored by the Institute of
International Economics, Washington, D.C.
4
and that domestic demand for each sector is supplied by a composite good which is a CES (Constant
Elasticity of Substitution) aggregation of domestically produced and imported goods. This is
represented in equation (1), for sector i.
(1)
where , represent the quantity index of the aggregate good, the imported good, and the
domestically produced good, respectively. The scale parameter is , and are the
substitution and the distribution parameters, respectively. The first of these indicates the degree of
substitutability between domestically produced and imported goods, and determines the shape of the
indifference curve that represents the smooth transition between these two goods in the preferences
of the representative consumer. Its role can be clearly seen by noting that, for , the composite
good is a linear combination of and the indifference curve is linear. The second parameter
indicates the shares of imported and domestically produced goods in the composite good.
The solution to the problem of minimizing the cost of supplying total demand, given expenditure and
the prices of the imported and domestically produced goods, gives the optimal mix of these two goods
in the composite good , and is represented by equation (2). This shows that the proportions of the
domestic and the imported good depend on the elasticity of substitution and on the
ratio of their prices, represented by and .
(2)
The internal price of the imported good, which is the relevant value for the consumer’s decision, is a
function of , its foreign-currency price on the foreign market, the exchange rate , and the
import tariff , as shown in equation (3):
(3)
(1)
4
and that domestic demand for each sector is supplied by a composite good which is a CES (Constant
Elasticity of Substitution) aggregation of domestically produced and imported goods. This is
represented in equation (1), for sector i.
(1)
where , represent the quantity index of the aggregate good, the imported good, and the
domestically produced good, respectively. The scale parameter is , and are the
substitution and the distribution parameters, respectively. The first of these indicates the degree of
substitutability between domestically produced and imported goods, and determines the shape of the
indifference curve that represents the smooth transition between these two goods in the preferences
of the representative consumer. Its role can be clearly seen by noting that, for , the composite
good is a linear combination of and the indifference curve is linear. The second parameter
indicates the shares of imported and domestically produced goods in the composite good.
The solution to the problem of minimizing the cost of supplying total demand, given expenditure and
the prices of the imported and domestically produced goods, gives the optimal mix of these two goods
in the composite good , and is represented by equation (2). This shows that the proportions of the
domestic and the imported good depend on the elasticity of substitution and on the
ratio of their prices, represented by and .
(2)
The internal price of the imported good, which is the relevant value for the consumer’s decision, is a
function of , its foreign-currency price on the foreign market, the exchange rate , and the
import tariff , as shown in equation (3):
(3)
(2)

Modeling Public Policies in Latin America and the Caribbean 289
The internal price of the imported good, which is the relevant value
for the consumer’s decision, is a function of
e
i
P
, its foreign-currency
price on the foreign market, the exchange rate (X), and the import tariff
(τi) as shown in equation (3):
It is useful to explore the behaviour of equation (2) for three
extreme cases of the elasticity of substitution. If ρi → ∞ and σi → 0, there is
no substitution between the two goods, and the ratio of their quantities
does not depend on their relative prices. When ρi → -1 and σi → ∞, the two
goods are perfect substitutes,9 and small changes in the relative prices are
sufficient to produce wide swings in the ratio
.
ii
MD
Lastly, when ρi = 0
and σi = 1, the CES function in equation (1) reduces to the Cobb-Douglas
function, and the ratio of expenditure on the imported and domestically
produced goods is constant and equal to δi/(1-δi ).
Equation (2) also shows that an estimate of the elasticity of
substitution, σi , can be obtained from the time series for the ratios
ii
MD
and
dm
ii
PP
. Nonetheless, a relatively long time period is
required for quantities to fully adjust to price changes. In the short run
(a few months) the impact will probably be small, since several years
are usually necessary for the quantity imported to fully reflect changes
in the relative price of imports. The short-run and long-run elasticities
are, therefore, different.
In this study we will estimate the long-run elasticities of
substitution, using the argument employed by Gallaway, McDaniel and
Rivera (2000) to justify adoption of that time horizon in their study.
They point out that Armington elasticity estimates are most often used
in comparative static analyses, in either partial- or general equilibrium
models. In this type of analysis we compare the results of the controlled
experiment to those obtained in the base year, assuming the economy
has had long enough to adjust, so that the results of the experiment reflect
the total effect of the policy experiment being evaluated.
To build a price series for imported goods that truly reflects the
actual cost paid by importers to bring them into the country, a number
of peculiarities of Brazilian tariff and import regulations in force
between 1986 and 2002 need to be taken into account. The period can be
divided into two distinct sub-periods that can be described in stylized
fashion as follows.
9 In this case we consider that the domestic price of good i is highly sensitive to the
imported competitor, and that the ratio between them is approximately constant.
4
and that domestic demand for each sector is supplied by a composite good which is a CES (Constant
Elasticity of Substitution) aggregation of domestically produced and imported goods. This is
represented in equation (1), for sector i.
(1)
where , represent the quantity index of the aggregate good, the imported good, and the
domestically produced good, respectively. The scale parameter is , and are the
substitution and the distribution parameters, respectively. The first of these indicates the degree of
substitutability between domestically produced and imported goods, and determines the shape of the
indifference curve that represents the smooth transition between these two goods in the preferences
of the representative consumer. Its role can be clearly seen by noting that, for , the composite
good is a linear combination of and the indifference curve is linear. The second parameter
indicates the shares of imported and domestically produced goods in the composite good.
The solution to the problem of minimizing the cost of supplying total demand, given expenditure and
the prices of the imported and domestically produced goods, gives the optimal mix of these two goods
in the composite good , and is represented by equation (2). This shows that the proportions of the
domestic and the imported good depend on the elasticity of substitution and on the
ratio of their prices, represented by and .
(2)
The internal price of the imported good, which is the relevant value for the consumer’s decision, is a
function of , its foreign-currency price on the foreign market, the exchange rate , and the
import tariff , as shown in equation (3):
(3)
(3)

290 ECLAC – IDB
Before the unilateral trade liberalization that began in 1990,
imports could be broadly classified in two categories:
(a) non-competing imports for which import tariffs were already
low, precisely because there was no need to protect the domestic
industry. Examples are metallurgy, coal, petroleum, some
fertilizers, and capital goods with no close national substitute, etc.
(b) competing imports, for which import tariffs were extremely high.
In this case, imports were only an economically viable alternative
to domestic products if purchased by agents with access to reduced
import tariffs or, in most cases, exemption. This special treatment
was extended to agents eligible to claim special tax regimes, such
as those applicable to State-owned enterprises, or those associated
with special investment projects which, despite being private, were
deemed to be of national interest. Examples are projects supported
by the Amazonia Development Superintendency (SUDAM), the
Northeast Development Superintendency (SUDENE), the Industrial
Development Council (CDI), the Manaus Duty Free Zone, etc.
This represents a situation of repressed demand, where potential
importers were driven out of the import goods market by a
combination of a prohibitive tariff and ineligibility for tariff-exempt
status.10 Consequently, there was a wedge between nominal tariffs,
which were very high, and the tariffs that were actually paid, which
were much lower because of these exemptions and reductions.
The dichotomy outlined above in the imported goods market was a
consequence of the crisis in the Brazilian balance of payments which began
in 1983 following a sudden stop in the flow of foreign savings to developing
countries, and deepened in 1987 when the country declared a unilateral
moratorium on its foreign-debt service. The situation only returned to
normality in 2002, when the country signed a wide-ranging foreign-debt
refinancing agreement with the international financial community.
After 1990, nominal tariffs were lowered, import restrictions were
lifted, and most special tax regimes for imports were removed, except
for those relating to the Manaus Free Trade Zone, the drawback regime,
the special provisions for imports of computers and computer parts, and
those relating to international agreements. As a consequence, the wedge
between nominal and effectively paid tariffs, which had been very large,
narrowed significantly.
10 According to Kume (1990), about 70% of imports, excluding oil, benefited from special
tax regimes in this period. Competitive imports were also prohibitive because tariff
redundancy was widespread.

Modeling Public Policies in Latin America and the Caribbean 291
The approach we propose captures these two situations, before and
after liberalization, in a unified framework, by calculating the equivalent
tariff faced by the average importer in each sector, taking into account
the dichotomy between the two types of imports that existed before
liberalization, as described above. Assuming that imports in each sector
were determined by the condition represented in equation (2), but that
the tariff faced by some of them was the nominal tariff, while for others
it was zero because they were exempt, we can write equations (4) and (5),
which determine the relative shares of imports and domestic production
in each of these cases, respectively:
where ai denotes the proportion of imports that pay the full nominal tariff
in sector i. Equation (6) sums these two types of imports, determined
in equations (4) and (5) to calculate the ratio of imports to domestic
production in sector i.
(6)
For estimation purposes, a logarithmic transformation is applied
to equation (6), to give equation (7).
(7)
The fact that equation (7) is non-linear in the elasticity of substitution
makes the estimation more difficult. To simplify, we take a Taylor series
expansion of the second term in the right-hand side of (7) with respect to
σi , in the neighbourhood of σi = 1, and obtain equation (8).
(8)
7
The approach we propose captures these two situations, before and after liberalization, in a unified
framework, by calculating the equivalent tariff faced by the average importer in each sector, taking
into account the dichotomy between the two types of imports that existed before liberalization, as
described above. Assuming that imports in each sector were determined by the condition represented
in equation (2), but that the tariff faced by some of them was the nominal tariff, while for others it was
zero because they were exempt, we can write equations (4) and (5), which determine the relative
shares of imports and domestic production in each of these cases, respectively:
(4)
(5)
where denotes the proportion of imports that pay the full nominal tariff in sector . Equation (6)
sums these two types of imports, determined in equations (4) and (5) to calculate the ratio of imports
to domestic production in sector .
(6)
For estimation purposes, a logarithmic transformation is applied to equation (6) , to give equation (7).
(7)
The fact that equation (7) is non-linear in the elasticity of substitution makes the estimation more
difficult. To simplify , we take a Taylor series expansion of the second term in the right-hand side of (7)
with respect to , in the neighbourhood of , and obtain equation (8).
7
The approach we propose captures these two situations, before and after liberalization, in a unified
framework, by calculating the equivalent tariff faced by the average importer in each sector, taking
into account the dichotomy between the two types of imports that existed before liberalization, as
described above. Assuming that imports in each sector were determined by the condition represented
in equation (2), but that the tariff faced by some of them was the nominal tariff, while for others it was
zero because they were exempt, we can write equations (4) and (5), which determine the relative
shares of imports and domestic production in each of these cases, respectively:
(4)
(5)
where denotes the proportion of imports that pay the full nominal tariff in sector . Equation (6)
sums these two types of imports, determined in equations (4) and (5) to calculate the ratio of imports
to domestic production in sector .
(6)
For estimation purposes, a logarithmic transformation is applied to equation (6) , to give equation (7).
(7)
The fact that equation (7) is non-linear in the elasticity of substitution makes the estimation more
difficult. To simplify , we take a Taylor series expansion of the second term in the right-hand side of (7)
with respect to , in the neighbourhood of , and obtain equation (8).
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
7
The approach we propose captures these two situations, before and after liberalization, in a unified
framework, by calculating the equivalent tariff faced by the average importer in each sector, taking
into account the dichotomy between the two types of imports that existed before liberalization, as
described above. Assuming that imports in each sector were determined by the condition represented
in equation (2), but that the tariff faced by some of them was the nominal tariff, while for others it was
zero because they were exempt, we can write equations (4) and (5), which determine the relative
shares of imports and domestic production in each of these cases, respectively:
(4)
(5)
where denotes the proportion of imports that pay the full nominal tariff in sector . Equation (6)
sums these two types of imports, determined in equations (4) and (5) to calculate the ratio of imports
to domestic production in sector .
(6)
For estimation purposes, a logarithmic transformation is applied to equation (6) , to give equation (7).
(7)
The fact that equation (7) is non-linear in the elasticity of substitution makes the estimation more
difficult. To simplify , we take a Taylor series expansion of the second term in the right-hand side of (7)
with respect to , in the neighbourhood of , and obtain equation (8).
(4)
7
The approach we propose captures these two situations, before and after liberalization, in a unified
framework, by calculating the equivalent tariff faced by the average importer in each sector, taking
into account the dichotomy between the two types of imports that existed before liberalization, as
described above. Assuming that imports in each sector were determined by the condition represented
in equation (2), but that the tariff faced by some of them was the nominal tariff, while for others it was
zero because they were exempt, we can write equations (4) and (5), which determine the relative
shares of imports and domestic production in each of these cases, respectively:
(4)
(5)
where denotes the proportion of imports that pay the full nominal tariff in sector . Equation (6)
sums these two types of imports, determined in equations (4) and (5) to calculate the ratio of imports
to domestic production in sector .
(6)
For estimation purposes, a logarithmic transformation is applied to equation (6) , to give equation (7).
(7)
The fact that equation (7) is non-linear in the elasticity of substitution makes the estimation more
difficult. To simplify , we take a Taylor series expansion of the second term in the right-hand side of (7)
with respect to , in the neighbourhood of , and obtain equation (8).
(5)
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
2

