Professor Alejandro Diaz Bautista Input Output Conference March 2013.

1. ““International Input Output Analysis and SustainableInternational Input Output Analysis and Sustainable
Regional DevelopmentRegional Development""
Dr. Alejandro Díaz-BautistaDr. Alejandro Díaz-Bautista
Profesor Investigador en Economía,Profesor Investigador en Economía,
ColefColef
Professor of International EconomicsProfessor of International Economics
adiazbau@gmail.comadiazbau@gmail.com
http://www.linkedin.com/pub/alejandro-diaz-bautista/6/619/691http://www.linkedin.com/pub/alejandro-diaz-bautista/6/619/691
Presentation prepared for the first conference of Input-Output Analysis,
Organized by the Universidad Autónoma de Yucatán, México y
Asociación Mexicana Matriz de Insumo Producto, March 14 -15, 2013,
Mérida, Yucatán, Mexico.

2. Input OutputInput Output
EconomicsEconomics
Input-output economics refers to the study of the effectsInput-output economics refers to the study of the effects
that different sectors have on the economy as a whole, forthat different sectors have on the economy as a whole, for
a particular nation or region. This type of economica particular nation or region. This type of economic
analysis was originally developed by Wassily Leontief,analysis was originally developed by Wassily Leontief,
who later won the Nobel Memorial Prize in Economicwho later won the Nobel Memorial Prize in Economic
Sciences for his work on this model.Sciences for his work on this model.
Input-output analysis allows the various relationshipsInput-output analysis allows the various relationships
within an economic system to be analyzed as a whole,within an economic system to be analyzed as a whole,
rather than individual components. The present studyrather than individual components. The present study
shows some of the empirical applications in Mexico andshows some of the empirical applications in Mexico and
the international experience in the development of Inputthe international experience in the development of Input
Output Matrix and analysis.Output Matrix and analysis.

3. Input Output EconomicsInput Output Economics
An understanding of the economy as consisting of linkedAn understanding of the economy as consisting of linked
sectors goes back to the French economist François Quesnay,sectors goes back to the French economist François Quesnay,
but was developed in general form by Léon Walras in 1874.but was developed in general form by Léon Walras in 1874.
Leontief's contribution was to state the model in such a way asLeontief's contribution was to state the model in such a way as
to make computation feasible.to make computation feasible.
With his first publications from 1936 to 1941 Leontief foundedWith his first publications from 1936 to 1941 Leontief founded
the input output analysis. Dantzig developed in 1951 the simplexthe input output analysis. Dantzig developed in 1951 the simplex
algorithm to solve linear optimization problems. His simplexalgorithm to solve linear optimization problems. His simplex
algorithm is still the basic foundation of linear programming andalgorithm is still the basic foundation of linear programming and
operations research. While Dorfman, Samuelson and Solowoperations research. While Dorfman, Samuelson and Solow
discussed in 1958 the close relationship between input-outputdiscussed in 1958 the close relationship between input-output
analysis and linear programminganalysis and linear programming

4. The input output equation model systemThe input output equation model system is the following:is the following:
Z = B(I - A)-1Y is the common equation system of input-outputZ = B(I - A)-1Y is the common equation system of input-output
analysis.analysis.
wherewhere
B = matrix of input coefficients for specific variable in economicB = matrix of input coefficients for specific variable in economic
analysis (intermediates, labor, capital, energy and emissions).analysis (intermediates, labor, capital, energy and emissions).
I = unit matrix.I = unit matrix.
A = matrix of input coefficients for intermediates.A = matrix of input coefficients for intermediates.
Y = diagonal matrix for final demand.Y = diagonal matrix for final demand.
Z = matrix with results for direct and indirect requirementsZ = matrix with results for direct and indirect requirements
(intermediates, labor, capital, energy and emissions).(intermediates, labor, capital, energy and emissions).
Matrix B includes the input coefficients of the variable underMatrix B includes the input coefficients of the variable under
investigation (intermediates, labor, capital, energy, emissions).investigation (intermediates, labor, capital, energy, emissions).
The diagonal matrix Y denotes exogenous final demand for goodsThe diagonal matrix Y denotes exogenous final demand for goods
and services.and services.
The matrix Z incorporates the results for the direct and indirectThe matrix Z incorporates the results for the direct and indirect
requirements (intermediates, labor, capital, energy) or joint productsrequirements (intermediates, labor, capital, energy) or joint products
(emissions) for the produced goods and services.(emissions) for the produced goods and services.

