Professor Alejandro Diaz Bautista, Input Output Conference, June 2012

““Input Output Economics: Empirical Applications in Mexico Input Output Economics: Empirical Applications in Mexico and International Experience in the Development of Input and International Experience in the Development of Input Output AnalysisOutput Analysis""

Dr. Alejandro Díaz-BautistaDr. Alejandro Díaz-BautistaCatedrático y Profesor Investigador en Catedrático y Profesor Investigador en Economía, ColefEconomía, Colef

Professor of Economics at Colef Professor of Economics at Colef

[email protected]

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

Input Output Input Output EconomicsEconomics

Input-output economics refers to the study of the effects Input-output economics refers to the study of the effects that different sectors have on the economy as a whole, for that different sectors have on the economy as a whole, for a particular nation or region. This type of economic a 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 Economic who 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 relationships Input-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 study rather than individual components. The present study shows some of the empirical applications in Mexico and shows some of the empirical applications in Mexico and the international experience in the development of Input the international experience in the development of Input Output Matrix and analysis.Output Matrix and analysis.

Input Output EconomicsInput Output EconomicsAn understanding of the economy as consisting of linked An 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 as Leontief'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 founded With his first publications from 1936 to 1941 Leontief founded the input output analysis. Dantzig developed in 1951 the simplex the input output analysis. Dantzig developed in 1951 the simplex algorithm to solve linear optimization problems. His simplex algorithm to solve linear optimization problems. His simplex algorithm is still the basic foundation of linear programming and algorithm is still the basic foundation of linear programming and operations research. While Dorfman, Samuelson and Solow operations research. While Dorfman, Samuelson and Solow discussed in 1958 the close relationship between input-output discussed in 1958 the close relationship between input-output analysis and linear programminganalysis and linear programming

Input-Output Input-Output TechniquesTechniques

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

International Input output International Input output AnalysesAnalyses

Input output analyses are widely used in highly Input output analyses are widely used in highly industrialized societies and developing countries. In the industrialized 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 the has 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 and France, Germany, the Netherlands, Norway, Spain and the United Kingdom, estimate input-output matrices every the United Kingdom, estimate input-output matrices every five years. In Latin America input-output matrices are five years. In Latin America input-output matrices are estimated every few years in Argentina, Colombia, Costa estimated every few years in Argentina, Colombia, Costa Rica, Cuba, Mexico and Puerto Rico. Other countries with Rica, Cuba, Mexico and Puerto Rico. Other countries with a long tradition of producing this analytical instrument are a long tradition of producing this analytical instrument are India, Japan and Russia.India, Japan and Russia.

OECD Input Output OECD Input Output TablesTables

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

Input-Output Analysis in Planned and Input-Output Analysis in Planned and Unplanned EconomiesUnplanned Economies

Before World War II, there was considerable debate Before World War II, there was considerable debate among economists about the benefits of having a planned among economists about the benefits of having a planned economy versus an unplanned economy. economy versus an unplanned economy.

A totally planned economy was the former Soviet Union A totally planned economy was the former Soviet Union which was generally considered the prototype, and an which was generally considered the prototype, and an unplanned economy by which was usually meant a unplanned economy by which was usually meant a laissez-faire system in which all economic decisions were laissez-faire system in which all economic decisions were made by the invisible hand of the market place.made by the invisible hand of the market place.

United States Input United States Input Output AnalysisOutput Analysis

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


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, consistent accounts provide a time series of detailed, consistent information on the flow of goods and services that make information on the flow of goods and services that make up the production processes of industries. For each year up the production processes of industries. For each year beginning with 1998, the accounts show how industries beginning 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 can each 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 all economy and the relative importance of an industry to all other industries. The accounts are an important tool for other industries. The accounts are an important tool for analysis because they show the production functions of analysis because they show the production functions of individual industries and the interactions among producers individual industries and the interactions among producers and between producers and final users in the economy. and between producers and final users in the economy.