292 ECLAC – IDB
Apart from the error term in the approximation, only the second
term on the right-hand side of (8) depends on σi , a nd it does so linea rly.
That term is reproduced in equation (9), which also represents that
fact explicitly.
Using (9) as an approximation for the part of (7) that depends on
σi , we obtain equation (10), where the constant term ki , defined in (11),
consolidates terms in which the elasticity of substitution does not appear.
Lastly, equation (11) can be simplified to yield equation (12), which
is similar to equation (2), but with the difference that the term capturing
the effect of the tariff is raised to the power θi .
The significance of the exponent θi in (12) can be understood by
considering its definition in (9) and recalling that ai is the proportion of
imports that pay the full nominal tariff τi . It is then trivial to verify that
equation (12) adequately reflects the two polar stylized types of imports
that occurred before trade liberalization, because they correspond to the
extreme values of ai ; and that it also correctly describes the intermediate
situations existing afterwards.
We first discuss the situation before 1990. When the imported
good was non-competing (case (a) described above), the tariff was low
and applied to all import operations, i.e. ai = 1, so θi = 1, and equation
(12) reduces to (4). When the imported good is competing (case (b)), the
pre-1990 tariff was very high, and the imports that actually entered the
country did so under tariff exemption, which implies θi = 0, and reduces
equation (12) to (5).
Following trade liberalization, all goods are in an intermediate
situation between the two polar cases that existed before 1990. They are
also adequately represented by equation (12), whose behaviour can be
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
where
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
(9)
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
(10)
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
(11)
8
(8)
Apart from the error term in the approximation, only the second term on the right-hand side of (8)
depends on , and it does so linearly. That term is reproduced in equation (9), which also represents
that fact explicitly.
(9)
Using (9) as an approximation for the part of (7) that depends on , we obtain equation (10), where
the constant term , defined in (11), consolidates terms in which the elasticity of substitution does
not appear.
(10)
(11)
Lastly, equation (11) can be simplified to yield equation (12), which is similar to equation (2), but with
the difference that the term capturing the effect of the tariff is raised to the power ,
(12)
The significance of the exponent in (12) can be understood by considering its definition in (9) and
recalling that is the proportion of imports that pay the full nominal tariff . It is then trivial to verify
that equation (12) adequately reflects the two polar stylized types of imports that occurred before trade
(12)

Modeling Public Policies in Latin America and the Caribbean 293
extrapolated by examining a linear approximation for the expression
that defines θi . This is given by equation (13), which is obtained by
expanding equation (9) in a Taylor series with respect to ai , τi ∈ [0,1] in the
neighbourhood of the origin. This shows that for low values of the tariff
τi → 0 , when most imports are taxed, ai → 1 , and θi → ai . When only a
small proportion of imports pay the nominal tariff ai → 0 , and θi → (1 - τi).
Estimation of equation (12) requires calculating θit , for which a
measure of ait is also needed.11 This can be obtained by assuming that,
in the context of the stylized situation described at the beginning of this
section, the observed tariff is a weighted average of the nominal tariff
applied to imports in case (b), and the zero tariff, which is relevant for
imports in case (a), and where the weighting factor is the estimated value
of ait . This is represented in equation (14), where τit stands for the mean
observed tariff.
From (14) we can then obtain an estimate for ait , which is
represented by ait in equation (15):
Lastly, we include a dummy variable in the estimated equations
to represent the shift in the demand curve for imports, reflecting the
possibility that became available to firms after the last quarter of 1990, of
importing goods that were previously restricted provided the full import
duty was paid.12
At this point the reader may be wondering why so much effort
has made in these adjustments to allow the use of the data covering the
period when foreign trade was restricted, and to take into account the
impact of unilateral trade liberalization in Brazil, given that in our study
this includes data for only five years (1986 to 1990). The main reason is
not the additional degrees of freedom it gives the estimation, but rather
to include a period in the empirical analysis where there were large
11 In the notation for ai we introduced the index t to emphasize that, besides being
exogenous, it varies through time.
12 Import restrictions were officially lifted in March 1990 when the new Federal Government
took office. Nonetheless, the non-tariff barriers that actually controlled most imports in
practice were only eliminated in July of that year. Thus, only in the last quarter did
economic agents effectively perceive and benefit from the new freedom to import.
9
liberalization, because they correspond to the extreme values of ; and that it also correctly describes
the intermediate situations existing afterwards.
We first discuss the situation before 1990. When the imported good was non-competing (case (a)
described above), the tariff was low and applied to all import operations, i.e. , so , and
equation (12) reduces to (4). When the imported good is competing (case (b)), the pre-1990 tariff was
very high, and the imports that actually entered the country did so under tariff exemption, which
implies , and reduces equation (12) to (5).
Following trade liberalization, all goods are in an intermediate situation between the two polar cases
that existed before 1990. They are also adequately represented by equation (12), whose behaviour
can be extrapolated by examining a linear approximation for the expression that defines . This is
given by equation (13), which is obtained by expanding equation (9) in a Taylor series with respect to
in the neighbourhood of the origin. This shows that for low values of the tariff ,
when most imports are taxed, , and . When only a small proportion of imports pay the
nominal tariff , and .
(13)
Estimation of equation (12) requires calculating , for which a measure of is also needed. 7 This
can be obtained by assuming that, in the context of the stylized situation described at the beginning of
this section, the observed tariff is a weighted average of the nominal tariff applied to imports in case
(b), and the zero tariff, which is relevant for imports in case (a), and where the weighting factor is the
estimated value of . This is represented in equation (14), where stands for the mean observed
tariff.
(14)
7 In the notation for we introduced the index to emphasize that, besides being exogenous, it varies through time.
(13)
9
liberalization, because they correspond to the extreme values of ; and that it also correctly describes
the intermediate situations existing afterwards.
We first discuss the situation before 1990. When the imported good was non-competing (case (a)
described above), the tariff was low and applied to all import operations, i.e. , so , and
equation (12) reduces to (4). When the imported good is competing (case (b)), the pre-1990 tariff was
very high, and the imports that actually entered the country did so under tariff exemption, which
implies , and reduces equation (12) to (5).
Following trade liberalization, all goods are in an intermediate situation between the two polar cases
that existed before 1990. They are also adequately represented by equation (12), whose behaviour
can be extrapolated by examining a linear approximation for the expression that defines . This is
given by equation (13), which is obtained by expanding equation (9) in a Taylor series with respect to
in the neighbourhood of the origin. This shows that for low values of the tariff ,
when most imports are taxed, , and . When only a small proportion of imports pay the
nominal tariff , and .
(13)
Estimation of equation (12) requires calculating , for which a measure of is also needed. 7 This
can be obtained by assuming that, in the context of the stylized situation described at the beginning of
this section, the observed tariff is a weighted average of the nominal tariff applied to imports in case
(b), and the zero tariff, which is relevant for imports in case (a), and where the weighting factor is the
estimated value of . This is represented in equation (14), where stands for the mean observed
tariff.
(14)
7 In the notation for we introduced the index to emphasize that, besides being exogenous, it varies through time.
(14)
10
From (14) we can then obtain an estimate for , which is represented by in equation (15):
(15)
Lastly, we include a dummy variable in the estimated equations to represent the shift in the demand
curve for imports, reflecting the possibility that became available to firms after the last quarter of 1990,
of importing goods that were previously restricted provided the full import duty was paid. 8
At this point the reader may be wondering why so much effort has made in these adjustments to allow
the use of the data covering the period when foreign trade was restricted, and to take into account the
impact of unilateral trade liberalization in Brazil, given that in our study this includes data for only five
years (1986 to 1990). The main reason is not the additional degrees of freedom it gives the estimation,
but rather to include a period in the empirical analysis where there were large changes in the relative
internal price of imported goods. This is important because the aim of this study is precisely to
estimate the curvature of the indifference curve for the CES function in equation (1), which can only
be measured correctly if we have a database that includes a wide range of relative prices of
domestically produced and imported goods.
At this point we speculate that the adjustments proposed here to make it possible to use a single
unified framework for data relating to periods when trade restrictions were in place and for data
relating to the liberalization and post liberalization periods, , are also applicable to other countries
besides Brazil. The reason is that the distortions we address, produced by very large nominal tariffs
together with a large number of special import regimes that entail exception and special treatment for
certain industries, firms or goods, are likely to arise in other countries that went through periods in
which similar protectionist policies were used.
3. Empirical analysis
We used quarterly data for each sector of the Brazilian input-output matrix (IBGE – level 50), for the
period 1986-2002. The database in electronic format is available to readers on demand, and its
construction is described in Annex A. 9
8 Import restrictions were officially lifted in March 1990 when the new Federal Government took office. Nonetheless, the non-tariff barriers that actually
controlled most imports in practice were only eliminated in July of that year. Thus, only in the last quarter did economic agents effectively perceive and
benefit from the new freedom to import.
(15)

294 ECLAC – IDB
changes in the relative internal price of imported goods. This is important
because the aim of this study is precisely to estimate the curvature of the
indifference curve for the CES function in equation (1), which can only
be measured correctly if we have a database that includes a wide range
of relative prices of domestically produced and imported goods.
At this point we speculate that the adjustments proposed here
to make it possible to use a single unified framework for data relating
to periods when trade restrictions were in place and for data relating
to the liberalization and post liberalization periods, are also applicable
to other countries besides Brazil. The reason is that the distortions we
address, produced by very large nominal tariffs together with a large
number of special import regimes that entail exception and special
treatment for certain industries, firms or goods, are likely to arise in
other countries that went through periods in which similar protectionist
policies were used.
C. Empirical analysis
We used quarterly data for each sector of the Brazilian input-output
matrix (IBGE – level 50), for the period 1986-2002. The database in
electronic format is available to readers on demand, and its construction
is described in Annex A.13
Estimating equation (12) for each sector requires examining the
order of integration of the time series involved in it. A comparison of
the stochastic characteristics of these series determined the model to be
estimated to obtain the elasticity of substitution. This section describes
the methodology used in these two steps of the estimation.
To implement the unit root test systematically with regard to
inclusion of the constant and the time trend, we adopted the procedure
proposed by Dolado, Jenkinson and Sosvilla-Rivero (1990). In cases where
this indicated the existence of a unit root, we also applied the Perron (1989)
test for a structural break in the fourth quarter of 1990, using the variant
that specifies a break of the type represented by the changing growth
13 The database in this study differs from that used in Tourinho, Kume and Pedroso (2002)
because the foreign trade statistics for 1996 were revised in July 2002 (Funcex, 2002).
The data for exports did not change significantly, but for several sectors expenditure
on imports underwent major revision, mainly due to changes in the physical quantities
imported. As the price and quantum indexes estimated by Funcex are chained in time,
using 1996 as the base year, all the data were revised. Thus, the change in that year
affected the level of the entire series, even though the rates of change were not altered,
except for those calculated in relation to 1996.

