Input Output Economics: Empirical Applications in Mexico and International Experience in the Development of Input Output Analysis. Professor Alejandro Diaz-Bautista, June 2012.

1. “Input Output Economics: Empirical Applications in Mexico
and International Experience in the Development of Input
Output Analysis"
Dr. Alejandro Díaz-Bautista
Catedrático y Profesor Investigador en
Economía, Colef
Professor of Economics at Colef
adiazbau@gmail.com
http://www.linkedin.com/pub/alejandro-diaz-bautista/6/619/691
Presentation prepared for “Estado Actual de la Investigación del
Análisis Insumo-Producto en México”, El Colegio de la Frontera Norte,
June 14 and 15, 2012, Baja California, Mexico

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

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

4. Input-Output
Techniques
Input-output techniques have been widely used in impact
economic analysis and forecasting models that combine
an economy-wide scope with a high degree of industrial
detail. One of the central problems with the input-output
(IO) tables is that their compilation is extremely time
consuming. This implies that they only become available
with a serious time lag and that typically they are
published only once every few years. A consequence is
that empirical analyses are always based on data that are
not up-to-date.

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

6. OECD Input Output
Tables
At the regional level, the OECD Input-Output tables
includes matrices of inter-industrial flows of transactions of
goods and services (domestically produced and imported)
in current prices, for all OECD countries (except Iceland)
and 15 non-member countries, covering the years 1995,
2000 and 2005 or nearest years. Tables for four countries
(Cyprus, Malta, Latvia and Lithuania) have been recently
added as well as an estimated table for the EU has a
whole. The latest set of OECD Input-Output tables
consists of 48 countries and economies with data for
years around 2005.

7. Input-Output Analysis in Planned and
Unplanned Economies
Before World War II, there was considerable debate
among economists about the benefits of having a planned
economy versus an unplanned economy.
A totally planned economy was the former Soviet Union
which was generally considered the prototype, and an
unplanned economy by which was usually meant a
laissez-faire system in which all economic decisions were
made by the invisible hand of the market place.

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

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

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

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

12. Germany’s IO Analysis
Input-output accounts in Germany are compiled centrally
at the Federal Statistical Office. As are the other sub areas
of national accounting, they are a secondary statistics
and, consequently, use a multitude of basic statistics.
Due to European requirements, the Federal Statistical
Office in Germany provides the supply and use table
annually, and not later than 36 months after the end of the
reference period to the European statistical office
(Eurostat). Although input-output tables must be supplied
to Eurostat only every five years, they are compiled and
published by the Federal Statistical Office for every
reference year.

13. Norwegian IO model
The Norwegian annual MODAG model has been
widely used for a range of issues over the last 20
years, mostly related to government demand and
recently about the effects of a membership of
Norway in the European Union.
MODAG is an input-output based model which is
used in short and medium term macroeconomic
planning and policy analysis.

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

15. Australia’s Input Output Tables
The Australian IO Tables provide detailed information about
the supply and use of products in the Australian economy
and about the structure of and inter-relationships between
Australian industries.
With the release of the 2005-2006 Tables Australia has
completed 21 input-output tables with the first set of tables
produced for 1958-59. The ABS now produces the IO tables
on an annual basis with a release date approximately three
years after the reference period.
The 2006-07 IO tables for Australia were released in
November 2010 and will be the first set of tables to
incorporate changes to the System of National Accounts
(SNA08) and a new industry classification (ANZSIC06).

16. Input-Output Analysis for the
BRICs
In recent years, India has attracted attentions together
with Brazil, China and Russia as one of the newly
emerging market economies called the “BRICs”.
BRIC is an acronym that refers to the economies of Brazil,
Russia, India, and China, which are seen as major
developing economies in the world. The general
consensus is that the term was first prominently used in a
Goldman Sachs report during 2003, which speculated that
by 2050 these four economies would be wealthier than
most of the current major economic powers. The BRIC
countries are now responsible for approximately 18% of
the world's Gross Domestic Product and home to 40% of
the earth's population.