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

Canada’s Input Output Canada’s Input Output AnalysisAnalysis

In Canada, input-output tables are published on an annual In Canada, input-output tables are published on an annual basis. The publications begin in 1961 for the national basis. The publications begin in 1961 for the national input-output tables, and the provincial input-output tables input-output tables, and the provincial input-output tables are available from 1997. Input-output tables are available are available from 1997. Input-output tables are available for different levels of aggregation. Statistics Canada for 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 and The models are open and they calculate the direct and indirect effects only. indirect effects only.

Statistics Canada calculates national and provincial Statistics 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 the Multipliers for special impact can be calculated using the National and Interprovincial input-output models.National and Interprovincial input-output models.

Germany’s IO AnalysisGermany’s IO AnalysisInput-output accounts in Germany are compiled centrally Input-output accounts in Germany are compiled centrally at the Federal Statistical Office. As are the other sub areas at the Federal Statistical Office. As are the other sub areas of national accounting, they are a secondary statistics of national accounting, they are a secondary statistics and, consequently, use a multitude of basic statistics. and, consequently, use a multitude of basic statistics.

Due to European requirements, the Federal Statistical Due to European requirements, the Federal Statistical Office in Germany provides the supply and use table Office in Germany provides the supply and use table annually, and not later than 36 months after the end of the annually, and not later than 36 months after the end of the reference period to the European statistical office reference period to the European statistical office (Eurostat). Although input-output tables must be supplied (Eurostat). Although input-output tables must be supplied to Eurostat only every five years, they are compiled and to Eurostat only every five years, they are compiled and published by the Federal Statistical Office for every published by the Federal Statistical Office for every reference year.reference year.

Norwegian IO modelNorwegian IO model

The Norwegian annual MODAG model has been The Norwegian annual MODAG model has been widely used for a range of issues over the last 20 widely used for a range of issues over the last 20 years, mostly related to government demand and years, mostly related to government demand and recently about the effects of a membership of recently about the effects of a membership of Norway in the European Union. Norway in the European Union.

MODAG is an input-output based model which is MODAG is an input-output based model which is used in short and medium term macroeconomic used in short and medium term macroeconomic planning and policy analysis. planning and policy analysis.

European Input Output European Input Output TableTable

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

Australia’s Input Output TablesAustralia’s Input Output Tables

The Australian IO Tables provide detailed information about The Australian IO Tables provide detailed information about the supply and use of products in the Australian economy the supply and use of products in the Australian economy and about the structure of and inter-relationships between and about the structure of and inter-relationships between Australian industries. Australian industries.

With the release of the 2005-2006 Tables Australia has With the release of the 2005-2006 Tables Australia has completed 21 input-output tables with the first set of tables completed 21 input-output tables with the first set of tables produced for 1958-59. The ABS now produces the IO tables produced for 1958-59. The ABS now produces the IO tables on an annual basis with a release date approximately three on an annual basis with a release date approximately three years after the reference period. years after the reference period.

The 2006-07 IO tables for Australia were released in The 2006-07 IO tables for Australia were released in November 2010 and will be the first set of tables to November 2010 and will be the first set of tables to incorporate changes to the System of National Accounts incorporate changes to the System of National Accounts (SNA08) and a new industry classification (ANZSIC06).(SNA08) and a new industry classification (ANZSIC06).

Input-Output Analysis for the Input-Output Analysis for the BRICsBRICs

In recent years, India has attracted attentions together In recent years, India has attracted attentions together with Brazil, China and Russia as one of the newly with Brazil, China and Russia as one of the newly emerging market economies called the “BRICs”. emerging market economies called the “BRICs”.