Modeling Public Policies in Latin America and the Caribbean 295
model, according to the typology proposed there.14 In all cases the level of
significance adopted in the tests was 10%,15 and the Akaike information
criterion was used to determine the number of lags to be used. Annex B
describes the methodology of the tests in greater detail.
To make the estimation methodology more explicit, we recall that
equation (12) represents a long-term relation between
it
p
and
it
q
,
defined in equations (16) to (19):
A stochastic version of equation (12) is represented in (20), where,
to simplify the notation, we drop the product index i. This convention
will be followed from now on and is justified by the fact that we apply the
same methodology to all sectors. The elasticity is estimated for each of the
products in isolation and individually, to be consistent with the Armington
hypothesis that specifies zero cross-elasticities between all products.
14 The Perron test for the changing growth model assumes, in the null hypothesis, the
existence of a unit root and a change in the intercept of the stochastic process at the time
of the structural break. The alternative hypothesis is that the process is stationary with
a change in the slope of the deterministic time trend at the time of the break.
15 The significance level of the ADF test indicates the probability of incorrectly rejecting
the existence of the unit root. We adopted the 10% level as a compromise solution, owing
to the well-known low-power property of the ADF statistic, i.e. a bias towards non-
rejection of the unit root when in fact is not present. A lower significance level would
reduce the power of the test even further in this relatively small sample.
12
(19)
A stochastic version of equation (12) is represented in (20), where, to simplify the notation, we drop
the product index . This convention will be followed from now on and is justified by the fact that we
apply the same methodology to all sectors. The elasticity is estimated for each of the products in
isolation and individually, to be consistent with the Armington hypothesis that specifies zero cross-
elasticities between all products.
where and (20)
Each of these series can be integrated. When a unit root is not present, the series may or may not be
stationary, but the procedure employed is the same, regardless, and is based on the assumption that
the series is I(0). Table 1 presents the four possible combinations of the order of integration of the two
series, along with the model employed in each case. As can be seen by comparing the lines in table 1,
it is the order of integration of that determines whether the estimation is done in terms of levels or
first differences, because it is the dependent variable in equation (20).
TABLE 1
DECISION TABLE FOR THE TYPE OF MODEL USED IN ESTIMATION
Prices
Quantities
I (0)
I (1)
I (0)
A: levels
C: levels
I (1)
B: differences
D and E: cointegration
Source: Prepared by the authors.
All of the models we estimate also include as an exogenous variable the coefficient of variation of the
ratio between the prices of domestic and imported varieties of the good.12 This allows the uncertainty
surrounding that relative price to affect the ratio between the amount imported and the amount
produced domestically. The expected sign on its coefficient depends on the net effect of the
speculative mechanism affecting imports, which may be positive or negative. For example, firms that
depend heavily on imported inputs may react to greater uncertainty in their expected relative import
12 The coefficient of variation is the ratio between the standard deviation of the variable and its mean. We chose this measure as a measure of variability
because it preserves the non-dimensional nature of equation (2).
12
(19)
A stochastic version of equation (12) is represented in (20), where, to simplify the notation, we drop
the product index . This convention will be followed from now on and is justified by the fact that we
apply the same methodology to all sectors. The elasticity is estimated for each of the products in
isolation and individually, to be consistent with the Armington hypothesis that specifies zero cross-
elasticities between all products.
where and (20)
Each of these series can be integrated. When a unit root is not present, the series may or may not be
stationary, but the procedure employed is the same, regardless, and is based on the assumption that
the series is I(0). Table 1 presents the four possible combinations of the order of integration of the two
series, along with the model employed in each case. As can be seen by comparing the lines in table 1,
it is the order of integration of that determines whether the estimation is done in terms of levels or
first differences, because it is the dependent variable in equation (20).
TABLE 1
DECISION TABLE FOR THE TYPE OF MODEL USED IN ESTIMATION
Prices
Quantities
I (0)
I (1)
I (0)
A: levels
C: levels
I (1)
B: differences
D and E: cointegration
Source: Prepared by the authors.
All of the models we estimate also include as an exogenous variable the coefficient of variation of the
ratio between the prices of domestic and imported varieties of the good.12 This allows the uncertainty
surrounding that relative price to affect the ratio between the amount imported and the amount
produced domestically. The expected sign on its coefficient depends on the net effect of the
speculative mechanism affecting imports, which may be positive or negative. For example, firms that
depend heavily on imported inputs may react to greater uncertainty in their expected relative import
12 The coefficient of variation is the ratio between the standard deviation of the variable and its mean. We chose this measure as a measure of variability
because it preserves the non-dimensional nature of equation (2).
(20) where
11
Estimating equation (12) for each sector requires examining the order of integration of the time series
involved in it. A comparison of the stochastic characteristics of these series determined the model to
be estimated to obtain the elasticity of substitution. This section describes the methodology used in
these two steps of the estimation.
To implement the unit root test systematically with regard to inclusion of the constant and the time
trend, we adopted the procedure proposed by Dolado, Jenkinson and Sosvilla-Rivero (1990). In cases
where this indicated the existence of a unit root, we also applied the Perron (1989) test for a structural
break in the fourth quarter of 1990, using the variant that specifies a break of the type represented by
the changing growth model, according to the typology proposed there.10 In all cases the level of
significance adopted in the tests was 10%,11 and the Akaike information criterion was used to
determine the number of lags to be used. Annex B describes the methodology of the tests in greater
detail.
To make the estimation methodology more explicit, we recall that equation (12) represents a long-term
relation between and , defined in equations (16) to (19):
(16)
(17)
(18)
9 The database in this study differs from that used in Tourinho, Kume and Pedroso (2002) because the foreign trade statistics for 1996 were revised in July
2002 (Funcex, 2002). The data for exports did not change significantly, but for several sectors expenditure on imports underwent major revision, mainly due
to changes in the physical quantities imported. As the price and
quantum
indexes estimated by Funcex are chained in time, using 1996 as the base year, all
the data were revised. Thus, the change in that year affected the level of the entire series, even though the rates of change were not altered, except for
those calculated in relation to 1996.
13 The Perron test for the
changing growth model
assumes, in the null hypothesis, the existence of a unit root and a change in the intercept of the
stochastic process at the time of the structural break. The alternative hypothesis is that the process is stationary with a change in the slope of the
deterministic time trend at the time of the break.
11 The significance level of the ADF test indicates the probability of incorrectly rejecting the existence of the unit root. We adopted the 10% level as a
compromise solution, owing to the well-known low-power property of the ADF statistic, i.e. a bias towards non-rejection of the unit root when in fact is not
present. A lower significance level would reduce the power of the test even further in this relatively small sample.
(16)
11
Estimating equation (12) for each sector requires examining the order of integration of the time series
involved in it. A comparison of the stochastic characteristics of these series determined the model to
be estimated to obtain the elasticity of substitution. This section describes the methodology used in
these two steps of the estimation.
To implement the unit root test systematically with regard to inclusion of the constant and the time
trend, we adopted the procedure proposed by Dolado, Jenkinson and Sosvilla-Rivero (1990). In cases
where this indicated the existence of a unit root, we also applied the Perron (1989) test for a structural
break in the fourth quarter of 1990, using the variant that specifies a break of the type represented by
the changing growth model, according to the typology proposed there.10 In all cases the level of
significance adopted in the tests was 10%,11 and the Akaike information criterion was used to
determine the number of lags to be used. Annex B describes the methodology of the tests in greater
detail.
To make the estimation methodology more explicit, we recall that equation (12) represents a long-term
relation between and , defined in equations (16) to (19):
(16)
(17)
(18)
9 The database in this study differs from that used in Tourinho, Kume and Pedroso (2002) because the foreign trade statistics for 1996 were revised in July
2002 (Funcex, 2002). The data for exports did not change significantly, but for several sectors expenditure on imports underwent major revision, mainly due
to changes in the physical quantities imported. As the price and
quantum
indexes estimated by Funcex are chained in time, using 1996 as the base year, all
the data were revised. Thus, the change in that year affected the level of the entire series, even though the rates of change were not altered, except for
those calculated in relation to 1996.
13 The Perron test for the
changing growth model
assumes, in the null hypothesis, the existence of a unit root and a change in the intercept of the
stochastic process at the time of the structural break. The alternative hypothesis is that the process is stationary with a change in the slope of the
deterministic time trend at the time of the break.
11 The significance level of the ADF test indicates the probability of incorrectly rejecting the existence of the unit root. We adopted the 10% level as a
compromise solution, owing to the well-known low-power property of the ADF statistic, i.e. a bias towards non-rejection of the unit root when in fact is not
present. A lower significance level would reduce the power of the test even further in this relatively small sample.
(17)
11
Estimating equation (12) for each sector requires examining the order of integration of the time series
involved in it. A comparison of the stochastic characteristics of these series determined the model to
be estimated to obtain the elasticity of substitution. This section describes the methodology used in
these two steps of the estimation.
To implement the unit root test systematically with regard to inclusion of the constant and the time
trend, we adopted the procedure proposed by Dolado, Jenkinson and Sosvilla-Rivero (1990). In cases
where this indicated the existence of a unit root, we also applied the Perron (1989) test for a structural
break in the fourth quarter of 1990, using the variant that specifies a break of the type represented by
the changing growth model, according to the typology proposed there.10 In all cases the level of
significance adopted in the tests was 10%,11 and the Akaike information criterion was used to
determine the number of lags to be used. Annex B describes the methodology of the tests in greater
detail.
To make the estimation methodology more explicit, we recall that equation (12) represents a long-term
relation between and , defined in equations (16) to (19):
(16)
(17)
(18)
9 The database in this study differs from that used in Tourinho, Kume and Pedroso (2002) because the foreign trade statistics for 1996 were revised in July
2002 (Funcex, 2002). The data for exports did not change significantly, but for several sectors expenditure on imports underwent major revision, mainly due
to changes in the physical quantities imported. As the price and
quantum
indexes estimated by Funcex are chained in time, using 1996 as the base year, all
the data were revised. Thus, the change in that year affected the level of the entire series, even though the rates of change were not altered, except for
those calculated in relation to 1996.
13 The Perron test for the
changing growth model
assumes, in the null hypothesis, the existence of a unit root and a change in the intercept of the
stochastic process at the time of the structural break. The alternative hypothesis is that the process is stationary with a change in the slope of the
deterministic time trend at the time of the break.
11 The significance level of the ADF test indicates the probability of incorrectly rejecting the existence of the unit root. We adopted the 10% level as a
compromise solution, owing to the well-known low-power property of the ADF statistic, i.e. a bias towards non-rejection of the unit root when in fact is not
present. A lower significance level would reduce the power of the test even further in this relatively small sample.
(18)
12
(19)
A stochastic version of equation (12) is represented in (20), where, to simplify the notation, we drop
the product index . This convention will be followed from now on and is justified by the fact that we
apply the same methodology to all sectors. The elasticity is estimated for each of the products in
isolation and individually, to be consistent with the Armington hypothesis that specifies zero cross-
elasticities between all products.
where and (20)
Each of these series can be integrated. When a unit root is not present, the series may or may not be
stationary, but the procedure employed is the same, regardless, and is based on the assumption that
the series is I(0). Table 1 presents the four possible combinations of the order of integration of the two
series, along with the model employed in each case. As can be seen by comparing the lines in table 1,
it is the order of integration of that determines whether the estimation is done in terms of levels or
first differences, because it is the dependent variable in equation (20).
TABLE 1
DECISION TABLE FOR THE TYPE OF MODEL USED IN ESTIMATION
Prices
Quantities
I (0)
I (1)
I (0)
A: levels
C: levels
I (1)
B: differences
D and E: cointegration
Source: Prepared by the authors.
All of the models we estimate also include as an exogenous variable the coefficient of variation of the
ratio between the prices of domestic and imported varieties of the good.12 This allows the uncertainty
surrounding that relative price to affect the ratio between the amount imported and the amount
produced domestically. The expected sign on its coefficient depends on the net effect of the
speculative mechanism affecting imports, which may be positive or negative. For example, firms that
depend heavily on imported inputs may react to greater uncertainty in their expected relative import
12 The coefficient of variation is the ratio between the standard deviation of the variable and its mean. We chose this measure as a measure of variability
because it preserves the non-dimensional nature of equation (2).
(19)
12
(19)
A stochastic version of equation (12) is represented in (20), where, to simplify the notation, we drop
the product index . This convention will be followed from now on and is justified by the fact that we
apply the same methodology to all sectors. The elasticity is estimated for each of the products in
isolation and individually, to be consistent with the Armington hypothesis that specifies zero cross-
elasticities between all products.
where and (20)
Each of these series can be integrated. When a unit root is not present, the series may or may not be
stationary, but the procedure employed is the same, regardless, and is based on the assumption that
the series is I(0). Table 1 presents the four possible combinations of the order of integration of the two
series, along with the model employed in each case. As can be seen by comparing the lines in table 1,
it is the order of integration of that determines whether the estimation is done in terms of levels or
first differences, because it is the dependent variable in equation (20).
TABLE 1
DECISION TABLE FOR THE TYPE OF MODEL USED IN ESTIMATION
Prices
Quantities
I (0)
I (1)
I (0)
A: levels
C: levels
I (1)
B: differences
D and E: cointegration
Source: Prepared by the authors.
All of the models we estimate also include as an exogenous variable the coefficient of variation of the
ratio between the prices of domestic and imported varieties of the good.12 This allows the uncertainty
surrounding that relative price to affect the ratio between the amount imported and the amount
produced domestically. The expected sign on its coefficient depends on the net effect of the
speculative mechanism affecting imports, which may be positive or negative. For example, firms that
depend heavily on imported inputs may react to greater uncertainty in their expected relative import
12 The coefficient of variation is the ratio between the standard deviation of the variable and its mean. We chose this measure as a measure of variability
because it preserves the non-dimensional nature of equation (2).
and