5. The Model of Dynamic Input-Output Analysis.The Model of Dynamic Input-Output Analysis.
Standard models of dynamic input output analysis consider that someStandard models of dynamic input output analysis consider that some
inputs contribute to the production process but are not immediatelyinputs contribute to the production process but are not immediately
used up during production. In other words, a sector has a certainused up during production. In other words, a sector has a certain
capital stock of machinery, buildings and transport equipment that iscapital stock of machinery, buildings and transport equipment that is
also necessary for production. In consequence, investments arealso necessary for production. In consequence, investments are
required for replacements and capacity additions.required for replacements and capacity additions.
The dynamic input-output models are designed in line with theThe dynamic input-output models are designed in line with the
multiplier-accelerator analysis of macroeconomic theory. According tomultiplier-accelerator analysis of macroeconomic theory. According to
this theory it is expected that investment is induced if final demand isthis theory it is expected that investment is induced if final demand is
expected to grow.expected to grow.

6. The Model of Dynamic Input-Output Analysis.The Model of Dynamic Input-Output Analysis.
We assume that induced investment is a function of expected growth.We assume that induced investment is a function of expected growth.
The model equations are:The model equations are:
Xt = AXt + Ct + DtXt = AXt + Ct + Dt
Dt = BXt+1 - BXtDt = BXt+1 - BXt
Xt = AXt + Ct + BXt+1 - BXtXt = AXt + Ct + BXt+1 - BXt
(I – A + B)Xt = Ct + BXt+1(I – A + B)Xt = Ct + BXt+1
The production of period t is defined:The production of period t is defined:
Xt = (I – A + B)-1 (Ct + BXt+1)Xt = (I – A + B)-1 (Ct + BXt+1)
while the production of period t+1 is determined by:while the production of period t+1 is determined by:
Xt+1 =B-1[(I – A + B)Xt - Ct]Xt+1 =B-1[(I – A + B)Xt - Ct]
X = output. Y = final demand. I = unit matrix ; A = input coefficients forX = output. Y = final demand. I = unit matrix ; A = input coefficients for
intermediates. (I-A)-1 = matrix of cumulative input coefficients (inverse).intermediates. (I-A)-1 = matrix of cumulative input coefficients (inverse).
B = input coefficients for capital; C = exogenous final demand (consumption);B = input coefficients for capital; C = exogenous final demand (consumption);
D = induced investment. T = time index.D = induced investment. T = time index.
This is a system of linear difference equations, since the values of theThis is a system of linear difference equations, since the values of the
variables are related to different periods of time.variables are related to different periods of time.
While consumption is expected to grow at the annual rate (1+m)t.While consumption is expected to grow at the annual rate (1+m)t.

7. Updating input output matrices.Updating input output matrices.
Methods for updating input-output tables can be categorized in univariate,Methods for updating input-output tables can be categorized in univariate,
bivariate, econometric and stochastic proceduresbivariate, econometric and stochastic procedures
The basic idea of univariate methods to update input-output tables is to correct theThe basic idea of univariate methods to update input-output tables is to correct the
matrix of input coefficients row wise with a diagonal matrix of correction factors.matrix of input coefficients row wise with a diagonal matrix of correction factors.
In contrast to univariate methods, which work with corrections of rows only,In contrast to univariate methods, which work with corrections of rows only,
bivariate models correct rows and columns of one input-output table at the samebivariate models correct rows and columns of one input-output table at the same
time.time.
The RAS procedure was developed by Richard Stone and named after the typicalThe RAS procedure was developed by Richard Stone and named after the typical
sequence of matrices. This time the matrix of input coefficients is pre-multipliedsequence of matrices. This time the matrix of input coefficients is pre-multiplied
with a diagonal matrix of row factors of correction and post multiplied with awith a diagonal matrix of row factors of correction and post multiplied with a
diagonal matrix of column factors of correction. Simple and modified RASdiagonal matrix of column factors of correction. Simple and modified RAS
procedures are widely used to update input output tables on the basis of aprocedures are widely used to update input output tables on the basis of a
benchmark table that has been compiled with the help of census and survey data.benchmark table that has been compiled with the help of census and survey data.
The basic idea is to adjust in an iterative procedure the matrix for intermediateThe basic idea is to adjust in an iterative procedure the matrix for intermediate
inputs column and row wise with appropriate multipliers until the given totals forinputs column and row wise with appropriate multipliers until the given totals for
intermediate input requirements are met.intermediate input requirements are met.
The RAS procedure seems to have a sound economic basis with the capability toThe RAS procedure seems to have a sound economic basis with the capability to
reflect technological change through the substitution and fabrication effects.reflect technological change through the substitution and fabrication effects.
However, many economists view the RAS procedure as a purely mathematicalHowever, many economists view the RAS procedure as a purely mathematical
procedure hardly capable of tracing the complex phenomenon of technologicalprocedure hardly capable of tracing the complex phenomenon of technological
change.change.