17. India’s Input Output
Tables
The compilation of I-O tables in India was started in the
early 1950’s.
India’s I-O tables have been constructed following the
principles of the System of National Account (SNA) that is
determined by the United Nations (UN) as an international
standard and thus the presentation format of the India’s
tables is similar to many other countries’ I-O tables.
Researchers are now examining the possibility of
compiling the BRICs international I-O table by
investigating the features of the BRICs I-O tables.

18. China’s Input Output
Table
In China, Input-output tables were published every 5
years. Extended tables were published in the middle of
every 5 years. The complete Input-output tables of China
(tables of 1987, 1990, 1992, 1995, and 1997).
The source of the current input-output (I-O) table for China
is the Input-Output Table of China 2002 from the
Department of National Economy Accounting, State
Statistical Bureau (SSB). The original 2002 table in China
includes 122 sectors, of which there are 5 sectors for
agriculture, 81 sectors for manufacture, and 36 sectors for
services.

19. Brazil’s Input Output
Table
In the view of constructing I-O tables, Brazil is relatively young in its
experience compared to other countries of the similar development
stage. Only after the 1970s, the Brazilian Institute of Geography and
Statistics (IBGE) took its leading role to construct input-output
accounts.
However, the Brazilian I-O table developed very rapidly from its
outset, and it is now considered to be one of the most advanced
statistical series in terms of the data availability, speed of release, and
conformity with the international standards. The official (symmetrical)
I-O tables of Brazil, together with supply and use tables, are available
for the years 1970, 1975, 1980, 1985, 1990, 1991, 1992, 1993, 1994,
1995 and 1996. For the years from 1997 to 2005, only the information
about supply and use tables at purchaser prices can be found in the
national accounts.

20. Russia’s Input Output Table
The work on compilation of IO tables in the Soviet Union started in the
late 1950’s. First IO tables for the year 1959 were compiled by the
Central Statistics Office for 83 industries in monetary form and for 157
commodities in physical form. Further, the IO table for the year 1966
was produced (110 industries and 237 commodities), and the one for
the year 1972 (112 industries and 247 commodities). Later, the
following tables were produced: the five-yearly IO tables for 1977,
1982, 1987. The detailed IO tables served as a base for annual IO
tables with 18 aggregate sectors.
Since 1993 the National Statistics Office has accepted the System of
National Accounts. The first IO table for the national economy under
this framework was compiled for the year 1995. So far, the annual IO
tables have been compiled on its basis. The latest IO table released
for the year 2003 is compiled for 22 aggregate sectors. The IO tables
for Russia now become available on average around 3 years after the
reference period.

21. Input-Output Analysis in Mexico
The input-output matrix represents an indispensable tool in
Mexico and the INEGI Institute develops input output
projects through the System of National Accounts of
Mexico, since it represents the starting point and frame of
reference of the products obtained.
It reflects and updates the formal relationships that carry
out the various sectors and economic agents involved in all
phases of the cycle (production, consumption and
accumulation), and also provides detailed logs that serve
basis for modifying the base years of the calculations are
carried out.

22. Input-Output Analysis in Mexico
Mexico has six input-output matrices referring to the years
1950, 1960, 1970, 1975, 1978 and 1980. Also, for this last
year, Mexico has a matrix for the agriculture and forestry
sector. In regards to the matrices of 1950 and 1960, they
were developed by the Bank of Mexico and were allowed to
integrate the first set of consolidated accounts of the country,
while the following matrices were made by the Department of
Statistics (DGE) of National Institute of Statistics, Geography
and Informatics (INEGI).
The matrix of 1970, which was first developed by the DGE,
introduced substantial improvements in relation to the
previous ones, in both the conceptual framework and data
processing, and the level of detail of the matrix. It also
established the methodological basis for the development of
further matrices prepared in Mexico. The matrices for 1975
and 1978 were part of an upgrade of 1970, while the matrix of
1980 introduced innovative features in relation to the
preceding matrix.

23. Input-Output Analysis in Mexico
The input-output matrices in Mexico are considered as
pictures of intersectoral transactions valued at producer
prices, in millions of pesos, from which other tables are
derived. The technical coefficients, direct and indirect
requirements and import matrices, in millions of dollars,
with corresponding technical coefficients. The breakdown
that occurs with different matrices corresponds to 32
sectors in 1950 and 45 sectors in 1960. Since 1970, the
breakdown is expanded to 73 branches of economic
activity.
The matrices follow the International Standard Industrial
Classification (ISIC) of all Economic Activities, Series M
prepared by the United Nations Organization (UN) and the
Mexican Classification of Activities and Products (CMAP) in
1994.