296 ECLAC – IDB
Each of these series can be integrated. When a unit root is not present,
the series may or may not be stationary, but the procedure employed is the
same, regardless, and is based on the assumption that the series is I(0). Table
IX.1 presents the four possible combinations of the order of integration of
the two series, along with the model employed in each case. As can be
seen by comparing the lines in table IX.1, it is the order of integration of q
that determines whether the estimation is done in terms of levels or first
differences, because it is the dependent variable in equation (20).
All of the models we estimate also include as an exogenous
variable the coefficient of variation of the ratio between the prices
of domestic and imported varieties of the good.16 This allows the
uncertainty surrounding that relative price to affect the ratio between
the amount imported and the amou nt produced domestically.
The expected sign on its coefficient depends on the net effect of the
speculative mechanism affecting imports, which may be positive or
negative. For example, firms that depend heavily on imported inputs
may react to greater uncertainty in their expected relative import costs
by increasing their imports (positive effect) or else by substituting for
them (negative effect). One cannot therefore anticipate the significance
of this variable in equation (5), or the sign of its coefficient.
We also use control variables to take account of several important
exogenous factors, as follows. The first is a dummy variable to capture the
stepwise response of the quantity imported following the 1990 foreign
trade liberalization. Its value is therefore dt = 1 for t ≥ 1990:4 and dt = 0 for
other periods. The second control variable is a time trend to capture other
factors that may have provoked structural changes in the quantum of
imports without affecting the relative price of imports. The third is a vector
of seasonal dummies (zt). The inclusion of a time trend and the dummy
variable can be rationalized as an attempt to take account of variations in
the quality of the goods and the composition of the sector price and quantity
16 The coefficient of variation is the ratio between the standard deviation of the variable
and its mean. We chose this measure as a measure of variability because it preserves the
non-dimensional nature of equation (2).
Table IX.1
DECISION TABLE FOR THE TYPE OF MODEL USED IN ESTIMATION
Quantities (q) Prices (p)
I (0) I (1)
I (0) A: levels C: levels
I (1) B: dif ferences D and E: cointegration
Source: Prepared by the authors.

Modeling Public Policies in Latin America and the Caribbean 297
aggregates that could not be adequately considered when constructing the
quantity index. Examples include imports of electro-electronic goods and
personal computers, which grew strongly in the later years of the period,
but for which there was also a significant quality change. Our formulation
assumes that part of those changes occurred progressively throughout the
period, while others happened suddenly in response to the change in the
foreign-trade regime; and it allows the empirical equations to distribute
these effects among the variables.
Lastly, the estimated equation is shown in (21), which includes all
the effects discussed above.
In the estimation of all models mentioned in table IX.1 we start
with the most general specification, assuming the maximum number
of lags for the price variable; and we progressively eliminate the non-
significant variables to arrive at the final equation. In the next section we
discuss the estimation of each of the models mentioned in table IX.1.
1. Model A
The simplest case is when both series are stationary, and we can
obtain the long-term elasticity in equation (21) from a regression on
the level variables. The equation is initially estimated by ordinary least
squares; but, when the Durbin-Watson statistic indicates the existence of
first-order serial correlation among the residuals, it is re-estimated using
the maximum likelihood method, assuming a first-order autoregressive
structure for the errors. This provides estimates of the coefficients and
confidence intervals for the parameters of equation (6), and for the
parameter of the autoregressive term (ρ), which allows us to calculate the
long-term Armington elasticity σ/(1-ρ).
In cases where this procedure suggests the possible existence of a
unit root on the residuals, i.e. the confidence interval of ρ includes 1, the
equation is re-estimated in first difference terms, in the form of equation
(7), which also includes lagged values of the price variable among the
explanatory variables. The number of lags included in the equation is the
same as used in the procedure to determine the order of integration of
the price series, and may be zero.17
17 Appendix B shows how we used a sequence of chained tests to endogenously obtain the
number of lags used in the ADF test.
13
costs by increasing their imports (positive effect) or else by substituting for them (negative effect). One
cannot therefore anticipate the significance of this variable in equation (5), or the sign of its coefficient.
We also use control variables to take account of several important exogenous factors, as follows. The
first is a dummy variable to capture the stepwise response of the quantity imported following the 1990
foreign trade liberalization. Its value is therefore for and for other periods.
The second control variable is a time trend to capture other factors that may have provoked structural
changes in the quantum of imports without affecting the relative price of imports. The third is a vector
of seasonal dummies ( ). The inclusion of a time trend and the dummy variable can be rationalized
as an attempt to take account of variations in the quality of the goods and the composition of the
sector price and quantity aggregates that could not be adequately considered when constructing the
quantity index. Examples include imports of electro-electronic goods and personal computers, which
grew strongly in the later years of the period, but for which there was also a significant quality change.
Our formulation assumes that part of those changes occurred progressively throughout the period,
while others happened suddenly in response to the change in the foreign-trade regime; and it allows
the empirical equations to distribute these effects among the variables.
Lastly, the estimated equation is shown in (21), which includes all the effects discussed above.
(21)
In the estimation of all models mentioned in table 1 we start with the most general specification,
assuming the maximum number of lags for the price variable; and we progressively eliminate the non-
significant variables to arrive at the final equation. In the next section we discuss the estimation of
each of the models mentioned in table 1
3.1. Model A
The simplest case is when both series are stationary, and we can obtain the long-term elasticity in
equation (21) from a regression on the level variables. The equation is initially estimated by ordinary
least squares; but, when the Durbin-Watson statistic indicates the existence of first-order serial
correlation among the residuals, it is re-estimated using the maximum likelihood method, assuming a
(21)
14
first-order autoregressive structure for the errors. This provides estimates of the coefficients and
confidence intervals for the parameters of equation (6), and for the parameter of the autoregressive
term , which allows us to calculate the long-term Armington elasticity .
In cases where this procedure suggests the possible existence of a unit root on the residuals, i.e. the
confidence interval of includes 1, the equation is re-estimated in first difference terms, in the form of
equation (7), which also includes lagged values of the price variable among the explanatory variables.
The number of lags included in the equation is the same as used in the procedure to determine the
order of integration of the price series, and may be zero.13
(22)
3.2 Models B and C
Cases where the order of integration of the two series is not the same are hard to rationalize from an
economic point of view. Moreover, these unbalanced equations are quite troublesome to estimate.
This difficulty has been noted by other authors, who nonetheless recognize the need to overcome the
problem in the best possible way.14 Below we indicate how we treat the two unbalanced cases of table
1.
When is I(1) and is I(0), the equation is estimated in terms of first differences, as in (22). This
avoids the possibility of spurious correlation, because differentiation produces stationary series.15
When is I(0) and is I(1), we estimate the equation in terms of levels, including as many lags as
those used in the tests of order of integration, plus one, as indicated in equation (23).
(23)
13 Appendix B shows how we used a sequence of chained tests to endogenously obtain the number of lags used in the ADF test.
14 See, for example, Maddala and Kim (1998, p. 252): “Should one estimate unbalanced equations? Of course not, if it can be avoided. But if it has to be
done, one has to be careful in their interpretation and use appropriate critical values”.
15. This procedure is also adopted in Gallaway, McDaniel and Rivera (2003).
(22)

298 ECLAC – IDB
2. Models B and C
Cases where the order of integration of the two series is not the
same are hard to rationalize from an economic point of view. Moreover,
these unbalanced equations are quite troublesome to estimate. This
difficulty has been noted by other authors, who nonetheless recognize
the need to overcome the problem in the best possible way.18 Below we
indicate how we treat the two unbalanced cases of table IX.1.
When q is I (1) and p is I (0), the equation is estimated in terms
of first differences, as in (22). This avoids the possibility of spurious
correlation, because differentiation produces stationary series.19 When q
is I (0) and p is I (1), we estimate the equation in terms of levels, including
as many lags as those used in the tests of order of integration, plus one,
as indicated in equation (23).
The asymmetric treatment of these two cases is justified by the
need to deal with the “integratedness” of the dependent variable, when
it has that property. On the other hand, the differencing operation we
perform when it is integrated does not impair the estimation when
the price variable is already stationary; and it preserves the possibility
of interpreting the coefficient on the price variable as the elasticity of
substitution. Any signs of serial correlation among the residuals when
estimating equation (23) are dealt with by using the same procedure as
in Model A.20
When the procedure described above is unable to produce an
elasticity that is significantly different from zero, we try to estimate it by
using the co-integration model described in the next section. We call this
case Model E. This procedure is adopted even though the series have not
been classified as integrated; but this can be justified in two ways. The
first is that there is a margin of error in the tests of order of integration
described at the start of this section and in appendix B, which may have
led to rejection of the unit root for one of the series, when it is in fact
present. The second argument has already been put forward above: there
is no entirely satisfactory procedure available to deal with the case of
unbalanced equations; and each of the procedures entails a compromise.
18 See, for example, Maddala and Kim (1998, p. 252): “Should one estimate unbalanced
equations? Of course not, if it can be avoided. But if it has to be done, one has to be
careful in their interpretation and use appropriate critical values”.
19 This procedure is also adopted in Gallaway, McDaniel and Rivera (2003).
20 This procedure is the estimation via quasi-first differences, as described in the previous
section (equation (22)).
14
first-order autoregressive structure for the errors. This provides estimates of the coefficients and
confidence intervals for the parameters of equation (6), and for the parameter of the autoregressive
term , which allows us to calculate the long-term Armington elasticity .
In cases where this procedure suggests the possible existence of a unit root on the residuals, i.e. the
confidence interval of includes 1, the equation is re-estimated in first difference terms, in the form of
equation (7), which also includes lagged values of the price variable among the explanatory variables.
The number of lags included in the equation is the same as used in the procedure to determine the
order of integration of the price series, and may be zero.13
(22)
3.2 Models B and C
Cases where the order of integration of the two series is not the same are hard to rationalize from an
economic point of view. Moreover, these unbalanced equations are quite troublesome to estimate.
This difficulty has been noted by other authors, who nonetheless recognize the need to overcome the
problem in the best possible way.14 Below we indicate how we treat the two unbalanced cases of table
1.
When is I(1) and is I(0), the equation is estimated in terms of first differences, as in (22). This
avoids the possibility of spurious correlation, because differentiation produces stationary series.15
When is I(0) and is I(1), we estimate the equation in terms of levels, including as many lags as
those used in the tests of order of integration, plus one, as indicated in equation (23).
(23)
13 Appendix B shows how we used a sequence of chained tests to endogenously obtain the number of lags used in the ADF test.
14 See, for example, Maddala and Kim (1998, p. 252): “Should one estimate unbalanced equations? Of course not, if it can be avoided. But if it has to be
done, one has to be careful in their interpretation and use appropriate critical values”.
15. This procedure is also adopted in Gallaway, McDaniel and Rivera (2003).
(23)