8. International Input outputInternational Input output
AnalysesAnalyses
Input output analyses are widely used in highlyInput output analyses are widely used in highly
industrialized societies and developing countries. In theindustrialized societies and developing countries. In the
United States, the Department of Commerce, for example,United States, the Department of Commerce, for example,
has generated several input-output matrices, including thehas generated several input-output matrices, including the
Bench-Mark Tables. In Europe, countries as Denmark,Bench-Mark Tables. In Europe, countries as Denmark,
France, Germany, the Netherlands, Norway, Spain andFrance, Germany, the Netherlands, Norway, Spain and
the United Kingdom, estimate input-output matrices everythe United Kingdom, estimate input-output matrices every
five years. In Latin America input-output matrices arefive years. In Latin America input-output matrices are
estimated every few years in Argentina, Colombia, Costaestimated every few years in Argentina, Colombia, Costa
Rica, Cuba, Mexico and Puerto Rico. Other countries withRica, Cuba, Mexico and Puerto Rico. Other countries with
a long tradition of producing this analytical instrument area long tradition of producing this analytical instrument are
India, Japan and Russia.India, Japan and Russia.

9. United States InputUnited States Input
Output AnalysisOutput Analysis
However, the first government agency to undertake theHowever, the first government agency to undertake the
construction of a full-scale national input-output table wasconstruction of a full-scale national input-output table was
the Bureau of Labor Statistics of the Department of Laborthe Bureau of Labor Statistics of the Department of Labor
in the U.S. This effort resulted in the publication of a 50-in the U.S. This effort resulted in the publication of a 50-
sector table of interindustry relations in the United Statessector table of interindustry relations in the United States
and of a much more detailed 200-sector table with finerand of a much more detailed 200-sector table with finer
industrial and sectoral classifications. To construct thisindustrial and sectoral classifications. To construct this
table, a separate Division of Interindustry Economics hadtable, a separate Division of Interindustry Economics had
been established in the Bureau of Labor Statistics. Anbeen established in the Bureau of Labor Statistics. An
important result of this early work in input-output analysisimportant result of this early work in input-output analysis
was a projection of the U.S. economy to 1950.was a projection of the U.S. economy to 1950.

10. United States InputUnited States Input
Output AnalysisOutput Analysis
In the United States the annual input-output (I-O)In the United States the annual input-output (I-O)
accounts provide a time series of detailed, consistentaccounts provide a time series of detailed, consistent
information on the flow of goods and services that makeinformation on the flow of goods and services that make
up the production processes of industries. For each yearup the production processes of industries. For each year
beginning with 1998, the accounts show how industriesbeginning with 1998, the accounts show how industries
interact as they provide inputs to, and use outputs from,interact as they provide inputs to, and use outputs from,
each other to produce GDP. The annual I-O accounts caneach other to produce GDP. The annual I-O accounts can
be used to study changes in structure of the U.S.be used to study changes in structure of the U.S.
economy and the relative importance of an industry to alleconomy and the relative importance of an industry to all
other industries. The accounts are an important tool forother industries. The accounts are an important tool for
analysis because they show the production functions ofanalysis because they show the production functions of
individual industries and the interactions among producersindividual industries and the interactions among producers
and between producers and final users in the economy.and between producers and final users in the economy.