24. Input-Output Analysis in Mexico
The estimates of the components of final demand were based on the
income-expenditure surveys of households, government administrative
records, the balance of payments and specific research in the area,
which have enabled the estimation of private consumption, government
consumption, gross capital formation and exports. Special mention
should be made for the use of the data presented in the current
account of the balance of payments, as well as allowing estimates for
exports that make possible to construct the arrays of imports.
At the regional and state levels, several input output matrices have
been constructed in recent years by universities and research centers
in Mexico. The results of input-output matrices are used especially as a
basis for structural studies of the economy and for analyses of the
direct and indirect impact of changes in demand, prices and wages on
the overall economy and on the various sectors. In addition, they are a
basis that can flexibly be used for model and simulation calculations as
well as forecasts.

25. Conclusions
The input output (IO) model gives an overview of the structure of an
economic system. It is important to note that an IO model can be quite
useful in viewing the world economy as an integrated system. The
input output method is now being used as a basic analytical tool by
government agencies in a large number of countries around the
world.
The structure of the input output model has been incorporated into
national accounting in many developed and developing countries, and
as such forms an important part of measures such as GDP.
In addition to studying the structure of national economies, input
output economics has been used to study regional economies within
a nation, and as a tool for national and regional economic planning.
Indeed a main use of input-output analysis is for measuring the
economic impacts of events and projects as well as public
investments or economic programs. Input output models are also
used to identify economically related industry clusters and key
industries that are most likely to enhance the internal structure of a
specified economy.

26. INFORUM Models
The recent Interindustry Forecasting at the University of Maryland
(INFORUM) models were developed by Clopper Almon at the
University of Maryland. The INFORUM models are internationally
linkable, dynamic, interindustry models which imitates as closely as
the economy behaves. They are intended for both public policy
analysis and business forecasting. The models are contrasted with
classical input output models, pure econometric models and
computable general equilibrium models. The model uses regression
analysis to describe the behavior of consumers, producers, exporters,
importers, investors, or other economic decision makers. It uses
explicit and usually changing input-output relations among industries.
That use assures absolute accounting consistency, on the production
side, among final demands, intermediate use, and production of
products and, on the price side, among prices of products, the costs
of materials used and the value added generating in making them.

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

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

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

30. Updating input output matrices.
Methods for updating input-output tables can be categorized in univariate,
bivariate, econometric and stochastic procedures
The 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.
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 same
time.
The RAS procedure was developed by Richard Stone and named after the typical
sequence 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 a
diagonal matrix of column factors of correction. Simple and modified RAS
procedures 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.
The 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 for
intermediate input requirements are met.
The RAS procedure seems to have a sound economic basis with the capability to
reflect technological change through the substitution and fabrication effects.
However, many economists view the RAS procedure as a purely mathematical
procedure hardly capable of tracing the complex phenomenon of technological
change.

31. INPUT OUTPUT INTERNATIONAL CONFERENCES
The first international Input Output conference met in Driebergen, Holland
in 1951, it brought together economists interested in the theoretical, the
statistical, and the computational problems of interindustry analysis.
A second conference was held between June 27 and July 10, 1954, at
Varenna, Italy.
A third international conference was held in September 1961 in Geneva.
Economists and statisticians from more than 41 different countries
participated in this conference. For the first time, representatives of the
Soviet Union and of other socialist countries, as well as planners from
underdeveloped countries, participated in the international input-output
conference.

32. “Input Output Economics: Empirical Applications in Mexico
and International Experience in the Development of Input
Output Analysis"
Dr. Alejandro Díaz-Bautista
Catedrático y Profesor Investigador en
Economía, Colef
Professor of Economics at Colef
adiazbau@gmail.com
http://www.linkedin.com/pub/alejandro-diaz-bautista/6/619/691
Presentation prepared for “Estado Actual de la Investigación del
Análisis Insumo-Producto en México”, El Colegio de la Frontera Norte,
June 14 and 15, 2012, Baja California, Mexico