Modeling Public Policies in Latin America and the Caribbean 299
In our opinion these arguments justify the attempt to estimate the
equation by cointegration methods when the other methods fail to find
an elasticity that is significantly different from zero.
3. Models D and E
When prices and quantities are integrated, the cointegration relation
provides an estimate of the long-term Armington elasticity, for which
we use the general formulation contained in Johansen (1988). We write
equation (20) in vector notation as equation (24).
where xt’ = (pt , qt), β’ = (1, - σ). This VAR model, can be put in a restricted
form as a vector error correction (VEC) model which can be written as
equation (25) when there is no time trend and the variables are lagged by
just one period,
where β is the co-integration vector and a is a vector that contains the
weights applied to components of the cointegration term, and is used to
adjust the value of x; in other words, it is the vector or coefficients of the
error correction term. The vector of residuals e must be i.i.d. with mean
zero and variance matrix Ω.
The VEC of equation (25) can be generalized and written as
equation (26) by including k lags of the first difference of the vector of
variables, and including the exogenous variables used to obtain equation
(21): a dummy variable that captures the shift in the intercept caused by
the trade liberalization, a time trend, and seasonal dummy variables:
(26)
In our case, the matrices Γτ are 2x2 and contain the weights of the
autoregressive components of the process. We chose the number of lags
to be included in the equation, represented by l, so as to maximize the
likelihood statistic for the system of equations.21 In equation (26), g is a
21 The number of lags was reduced progressively starting from a maximum of eight
quarters, until the remaining terms were significant. To choose the maximum number of
lags we assumed that the effects of a given shock would mostly have been absorbed by
the system within two years.
16
where is the co-integration vector and is a vector that contains the weights applied to
components of the cointegration term, and is used to adjust the value of ; in other words, it is the
vector or coefficients of the error correction term. The vector of residuals must be i.i.d. with mean
zero and variance matrix .
The VEC of equation (25) can be generalized and written as equation (26) by including k lags of the
first difference of the vector of variables, and including the exogenous variables used to obtain
equation (21): a dummy variable that captures the shift in the intercept caused by the trade
liberalization, a time trend, and seasonal dummy variables:
(26)
In our case, the matrices are 2x2 and contain the weights of the autoregressive components of
the process. We chose the number of lags to be included in the equation, represented by , so as to
maximize the likelihood statistic for the system of equations.17 In equation (26), is a 2x1 vector
containing the time-trend parameters for the growth of the variables. Thus, is a scalar term
that shows how the time trend of prices and quantities affects the cointegration relation.
Since the cointegration relation was normalized with respect to the quantities (the first dimension of
vector ), one can interpret the term in parentheses in equation (26) as the long-term effect that
would occur if the distribution parameter of the CES function in equation (1) had a time trend and were
independent of the foreign trade regime. That dependence is captured in our formulation through ,
the dummy variable that captures the effect of liberalization; and it is represented by its effect on a
generalized distribution parameter of the CES formulation, which is defined (implicitly) by equation
(27).
(27)
17. The number of lags was reduced progressively starting from a maximum of eight quarters, until the remaining terms were significant. To choose the
maximum number of lags we assumed that the effects of a given shock would mostly have been absorbed by the system within two years.
15
The asymmetric treatment of these two cases is justified by the need to deal with the "integratedness"
of the dependent variable, when it has that property. On the other hand, the differencing operation we
perform when it is integrated does not impair the estimation when the price variable is already
stationary; and it preserves the possibility of interpreting the coefficient on the price variable as the
elasticity of substitution. Any signs of serial correlation among the residuals when estimating equation
(23) are dealt with by using the same procedure as in Model A.16
When the procedure described above is unable to produce an elasticity that is significantly different
from zero, we try to estimate it by using the co-integration model described in the next section. We call
this case Model E. This procedure is adopted even though the series have not been classified as
integrated; but this can be justified in two ways. The first is that there is a margin of error in the tests of
order of integration described at the start of this section and in appendix B, which may have led to
rejection of the unit root for one of the series, when it is in fact present. The second argument has
already been put forward above: there is no entirely satisfactory procedure available to deal with the
case of unbalanced equations; and each of the procedures entails a compromise. In our opinion these
arguments justify the attempt to estimate the equation by cointegration methods when the other
methods fail to find an elasticity that is significantly different from zero.
3.3 Models D and E
When prices and quantities are integrated, the cointegration relation provides an estimate of the long-
term Armington elasticity, for which we use the general formulation contained in Johansen (1988). We
write equation (20) in vector notation as equation (24).
(24)
where , . This VAR model, can be put in a restricted form as a vector error
correction (VEC) model which can be written as equation (25) when there is no time trend and the
variables are lagged by just one period,
(25)
16 This procedure is the estimation via quasi-first differences, as described in the previous section (equation (22)).
(24)
15
The asymmetric treatment of these two cases is justified by the need to deal with the "integratedness"
of the dependent variable, when it has that property. On the other hand, the differencing operation we
perform when it is integrated does not impair the estimation when the price variable is already
stationary; and it preserves the possibility of interpreting the coefficient on the price variable as the
elasticity of substitution. Any signs of serial correlation among the residuals when estimating equation
(23) are dealt with by using the same procedure as in Model A.16
When the procedure described above is unable to produce an elasticity that is significantly different
from zero, we try to estimate it by using the co-integration model described in the next section. We call
this case Model E. This procedure is adopted even though the series have not been classified as
integrated; but this can be justified in two ways. The first is that there is a margin of error in the tests of
order of integration described at the start of this section and in appendix B, which may have led to
rejection of the unit root for one of the series, when it is in fact present. The second argument has
already been put forward above: there is no entirely satisfactory procedure available to deal with the
case of unbalanced equations; and each of the procedures entails a compromise. In our opinion these
arguments justify the attempt to estimate the equation by cointegration methods when the other
methods fail to find an elasticity that is significantly different from zero.
3.3 Models D and E
When prices and quantities are integrated, the cointegration relation provides an estimate of the long-
term Armington elasticity, for which we use the general formulation contained in Johansen (1988). We
write equation (20) in vector notation as equation (24).
(24)
where , . This VAR model, can be put in a restricted form as a vector error
correction (VEC) model which can be written as equation (25) when there is no time trend and the
variables are lagged by just one period,
(25)
16 This procedure is the estimation via quasi-first differences, as described in the previous section (equation (22)).
(25)

300 ECLAC – IDB
2x1 vector containing the time-trend parameters for the growth of the
variables. Thus, β’g ⋅ (t –1) is a scalar term that shows how the time trend
of prices and quantities affects the cointegration relation.
Since the cointegration relation was normalized with respect
to the quantities (the first dimension of vector x), one can interpret the
term in parentheses in equation (26) as the long-term effect that would
occur if the distribution parameter of the CES function in equation (1)
had a time trend and were independent of the foreign trade regime.
That dependence is captured in our formulation through dt , the dummy
variable that captures the effect of liberalization; and it is represented by
its effect on a generalized distribution parameter of the CES formulation,
δt which is defined (implicitly) by equation (27).
To summarize, equation (26) takes account of the major shifts
that may have occurred in the demand function for imports, based
on the hypothesis that the elasticity of substitution σ was constant
throughout the period.
D. Results
We applied the procedure described above to identify the order of
integration of the series and to choose the most suitable model to estimate
data from the period 1985-2002, for the 28 sectors of the Brazilian input-
output matrix where imports were positive in 2002, except for agriculture
(including livestock) and the service sectors.
Table IX.2 sets out the types of series considered in our classification,
in terms of their stochastic properties and the code adopted for each one.
We also show, for each variable in the model, the frequency with which
each type of series was encountered. Only 16 quantum series and 11 price
series do not have a unit root; but, of these, only six quantum series and
five price series are stationary. For 10 quantum series and 17 price series,
we are able to find evidence of a unit root.22 For two quantum series we
cannot rule out the existence of a unit root. Lastly, there is evidence of a
structural break in the fourth quarter of 1990 for 10 quantum series and
six price series.
22 It is possible to put forward theoretical arguments against the possibility that a price
series is integrated. However, we admit that if they behave like integrated series in our
sample, it is preferable to treat them as such in the estimation.
16
where is the co-integration vector and is a vector that contains the weights applied to
components of the cointegration term, and is used to adjust the value of ; in other words, it is the
vector or coefficients of the error correction term. The vector of residuals must be i.i.d. with mean
zero and variance matrix .
The VEC of equation (25) can be generalized and written as equation (26) by including k lags of the
first difference of the vector of variables, and including the exogenous variables used to obtain
equation (21): a dummy variable that captures the shift in the intercept caused by the trade
liberalization, a time trend, and seasonal dummy variables:
(26)
In our case, the matrices are 2x2 and contain the weights of the autoregressive components of
the process. We chose the number of lags to be included in the equation, represented by , so as to
maximize the likelihood statistic for the system of equations.17 In equation (26), is a 2x1 vector
containing the time-trend parameters for the growth of the variables. Thus, is a scalar term
that shows how the time trend of prices and quantities affects the cointegration relation.
Since the cointegration relation was normalized with respect to the quantities (the first dimension of
vector ), one can interpret the term in parentheses in equation (26) as the long-term effect that
would occur if the distribution parameter of the CES function in equation (1) had a time trend and were
independent of the foreign trade regime. That dependence is captured in our formulation through ,
the dummy variable that captures the effect of liberalization; and it is represented by its effect on a
generalized distribution parameter of the CES formulation, which is defined (implicitly) by equation
(27).
(27)
17. The number of lags was reduced progressively starting from a maximum of eight quarters, until the remaining terms were significant. To choose the
maximum number of lags we assumed that the effects of a given shock would mostly have been absorbed by the system within two years.
(27)

Modeling Public Policies in Latin America and the Caribbean 301
The classification of model types presented in table IX.1 shows that
most cases refer to situations where the order of integration of the price
and quantity series coincide: this happens in 11 instances of Model A
(estimation in terms of levels), and 11 of Model D (cointegration). There
are six cases of unbalanced equations, but we estimated four of them
using cointegration (Model E) since Models B and C did not produce
estimates that were significantly different from zero in these cases. There
are also two cases where the estimation through models B and C was
satisfactory — one of each type.
The results, in table IX.3, show that the estimate of the Armington
elasticity has the correct sign and is significantly different from zero for
20 sectors at the 5% significance level. For two sectors it is significant
only at the 10% level, and for two others it is significant only at 20%.
For one sector the estimated value is significant but its sign is incorrect
(negative); and for the three remaining sectors the estimated elasticity is
not significantly different from zero.
The coefficient of variation of prices proved significant in just
two sectors, and in both cases it is positive, indicating an increase in the
share of imports relative to domestic production, in response to greater
uncertainty in the relative price of imports. The lack of significance of
this variable in most sectors was somewhat surprising, because we had
expected it to be significant in several sectors.
The dummy variable that captures the occurrence of a structural
break in 1990:4 was significant at the 5% level in 11 sectors, and at 10%
in one other, thus confirming the importance of the point discussed in
Number o f series
Code Type Quantum Price
1 Stationar y around a non-zero average 2 3
2 Stationar y around a zero average – 1
3 Stationar y around a linear trend 4 1
4 Has a unit root wi th zero time trend 10 17
5 Has a unit root wi th non-zero time trend – –
6 The existence of a unit root cannot be rejected 2 –
7 Does not have a unit root 10 6
– Evidence of the existence of a struc tural break in 1990:4 10 6
Table IX.2
TYPOLOGY OF QUANTUM AND PRICE SERIES
Source: Prepared by the authors.