11. United States InputUnited States Input
Output AnalysisOutput Analysis
The Industry Economic Accounts (IEA) preparesThe Industry Economic Accounts (IEA) prepares
benchmark input-output (I-O) accounts in the U.S. forbenchmark input-output (I-O) accounts in the U.S. for
years ending in 2 and 7, which are based on detailedyears ending in 2 and 7, which are based on detailed
data from the quinquennial economic censuses thatdata from the quinquennial economic censuses that
are conducted by the Bureau of the Census. Theare conducted by the Bureau of the Census. The
benchmark accounts show how industries interact atbenchmark accounts show how industries interact at
the detailed level; specifically, they show howthe detailed level; specifically, they show how
approximately 500 industries provide input to, and useapproximately 500 industries provide input to, and use
output from, each other to produce gross domesticoutput from, each other to produce gross domestic
product. These accounts provide detailed informationproduct. These accounts provide detailed information
on the flows of the goods and services that make upon the flows of the goods and services that make up
the production processes of industries.the production processes of industries.
The 2002 benchmark I-O accounts are presented inThe 2002 benchmark I-O accounts are presented in
the standard make and use tables and severalthe standard make and use tables and several
supplementary tables.supplementary tables.

12. Canada’s Input OutputCanada’s Input Output
AnalysisAnalysis
In Canada, input-output tables are published on an annualIn Canada, input-output tables are published on an annual
basis. The publications begin in 1961 for the nationalbasis. The publications begin in 1961 for the national
input-output tables, and the provincial input-output tablesinput-output tables, and the provincial input-output tables
are available from 1997. Input-output tables are availableare available from 1997. Input-output tables are available
for different levels of aggregation. Statistics Canadafor different levels of aggregation. Statistics Canada
operates national and interprovincial input-output models.operates national and interprovincial input-output models.
The models are open and they calculate the direct andThe models are open and they calculate the direct and
indirect effects only.indirect effects only.
Statistics Canada calculates national and provincialStatistics Canada calculates national and provincial
multipliers for all industries at all levels of aggregation.multipliers for all industries at all levels of aggregation.
Multipliers for special impact can be calculated using theMultipliers for special impact can be calculated using the
National and Interprovincial input-output models.National and Interprovincial input-output models.

13. European Input OutputEuropean Input Output
TableTable
While the European Input Output Table can be used to evaluate theWhile the European Input Output Table can be used to evaluate the
impact of different policies on macroeconomic variables such as grossimpact of different policies on macroeconomic variables such as gross
domestic product, employment, consumption, productivity,domestic product, employment, consumption, productivity,
competitiveness, etc, as well as on the environment. Moreover, inputcompetitiveness, etc, as well as on the environment. Moreover, input
output techniques allow quantitative impact assessment of policyoutput techniques allow quantitative impact assessment of policy
actions either for regional, national or international levels.actions either for regional, national or international levels.
The Institute for Prospective Technological Studies (IPTS) of theThe Institute for Prospective Technological Studies (IPTS) of the
European Commission's DG Joint Research Centre is developingEuropean Commission's DG Joint Research Centre is developing
input-output based models as a tool to support the development ofinput-output based models as a tool to support the development of
European policies. The latest progress is the elaboration of aEuropean policies. The latest progress is the elaboration of a
complete homogeneous set of 27 symmetric input-output tables atcomplete homogeneous set of 27 symmetric input-output tables at
individual Member State level and an aggregate EU 27 table.individual Member State level and an aggregate EU 27 table.

14. Input-Output Analysis in MexicoInput-Output Analysis in Mexico
Mexico has several input-output matrices referring to theMexico has several input-output matrices referring to the
years 1950, 1960, 1970, 1975, 1978 and 1980. Also, for thisyears 1950, 1960, 1970, 1975, 1978 and 1980. Also, for this
last year, Mexico has a matrix for the agriculture and forestrylast year, Mexico has a matrix for the agriculture and forestry
sector. In regards to the matrices of 1950 and 1960, theysector. In regards to the matrices of 1950 and 1960, they
were developed by the Bank of Mexico and were allowed towere developed by the Bank of Mexico and were allowed to
integrate the first set of consolidated accounts of the country,integrate the first set of consolidated accounts of the country,
while the following matrices were made by the Department ofwhile the following matrices were made by the Department of
Statistics (DGE) of National Institute of Statistics, GeographyStatistics (DGE) of National Institute of Statistics, Geography
and Informatics (INEGI).and Informatics (INEGI).
The matrices for 1975 and 1978 were part of an upgrade ofThe matrices for 1975 and 1978 were part of an upgrade of
1970, while the matrix of 1980 introduced innovative features1970, while the matrix of 1980 introduced innovative features
in relation to the preceding matrix.in relation to the preceding matrix.
In 2003, Inegi worked on the National MIP.In 2003, Inegi worked on the National MIP.
The most recent work on the national matrix was conductedThe most recent work on the national matrix was conducted
around 2008.around 2008.

15. Applied Input-Output Analysis forApplied Input-Output Analysis for
Mexico’s Energy SectorMexico’s Energy Sector

16. Proposed Applied Analysis for Mexico’sProposed Applied Analysis for Mexico’s
National Energy SectorNational Energy Sector

17. Proposed Applied Analysis for Mexico’sProposed Applied Analysis for Mexico’s
National Energy SectorNational Energy Sector

18. Mexico’s Energy SectorMexico’s Energy Sector
The National Energy Strategy 2013-27 was approved by majority voteThe National Energy Strategy 2013-27 was approved by majority vote
in the Senate during March of 2013.in the Senate during March of 2013.
The strategy outlines plans to deal with the country’s growing energyThe strategy outlines plans to deal with the country’s growing energy
needs in an efficient, safe and sustainable way.needs in an efficient, safe and sustainable way.
Mexico’s energy policy looks for opportunities in energy conservation;Mexico’s energy policy looks for opportunities in energy conservation;
expands energy services to regions with fewer resources; and seeks toexpands energy services to regions with fewer resources; and seeks to
minimize the health and environmental impacts that result from theminimize the health and environmental impacts that result from the
generation and consumption of energy, both regionally and globally.generation and consumption of energy, both regionally and globally.
The strategy promotes sharing the benefits of energy use with all ofThe strategy promotes sharing the benefits of energy use with all of
society, while exploring the sector’s long-term sustainability and wayssociety, while exploring the sector’s long-term sustainability and ways
to mitigate greenhouse gas emissions.to mitigate greenhouse gas emissions.
The upcoming energy reform shows a clear goal of expanding foreignThe upcoming energy reform shows a clear goal of expanding foreign
direct investment in the energy sector.direct investment in the energy sector.

19. ConclusionsConclusions
One of the key conclusions of the use of this type of modeling, whichOne of the key conclusions of the use of this type of modeling, which
integrates economic, energy and environmental interactions in anintegrates economic, energy and environmental interactions in an
input-output framework, is that it allows the analysis of how energy,input-output framework, is that it allows the analysis of how energy,
and therefore emissions, are related to industrial production, andand therefore emissions, are related to industrial production, and
ultimately to final demand, making it a tool particularly important forultimately to final demand, making it a tool particularly important for
policy analysis purposes.policy analysis purposes.
In addition to studying the structure of national economies, inputIn addition to studying the structure of national economies, input
output economics has been used to study regional economies withinoutput economics has been used to study regional economies within
a nation, and as a tool for national and regional economic planning.a nation, and as a tool for national and regional economic planning.
Indeed a main use of input-output analysis is for measuring theIndeed a main use of input-output analysis is for measuring the
economic impacts of events and projects as well as publiceconomic impacts of events and projects as well as public
investments or economic programs. Input output models are alsoinvestments or economic programs. Input output models are also
used to identify economically related industry clusters and keyused to identify economically related industry clusters and key
industries that are most likely to enhance the internal structure of aindustries that are most likely to enhance the internal structure of a
specified economy.specified economy.

20. ““International Input Output Analysis and SustainableInternational Input Output Analysis and Sustainable
Regional DevelopmentRegional Development""
Dr. Alejandro Díaz-BautistaDr. Alejandro Díaz-Bautista
Profesor Investigador en Economía,Profesor Investigador en Economía,
ColefColef
Professor of International EconomicsProfessor of International Economics
adiazbau@gmail.comadiazbau@gmail.com
http://www.linkedin.com/pub/alejandro-diaz-bautista/6/619/691http://www.linkedin.com/pub/alejandro-diaz-bautista/6/619/691
Presentation prepared for the first conference of Input-Output Analysis,
Organized by the Universidad Autónoma de Yucatán, México y
Asociación Mexicana Matriz de Insumo Producto, March 14 -15, 2013,
Mérida, Yucatán, Mexico.