302 ECLAC – IDB
section 2 regarding the nature of the impact of the liberalization that
began in 1990. Its coefficient is positive for eight sectors, where the
proportion of imports increased, and it is negative in the other four.
When interpreting the coefficient on this variable it is important to
remember that part of the impact of liberalization appears in the equation
as a tariff reduction and is therefore already taken into account in the
estimated value of the Armington elasticity. The dummy variable captures
the rest of the impact of liberalization, which can be attributed to other
factors such as the existence of repressed demand for imports, which was
revealed when non-tariff barriers were removed on that occasion.23
The coefficient of the time trend variable is significant in 20
sectors, and is positive in all cases except one. This is consistent with the
interpretation that during the period 1986-2002 there was an increase in the
relative demand for imports that is not explained by the other three factors;
and it is possibly related to the modernization and internationalization of
the basket goods produced and consumed by domestic industry.
Table IX.4 summarizes the values we obtained for the Armington
elasticity for the different the sectors, classified as: very high, high, average,
low, zero or negative. The range of values in each category is not uniform
because the purpose of the classification is to provide an indication of the
curvature of the indifference curve between imports and domestically
produced goods, for each sector. This curvature does not vary linearly
with the elasticity, however, as can be seen in figure IX.1.
Figure IX.1 is also useful for illustrating the difficulty of estimating
the Armington elasticity when its value is small and the indifference
function has a high degree of curvature. This is the case in the two
sectors where the elasticity is classified as low, and in the three cases
where it is zero or negative (table IX.4). Considering that, at each point on
the plane in figure IX.1, the elasticity of substitution is the ratio between
the slope of the indifference curve passing through that point and the
slope of the line segment that connects it to the origin of the coordinate
23 The presence of repressed demand is a possible explanation for the sign of the dummy
variable in imports of automobiles, trucks and buses, tractors and machinery, other
vehicles and autoparts, textiles and clothing. The negative value of that variable can be
rationalized for cases where imports did not grow by as much as expected, given the tariff
reduction. This may have occurred because of pricing policies implemented by domestic
producers to control import penetration in the following sectors: the rubber industry,
electronic equipment, miscellaneous chemical products and mineral extraction.

Modeling Public Policies in Latin America and the Caribbean 303
Other food pro ducts and beverage s 4 4 - - D 1.9 3.59 5.13 - -
(6.12) (1.58) - -
Textile industry 4 4 - - D 2.0 3.3 6 - 0.6 5 0.03
(9.66) - (3.52) (6.5 3)
Miscellaneous industry 4 4 - - D 4.3 2.42 - - 0.02
(6.08) - - 2.82
Clothing articles and acc essories 4 4 - - D 0.4 2.23 - 0.63 0.05
(8.07) - (1.90) ( 6.07)
Rubber in dustr y 4 4 - - D 1.3 2.16 - -0.54 0.01
(7.61) - (-3.11) (2. 21)
Meat pr eparation and animal slaughtering 7 7 - - A 0.3 2.03 - - -
(3.30) - - -
Wood products and furniture 4 4 - - D 0.4 1.8 6 - - 0.03
(6.04) - - (5.26)
Tractor s and machiner y 4 4 - - D 12.3 1.78 - 0.89 -
(8.29) - (7.84) -
Plastics 4 4 - - D 0.6 1.75 - - 0.03
(9.54) - - (5.23)
Other metallurgical products 4 4 - - D 1.9 1.50 - - 0.03
(6.84) - - (5.9 9)
Milk and d erivative s 7 1 - - A 0.7 1.47 - - -
(2.53) - - -
Automobiles , trucks and buses 3 3 S S A 4.3 1.43 - 1.60 0.06
(2.80) - (2.8 8) (3.61)
Processing of plant produc ts and tobacco 7 7 - - A 2.5 1.18 - - -
(3.80) - - -
Petroleum re fining and petrochemicals 6 4 S - D 10.8 1.18 - 0.5 3 0.01
(4.22) - (3.49) (3.81)
Paper, pulp and print 4 2 - - B 2.0 1.01 0.71 - -
(6.11) (1.77) - -
Metallurgy of non-ferrous materials 7 1 - - A 2.1 0.98 - - 0.01
(5.04) - - (8.09)
Table IX.3
ARMINGTON ELASTICITIES FOR BRAZIL, 1986-2002
Sector Classificationa Structural b reak b Modelc Share (%)d Estimated co effi cients (t- statistic in br acke ts)
Quantum Price Quantum Pric e Substitution Variation Br eak Trend
(Continues)

304 ECLAC – IDB
Non-metallic minerals 7 2 S S A 0.9 0.75 - 0.55 0.02
(4.00) - (3.43) (5.17)
Vegetable oils and edible fats 3 7 S S A 0.5 0.61 - - -
(1.77) - - -
Steel 7 4 - - E 1.3 0.57 - - 0.02
(2.16) - - (4.24)
Other vehicles, par ts and accessories 6 4 S - D 8.9 0.41 - 0.32 0.02
(2.27) - (2.26) (7.27)
Pharmaceutical s and per fumery 7 4 - - C 3.8 0.40 - - 0.0 3
(3.62) - - (11.34)
Electrical materials 7 4 - - E 5. 2 0.36 - - 0.02
(1.94) - - (10.03)
Petroleum, natural gas, coal and other fuels 1 7 S S A 1.0 0.27 - 0.45 -0.03
(1.34) - (2.45) (-5.95)
Electronic equipment 3 4 S - E 12.0 0.16 - -0.46 0.01
(1.37) - ( -4.67 ) (5.72)
Non-petrochemic al chemicals 3 2 S S A 5.3 0.36 - - 0.03
(1.23) - - (5.28)
Miscellaneous chemicals 7 7 S S A 4.6 0.14 - -0.24 0.02
(0.58) - (-2.28) (7.82)
Foot wear, leather articles and fur 7 4 S - E 0.5 -0.18 - - 0.02
(-0.54) - - ( 5.21)
Mineral extract ion 1 7 - - A 1.8 -1.34 - -0.70 -
(-3.24) - (-3.02) -
Weighted ave rage share of impor ts 0.93 0.11 0.20 0.02
a Code for series classication:
1 – Stationary around a non-zero average
2 – Stationary around a zero average
3 – Stationary around a linear trend
4 – Has a unit root with zero time trend
5 – Has a unit root with non-zero time trend
6 – The existence of a unit root cannot be rejected
7 – Does not have a unit root
Source: Prepared by the authors.
Notes: For 60 degrees of freedom and bilateral condence intervals, t20% = 1.296, t10% = 1.671 and t5% = 2.000.
b Code for structural break: S when there is structural break in 1990:4
c Code for estimated model (see text for details):
A – Regression on levels
B – Regression on rst differences
C – Regression on levels, with lagged dependent variable
D – Cointegration model between integrated series
E – Estimation by cointegration owing to zero elasticity in models B and C
d Share of the sector in Brazil’s total imports, average 1997-2002
Sector Classificationa Structural b reak b Modelc Share (%)d Estimated co effi cients (t- statistic in br acke ts)
Quantum Price Quantum Pric e Substitution Variation Br eak Trend
Table IX.3 (concluded)

Modeling Public Policies in Latin America and the Caribbean 305
Sect or This pape r US ITC and GTAP
Categor y Definition Elasticity Average USITC GTAP
Othe r food pr oduct s and beverages Very Hi gh σ ≥ 3 3.59 3.2 4.2 2. 2
Textil e industry 3.36 2.3 2 .3 2. 2
Misce llaneous in dustr y 2.42 2.3 1.7 2 .8
Cloth ing articl es and accessorie s 2.23 3.2 2. 0 4. 4
Rubber i ndustry 2.16 2.0 2.0 1.9
Meat pr eparatio n and animal slaughtering High 1,5 ≤ σ < 3 2.03 2 .5 2.7 2.2
Wood pro ducts and furnitu re 1.86 2.8 2.8 2.8
Tractor s and machinery 1.78 2. 5 2.2 2.8
Plas tics 1.75 2.0 2.0 1.9
Othe r meta llurgi cal produc ts 1.50 3.5 4.1 2.8
Milk an d milk der ivatives 1.47 3.6 5. 0 2. 2
Autom obiles, tru cks and b uses 1.43 4.0 2 .7 5. 2
Proce ssing of plan t products a nd toba cco 1.18 3.3 3. 5 3.1
Petro leum refinin g and petroch emical indu stry 1.18 2. 2 2.5 1.9
Paper, pu lp and print Ave rage 0,5 ≤ σ < 1,5 1.01 2 .9 3.9 1.8
Meta llurgy of non -ferro us material s 0.98 3.6 4. 4 2. 8
Non-m etallic min erals 0.75 2.7 2. 5 2. 8
Veget able oils and e dible fats 0.61 3. 6 5.0 2. 2
Stee l 0.57 3.5 4.1 2.8
Othe rs vehi cles, part s and access ories 0.41 4.0 2 .7 5. 2
Pharm aceutica ls and perfu mery 0.40 2.0 2. 0 1.9
Elec trical mate rials Low 0 < σ < 0,5 0. 36 2 .5 2.2 2.8
Petro leum, natur al gas, coal and othe r fuels 0.2 7 2. 8 2.8 2 .8
Elec troni c equipm ent 0.16 2.7 2.6 2.8
Non-p etrochemi cal chemic als 0.0 0 2. 0 2.0 1.9
Miscellaneous chemicals Null σ ≈ 0 0.0 0 2.0 2.0 1.9
Foot wear, leathe r articles a nd fur 0 .00 3.1 1.7 4. 4
Miner al extrac tion Wrong sign σ < 0 -1.34 2.4 2.0 2.8
Arithmetic meana 1.24 2.8 2.8 2.8
Minimuma 0 .00 2.0 1.7 1.8
Max imum 3.5 9 4.0 5.0 5. 2
Range 3.59 2 .0 3.3 3.4
Standard deviationa 0.98 0.6 1.0 0.9
Table IX.4
RANGES OF THE ESTIMATED ELASTICITIES AND INTERNATIONAL COMPARISON
Source: Donnelly et al (2004) and authors’ calculations.
a Excludes sector where the elasticity has the incorrect sign.

306 ECLAC – IDB
system, we note that when the curvature is high, only a small segment
of the indifference curve is spanned when the relative price changes,
even when that change is large. This make the estimation more difficult
because large variations in p elicit only small changes in q; and in this
situation the error term e in equation (21) is larger. One might therefore
expect a large standard error in the estimate of σ in those cases.
Table IX.4 also shows that there are two sectors with very high
elasticity (σ ≅ 3), eight with high elasticity (σ ≅ 2), nine average (σ ≅ 1), five
low (σ < 0.5), three zero and one with negative elasticity. The arithmetic
mean of the estimated elasticities is 1.24 and their frequency distribution
is roughly symmetric.
We now compare the elasticities we estimated for Brazil with
those produced by other studies. As noted above, there are no previous
estimates for our country; and the difficulty in contrasting them with
elasticities for other countries is compounded by differences in the
sector classification and the small number of studies available in the
international literature. Nonetheless, this obstacle can be partially avoided
using the study by Donnelly et al (2004), which presents the Armington
elasticities adopted in the applied general equilibrium models of the
Figure IX.1
INDIFFERENCE CURVES BETWEEN IMPORTS AND DOMESTIC PRODUCTION
Source: Prepared by the authors.
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
00.2 0.40.6 0.8 1.0 1.21.4 1.61.8 2.0
Domestic production
Imports
0.25 0.50 0.99 2.00 5.00
Armington elasticity
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
00.2 0.40.6 0.8 1.0 1.21.4 1.61.8 2.0
Domestic production
Imports
0.25 0.50 0.99 2.00 5.00
Armington elasticity
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
00.2 0.40.6 0.8 1.0 1.21.4 1.61.8 2.0
Domestic production
Imports
0.25 0.50 0.99 2.00 5.00
Armington elasticity

Modeling Public Policies in Latin America and the Caribbean 307
United States International Trade Commission (USITC) and the Global
Trade Analysis Project (GTAP),24 using a sector classification similar to
the one we adopted.25
Although table IX.4 compares these three measures of sector
elasticities, the comparison may be of questionable relevance in itself, since
there is no a priori reason for them to be equal, or even similar, because
they reflect country-specific characteristics in the respective consumption
and production structures. We proceed with the comparison nonetheless.
Initially we note that the arithmetic mean of the estimated sector
elasticities (1.24) is only 44% of the 2.8 average value of the USITC and
GTAP sector elasticities. This suggests that substitution between imports
and domestic production is more difficult in Brazil than in the United
States, or in other hypothetical “conventional” countries, because, to
produce the same relative change in import share the change in relative
price needed in Brazil is twice as large, owing to the lower elasticity.
This is consistent with the perception that, even after liberalization,
Brazil still is relatively closed to international trade. Another possible
interpretation of this very large difference in elasticities is that those
calibrated by USITC and GTAP are in fact too high for a country with
our characteristics, and thus do not represent the behaviour of the
import share our case.
On the other hand, this difference in elasticity values does not
represent a very significant difference in the curvature of the indifference
curve, as can be inferred from figure IX.1 by noting that the curves for
σ = 1 and σ = 3 , are very close to each other.26
As can be seen by comparing the ranges and standard deviations
of the sector-level Armington elasticities in our study and those of
USITC and GTAP, shown in the bottom lines of table IX.4, the variability
of our estimates is similar to those reported by Donnelly et al (2004).
24 The United States International Trade Commission (USITC) developed a CGE model
for the United States to evaluate the impacts of changes in trade policy in that
economy. Its elasticities refer to the United States, and they were obtained from the
literature and later calibrated by sector experts. The Global Trade Analysis Project
(GTAP) developed a global-scope multi-regional model which is used to evaluate the
global impacts of trade agreements. The generic elasticities obtained from it are used
by the model when specific values are not available for a given country. They are
derived from the SALTER project of the Australian Industry Commission (Huff, 1997)
and other data contained in the literature.
25 In sectors for which we were able to find a direct correspondence with those in our
study, we transcribed the values directly. For the other sectors we repeated the values of
that study for the broader sector classification.
26 Although the curve for elasticity equal to 3 is not shown in the figure, to preserve clarity,
its position can be easily inferred from the curves for elasticities equal to 2 and 5, as
between these two but closer to the former.

308 ECLAC – IDB
Nonetheless, the fact that the minimum value of the sector elasticities
is so high (1.7 and 1.8 for USITC and GTAP, respectively) clearly stands
out in comparison to the zero value we found for Brazil. There is also
a significant numerical difference in the maximum value of the sector
elasticities (3.6 versus 5). Nonetheless, that does not imply a large
difference in the curvature of the indifference curve, which is practically
zero in both cases, since substitution is near perfect in those sectors, both
in Brazil and in the countries represented in those two CGE models.
Lastly, it is important to note that the differences between our
estimates and those reported in Donelly et al (2004) may be due not
only to the characteristics of the countries, but also to differences in
the methodologies used to obtain them. The calibration of elasticities,
based on expert opinions expressed in relation to sector studies using
the Delphi methodology, may have led the institutions in question to
eliminate outlying or uncommon values, as a result of error-risk aversion
on the part of the specialists consulted.
We can conclude this international comparison by making a more
general assessment of the comparison of sector elasticities, noting that the
discrepancies are substantial and more frequent than the coincidences.
This eloquent evidence advises against a procedure that is frequently
encountered in the literature, whereby the impacts of trade and exchange-
rate policies are analysed using elasticities calibrated on the basis of
values adopted for other countries, on the assumption that differences
are insignificant. This procedure is not valid for Brazil, at least for the
period we have analysed, and it may easily lead to false conclusions.
E. Conclusions
This paper has estimated a new set of Armington substitution elasticities
for the 28 industrial sectors of the Brazilian input-output matrix, for the
period 1986-2002. We develop an estimation methodology that measures
the effects on observed data of the trade restrictions that existed before
1990, and the impact of the trade liberalization that began in that year.
The methodology also carefully examines and takes into account the
stochastic and dynamic properties of the variables involved, and chooses
the estimation method so as to be consistent with those properties. We
speculate that this methodology could be applicable to other countries
that have undergone trade liberalization; and we argue that this is
relevant and needs to be included in the estimation data for the trade
liberalization period, since it contains information that is very important
for estimating the elasticity of substitution and the curvature of the
indifference curve between imports and domestic production.

Modeling Public Policies in Latin America and the Caribbean 309
The Armington elasticities we estimate have the correct sign; and
they are significant at the 5% level for 20 sectors, at 10% for two sectors,
and at 20% for two others. In one sector the estimated value is significant
but has the incorrect sign (negative). Although the estimated elasticity is
not significantly different from zero in three sectors, these represent only
12% of the average total value of imports in the period 1997-2002. The
point estimate of the elasticity of substitution ranges from 0.16 to 3.6 in
the sectors where it is positive and statistically non-zero; and its weighted
average value is 0.93, the weights being the value of sector imports.
A classification was used to group sectors according to the
range of variation of the substitution elasticity. This shows that
the Armington elasticity is very high in two sectors, high in eight,
average in nine, low in five, zero in three, and negative in one. The
arithmetic mean of their value is 1.24 and the frequency distribution
of the elasticities is roughly symmetric.
The international comparison shows that the average of the sector
elasticities we obtain is only 44% of those used in the USITC and GTAP
general equilibrium models; but this numerical difference in elasticity
values only has a small effect on the curvature of the indifference curve
between imports and domestic production. Nonetheless, there are large
sector differences in elasticity values when the estimates for different
sectors are compared individually; and there are also differences in the
minimum and maximum elasticities across sectors.
Lastly, we believe that using these elasticities will enable
researchers to more precisely evaluate the economic impacts of a change
in trade policy, in both partial and general equilibrium models.

310 ECLAC – IDB
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Modeling Public Policies in Latin America and the Caribbean 311
Annex A
Source and treatment of the data
We used quarterly data for each sector of the Brazilian input-output
matrix (IBGE – level 50), for the period 1986-2002.
The price and quantum indices
()
m
i
P
and
()
i
M
, respectively, are
those produced by Fundação Centro do Comércio Exterior (Funcex), using
the methodology described in Markwald et al (1998); they are available
in the electronic database system IPEADATA (www.ipea.gov.br). The
exchange rate (e) is the monthly average of the official dollar selling price.
We approximated the domestic price index (PDi ) by the corresponding
wholesale price index, Índice de Preço no Atacado (Oferta Global) calculated by
the Getulio Vargas Foundation (IPA-OG-FGV), having reconciled its sectors
with those of the input-output matrix described in table A1. We calculate
the average price index in cases where an activity of the input-output
matrix corresponds to more than one IPA sector, using a weighted average
when the necessary data was available, otherwise the simple average.
The coefficient of variation of the relative price
()
dm
ii
PP
measures
the effect of uncertainty and was calculated as the ratio between the
standard deviation and the average of this price ratio over a six-month
“window” centred on the median month of the period in question.
The domestic sales quantum index (Di ) was estimated by deflating
the value of domestic sales for each sector (VDTi ) by the corresponding
domestic price index
()
d
i
P
.
The sector VDTi was calculated by deducting the value of exports
from the corresponding sector-production value (VPi ), which was
inferred from its value in the most recent input-output matrix, together
with the variation in the production and price indices between the year
to which it refers and the date for which the calculation is being made.
As data availability prior to 1990 is limited, the procedure was slightly
adapted in the earlier period, as follows.
For 1986-1990 the value of total domestic sales (VDTi ) was estimated
by equation (A1), which shows that the value for each month was
calculated by applying the observed monthly variations in the quantum
and price indices to the average value of total domestic sales in 1985, and
then deducting the value of exports for the respective month. This uses
the domestic production quantum index calculated by IBGE (www.ipea.
gov.br) for each sector of the matrix, adjusted to the aggregation used
here as described in table A2.

312 ECLAC – IDB
Sector of the IPA-OG-FGV (column)
Mineral extraction (28)
Fuels and lubricants (54)
Limestones and silicates (30)
Iron, steel and derivatives (32)
Non-ferrous metals (33)
Total met allurgical (31)
Machinery and industrial equipment (36)
Total electric material (38)
Electric material and others (41)
Motor vehicles (43)
Motor vehicles (43)
Wood (45), total furniture (46)
Paper, paperboard (50)
Rubber (51)
Chemicals and others (58)
Total chemicals (53)
Total chemicals (53)
Pharmaceutical products (81), perfumery, soaps
and candles (82)
Plastics (56), plastic products (83)
Natural fabrics and yarns ( 60) , man-made fabrics
and yarns (61), knitted or crocheted fabrics (62)
Clothing (63)
Footwear (64)
Plant products (71)
Meat and fish (78)
Milk and milk derivatives (79)
Vegetable oils and fats (74)
Salt, animal feed and others (80), beverages ( 66)
Total manufacturing industr y (29)
Meat and fish (78)
Table A1
RECONCILIATION BETWEEN THE SECTORS OF THE INPUT-OUTPUT MATRIX AND
THE IPA INDUSTRY CLASSIFICATION
Source: IBGE and FGV. Prepared by the authors.
Sector of input-output matrix (level 50)
Mineral extraction
Petroleum, natural gas, coal and other fuels
Non-metallic minerals
Steel
Metallurgy of non-ferrous materials
Other metallurgic al products
Tractors and machiner y
Elec tri c materi al
Electronic equipment
Automobiles, trucks and buses
Other vehicles, par ts and accessories
Wood products and furniture
Paper, pulp and print
Rubber industr y
Non-petrochemical chemicals
Petroleum refining and petrochemical industr y
Miscellaneous chemicals
Pharmaceuticals and per fumery
Plastics
Textile industry
Clothing articles and accessories
Footwear, leather ar ticles and fur
Processing of plant products and tobacco
Meat preparation and animal slaughtering
Milk and milk derivatives
Vegetable oils and edible fat s
Other food products and beverages
Other miscellaneous industries
Meat preparation and animal slaughtering

Modeling Public Policies in Latin America and the Caribbean 313
where:
VDTit = value in R$ of total sector i domestic sales in month t;
VPit85 = value in R$ (base price) of sector i production in 1985;
qit = index of sector i physical production in month t;
qit85 = index of sector i physical production, monthly average in 1985;
Pit = index of sector i domestic price in month t;
Pi85 = index of sector i domestic price, monthly average in 1985; and
VEit = value in R$ of sector i exports in month t.
After 1991, the procedure described above for the reference year 1985
was repeated, but using previous year’s average values as the base, because
the value of domestic production each year is available in the input-output
matrix for 1991-1996, and in the National Accounts for 1997-2002.
We used a two-step procedure to calculate the nominal tariff in
each sector τit . First, we distributed the products and respective tariffs
obtained from the foreign trade classification table —the Brazilian
Merchandise Nomenclature: Harmonized System (NBM-SH) and the
Common Mercosur Nomenclature (NCM-SH)— for each sector (level
80) of the input-output matrix. Next, we calculated the average nominal
tariff for each activity in the input-output matrix (level 50), weighted
by the value of production of each sector (level 80) belonging to each
activity (level 50).
The effectively paid tariff series ( τit ) was calculated as the ratio
between tariff revenue and the total value of imports for each category
of use, using data obtained from the Brazilian Internal Revenue Service
(SRF/MF). This was adjusted to be consistent with the sector classification
of the input-output matrix.
32
The sector was calculated by deducting the value of exports from the corresponding sector-
production value , which was inferred from its value in the most recent input-output matrix,
together with the variation in the production and price indices between the year to which it refers and
the date for which the calculation is being made. As data availability prior to 1990 is limited, the
procedure was slightly adapted in the earlier period, as follows.
For 1986-1990 the value of total domestic sales was estimated by equation (A1), which
shows that the value for each month was calculated by applying the observed monthly variations in
the quantum and price indices to the average value of total domestic sales in 1985, and then
deducting the value of exports for the respective month. This uses the domestic production quantum
index calculated by IBGE (www.ibge.gov.br) for each sector of the matrix, adjusted to the aggregation
used here as described in Table A2.
(A1)
where:
= value in R$ of total sector i domestic sales in month t;
= value in R$ (base price) of sector i production in 1985;
= index of sector i physical production in month t;
= index of sector i physical production, monthly average in 1985;
= index of sector i domestic price in month t;
= index of sector i domestic price, monthly average in 1985; and
= value in R$ of sector i exports in month t.
After 1991, the procedure described above for the reference year 1985 was repeated, but using
previous year's average values as the base, because the value of domestic production each year is
available in the input-output matrix for 1991-1996, and in the National Accounts for 1997-2002.
We used a two-step procedure to calculate the nominal tariff in each sector . First, we distributed
the products and respective tariffs obtained from the foreign trade classification table – the Brazilian
(A1)

314 ECLAC – IDB
Table A2
RECONCILIATION BETWEEN THE SECTORS OF THE INPUT-OUTPUT MATRIX AND THE INDUSTRY CLASSIFICATION
Classification
Mineral extraction
Petroleum, nat’l gas, coal & other fuels
Non-metallic metals
Steel
Metallurgy of non-ferrous materials
Other metallurgical products
Tractor s and machiner y
Electrical materials
Electronic equipment
Automobiles , trucks and buses
Other vehicles, par ts & accessories
Wood products and furniture
Paper and pulp
Rubber in dustr y
Non- petrochemical c hemicals
Petroleum re fining & petrochem. ind.
Miscellaneous chemicals
Pharmaceuticals and perfumery
Plastics
Textile industry
Clothing articles and accessories
Foot wear, leather articles and fur
Processing of plant prod’s & tobacco
Meat pr ep. & anim al slaughtering
Milk and milk derivatives
Vegetable oils and edible fats
Other food pro ducts and beverage s
Miscellaneous industries
Source: IBGE, prepared by the authors.
Sect or: IBGE (g ) or matrix (m ): 1986-199 0
Non-metallic minerals ex traction (m)
Petroleum and natural gas extraction (m)
Non-metallic met als products (g)
Flat-rolled steel products (m)
Basic metallurgy ( g)
Other metallurgy ( g)
Mechanical produc ts (g)
Electrical and communication materi als (g)
Electrical and communication materi als (g)
Automobiles (m)
Autoparts and acc essories (m )
Total manufacturing industry (g )
Paper and paperboar d (g)
Rubber (g)
Total chemicals (g)
Petro chemicals, coal re fining ( g)
Other chemic als (g)
Pharm. & vet. prod’s (g) & p erf., soaps & candles (g)
Plastics (g)
Textiles (g)
Clothing, footwear and fabrics ( g)
Foot wear (m)
Food products (g)
Meat pr eparation & animal slaughtering ( m)
Milk der ivatives (m)
Oil refi ning and edible fats (m)
Food products (g) and bever ages (g)
Total manufacturing industry (g )
Sect or: IBGE (g ) or matrix (m ): 1991-1999
Mineral extract ion (g)
Petroleum and natural gas extraction (m)
Petroleum and natural gas extraction (g)
Steel (m)
Met allurgy of non-fer rous materia ls (m)
Other metallurgical products (m)
Mechanical produc ts (g)
Electrical machinery and equipment, including household appliances (m)
Mater ial for electronic & comm. equipment (m), and TVs, r adios & sound equipment (m)
Automobiles , trucks and buses (m)
Autoparts and acc essories (m )
Wood (m) a nd furniture industry (m)
Paper and paperboar d (g)
Rubber in dustr y (g)
Chemic al, non -petrochemical or carbon-based (m) and alcohol dis tilling (m)
Petroleum re fining (m), basic & interm. pe trochem. (m), resin, fibres & elastomers (m)
Fertilizers (m) and misc ellaneous chemical products (m)
Pharmaceutical industry (m) and per fumery, soaps and candles (m)
Plastics (g)
Textiles (g)
Clothing articles and acc essories (m )
Foot wear (m)
Processing of rice (m), wheat milling (m) & proce ssing of other plant prod’s for food (m)
Meat pr eparation and animal slaughtering (excl. poultry) (m) & meat prep. poultr y (m)
Preparation of milk and milk derivatives (m)
Natur al vegetable oils (m ) and re fining and edibl e fats (m)
Other food industri es (m) and beverage industr y (m)
Total manufacturing industry (g )

Modeling Public Policies in Latin America and the Caribbean 315
Annex B
Determination of the order of integration
of the price and quantum series
We used the methodology proposed by Enders (1995) to determine the
order of integration of the price and quantity series involved in the
estimation equation, complemented by the Perron (1989) test to deal with
the possibility of structural breaks in the series.
We initially estimate equation (B1), which contains a trend, a
constant term and autoregressive components; and we test for the
existence of a unit root (g = 0), using the augmented Dickey-Fuller (ADF)
statistic.27 If that hypothesis is rejected, we conclude there is no unit root
and terminate the search.
As this is a low-power test, if the unit root cannot be rejected we
must also test the joint hypothesis of its existence and the absence of a
trend (a2 = g = 0), using the Dickey-Fuller f3 statistic (1981). If this joint
hypothesis is rejected, we test again for g = 0, using a normal distribution,
and the procedure is then ended. If this joint hypothesis cannot be rejected,
we assume that we can cast the data-generating process in the form of
equation (B2), and we again test for a unit root with the ADF statistic.
If the null hypothesis of a unit root is rejected in this specification,
we terminate the procedure. If it cannot be rejected, we test for the joint
null hypothesis a0 = g = 0 using the Dickey-Fuller f2 statistic (1981). If
joint hypothesis is rejected, we test again for g = 0, using the normal
distribution, and the procedure is completed. If the hypothesis c1= g = 0 is
not rejected, we test for the existence of the unit root in the specification of
equation (15), again using the ADF statistic. If g = 0 is accepted (rejected),
we conclude that the series contains (does not contain) a unit root.
27 The critical values for the ADF statistics were taken from Hamilton (1994) for a 10%
significance level.
ANNEX B
DETERMINATION OF THE ORDER OF INTEGRATION OF THE PRICE AND QUANTUM SERIES
We used the methodology proposed by Enders (1995) to determine the order of integration of the
price and quantity series involved in the estimation equation, complemented by the Perron (1989) test
to deal with the possibility of structural breaks in the series.
We initially estimate equation (B.1), which contains a trend, a constant term and autoregressive
components; and we test for the existence of a unit root (! = 0), using the augmented Dickey-Fuller
(ADF) statistic.23 If that hypothesis is rejected, we conclude there is no unit root and terminate the
search.
(B.1)
As this is a low-power test, if the unit root cannot be rejected we must also test the joint hypothesis of
its existence and the absence of a trend , using the Dickey-Fuller statistic (1981). If
this joint hypothesis is rejected, we test again for ! = 0, using a normal distribution, and the procedure
is then ended. If this joint hypothesis cannot be rejected, we assume that we can cast the data-
generating process in the form of equation (B.2), and we again test for a unit root with the ADF
statistic.
(B.2)
If the null hypothesis of a unit root is rejected in this specification, we terminate the procedure. If it
cannot be rejected, we test for the joint null hypothesis using the Dickey-Fuller statistic
(1981). If joint hypothesis is rejected, we test again for ! = 0, using the normal distribution, and the
procedure is completed. If the hypothesis is not rejected, we test for the existence of the
23. The critical values for the ADF statistics were taken from Hamilton (1994) for a 10% significance level.
(B1)
ANNEX B
DETERMINATION OF THE ORDER OF INTEGRATION OF THE PRICE AND QUANTUM SERIES
We used the methodology proposed by Enders (1995) to determine the order of integration of the
price and quantity series involved in the estimation equation, complemented by the Perron (1989) test
to deal with the possibility of structural breaks in the series.
We initially estimate equation (B.1), which contains a trend, a constant term and autoregressive
components; and we test for the existence of a unit root (! = 0), using the augmented Dickey-Fuller
(ADF) statistic.23 If that hypothesis is rejected, we conclude there is no unit root and terminate the
search.
(B.1)
As this is a low-power test, if the unit root cannot be rejected we must also test the joint hypothesis of
its existence and the absence of a trend , using the Dickey-Fuller statistic (1981). If
this joint hypothesis is rejected, we test again for ! = 0, using a normal distribution, and the procedure
is then ended. If this joint hypothesis cannot be rejected, we assume that we can cast the data-
generating process in the form of equation (B.2), and we again test for a unit root with the ADF
statistic.
(B.2)
If the null hypothesis of a unit root is rejected in this specification, we terminate the procedure. If it
cannot be rejected, we test for the joint null hypothesis using the Dickey-Fuller statistic
(1981). If joint hypothesis is rejected, we test again for ! = 0, using the normal distribution, and the
procedure is completed. If the hypothesis is not rejected, we test for the existence of the
23. The critical values for the ADF statistics were taken from Hamilton (1994) for a 10% significance level.
(B2)
36
unit root in the specification of equation (15), again using the ADF statistic. If ! = 0 is accepted
(rejected), we conclude that the series contains (does not contain) a unit root.
(B.3)
In equations (B.1), (B.2) and (B.3), the number of lags (p) was chosen according to the general-to-
simple criterion, starting with a maximum of five. The fifth lag is retained if it is significant at the 5%
level. Otherwise, we re-estimate the equation with four lags, and again assess the level of significance
of the last lag. The procedure continues until the coefficient of the last autoregressive component is
significant at the 5% level.
It should be noted that the results of the tests described above may not be conclusive if there is a
structural break in the series; in that case the ADF statistic has a bias towards non-rejection of the
unit root. To account for this and take into consideration the likelihood of a structural break in the
fourth quarter of 1990, we apply the Perron (1989) test to series displaying a unit root. Using the
taxonomy proposed by that author, we assume the break is of the type represented by the changing
growth model. Equation (B.4) describes this model, and accommodates both the null and the
alternative hypothesis of the test. In the null hypothesis, a unit root is assumed with a change in the
intercept of the process at the time of the structural break. The alternative hypothesis assumes that
the process is stationary with a change in the slope of the deterministic trend line at the time of the
break.
(B.4)
where:
date of the structural break;
(B3)

316 ECLAC – IDB
In equations (B1), (B2) and (B3), the number of lags (p) was chosen
according to the general-to-simple criterion, starting with a maximum of
five. The fifth lag is retained if it is significant at the 5% level. Otherwise,
we re-estimate the equation with four lags, and again assess the level of
significance of the last lag. The procedure continues until the coefficient
of the last autoregressive component is significant at the 5% level.
It should be noted that the results of the tests described above may
not be conclusive if there is a structural break in the series; in that case the
ADF statistic has a bias towards non-rejection of the unit root. To account
for this and take into consideration the likelihood of a structural break
in the fourth quarter of 1990, we apply the Perron (1989) test to series
displaying a unit root. Using the taxonomy proposed by that author, we
assume the break is of the type represented by the changing growth model.
Equation (B4) describes this model, and accommodates both the null and
the alternative hypothesis of the test. In the null hypothesis, a unit root is
assumed with a change in the intercept of the process at the time of the
structural break. The alternative hypothesis assumes that the process is
stationary with a change in the slope of the deterministic trend line at
the time of the break.
where:
TB = date of the structural break;
DUt = 1 , if t > TB and DUt = 0 ; and
DTt* = t – TB , if t > TB and DTt* = 0 , otherwise.
The null hypothesis imposes the following restrictions on the
parameters of equation (B4):
a = 1 , g = 0 , θ ≠ C
The alternative hypothesis imposes the following restrictions on
the parameters of equation (B4):
a < 1 , g ≠ 0 , θ = C
We assumed that the structural break occurred in the fourth quarter
of 1990, and the critical values used were those of Perron (1989), with a 10%
significance level. We applied the test sequentially, adding autoregressive
components until the hypothesis of residual autocorrelation was rejected
in the Ljung-Box test, at a 5% significance level.
36
unit root in the specification of equation (15), again using the ADF statistic. If ! = 0 is accepted
(rejected), we conclude that the series contains (does not contain) a unit root.
(B.3)
In equations (B.1), (B.2) and (B.3), the number of lags (p) was chosen according to the general-to-
simple criterion, starting with a maximum of five. The fifth lag is retained if it is significant at the 5%
level. Otherwise, we re-estimate the equation with four lags, and again assess the level of significance
of the last lag. The procedure continues until the coefficient of the last autoregressive component is
significant at the 5% level.
It should be noted that the results of the tests described above may not be conclusive if there is a
structural break in the series; in that case the ADF statistic has a bias towards non-rejection of the
unit root. To account for this and take into consideration the likelihood of a structural break in the
fourth quarter of 1990, we apply the Perron (1989) test to series displaying a unit root. Using the
taxonomy proposed by that author, we assume the break is of the type represented by the changing
growth model. Equation (B.4) describes this model, and accommodates both the null and the
alternative hypothesis of the test. In the null hypothesis, a unit root is assumed with a change in the
intercept of the process at the time of the structural break. The alternative hypothesis assumes that
the process is stationary with a change in the slope of the deterministic trend line at the time of the
break.
(B.4)
where:
date of the structural break;
(B4)