BRIC is an acronym that refers to the economies of Brazil, BRIC is an acronym that refers to the economies of Brazil, Russia, India, and China, which are seen as major Russia, India, and China, which are seen as major developing economies in the world. The general developing economies in the world. The general consensus is that the term was first prominently used in a consensus is that the term was first prominently used in a Goldman Sachs report during 2003, which speculated that Goldman Sachs report during 2003, which speculated that by 2050 these four economies would be wealthier than by 2050 these four economies would be wealthier than most of the current major economic powers. The BRIC most of the current major economic powers. The BRIC countries are now responsible for approximately 18% of countries are now responsible for approximately 18% of the world's Gross Domestic Product and home to 40% of the world's Gross Domestic Product and home to 40% of the earth's population.the earth's population.

India’s Input Output India’s Input Output TablesTables

The compilation of I-O tables in India was started in the The compilation of I-O tables in India was started in the early 1950’s. early 1950’s.

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

China’s Input Output China’s Input Output TableTable

In China, Input-output tables were published every 5 In China, Input-output tables were published every 5 years. Extended tables were published in the middle of years. Extended tables were published in the middle of every 5 years. The complete Input-output tables of China every 5 years. The complete Input-output tables of China (tables of 1987, 1990, 1992, 1995, and 1997). (tables of 1987, 1990, 1992, 1995, and 1997).

The source of the current input-output (I-O) table for China The source of the current input-output (I-O) table for China is the Input-Output Table of China 2002 from the is the Input-Output Table of China 2002 from the Department of National Economy Accounting, State Department of National Economy Accounting, State Statistical Bureau (SSB). The original 2002 table in China Statistical Bureau (SSB). The original 2002 table in China includes 122 sectors, of which there are 5 sectors for includes 122 sectors, of which there are 5 sectors for agriculture, 81 sectors for manufacture, and 36 sectors for agriculture, 81 sectors for manufacture, and 36 sectors for services. services.

Brazil’s Input Output Brazil’s Input Output TableTable

In the view of constructing I-O tables, Brazil is relatively young in its In the view of constructing I-O tables, Brazil is relatively young in its experience compared to other countries of the similar development experience compared to other countries of the similar development stage. Only after the 1970s, the Brazilian Institute of Geography and stage. Only after the 1970s, the Brazilian Institute of Geography and Statistics (IBGE) took its leading role to construct input-output Statistics (IBGE) took its leading role to construct input-output accounts. accounts.

However, the Brazilian I-O table developed very rapidly from its However, the Brazilian I-O table developed very rapidly from its outset, and it is now considered to be one of the most advanced 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 statistical series in terms of the data availability, speed of release, and conformity with the international standards. The official (symmetrical) conformity with the international standards. The official (symmetrical) I-O tables of Brazil, together with supply and use tables, are available 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, 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 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 about supply and use tables at purchaser prices can be found in the national accounts.national accounts.

Russia’s Input Output TableRussia’s Input Output Table

The work on compilation of IO tables in the Soviet Union started in the 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 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 Central Statistics Office for 83 industries in monetary form and for 157 commodities in physical form. Further, the IO table for the year 1966 commodities in physical form. Further, the IO table for the year 1966 was produced (110 industries and 237 commodities), and the one for was produced (110 industries and 237 commodities), and the one for the year 1972 (112 industries and 247 commodities). Later, the the year 1972 (112 industries and 247 commodities). Later, the following tables were produced: the five-yearly IO tables for 1977, following tables were produced: the five-yearly IO tables for 1977, 1982, 1987. The detailed IO tables served as a base for annual IO 1982, 1987. The detailed IO tables served as a base for annual IO tables with 18 aggregate sectors.tables with 18 aggregate sectors.

Since 1993 the National Statistics Office has accepted the System of Since 1993 the National Statistics Office has accepted the System of National Accounts. The first IO table for the national economy under National Accounts. The first IO table for the national economy under this framework was compiled for the year 1995. So far, the annual IO 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 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 the year 2003 is compiled for 22 aggregate sectors. The IO tables for Russia now become available on average around 3 years after the for Russia now become available on average around 3 years after the reference period.reference period.

Input-Output Analysis in MexicoInput-Output Analysis in Mexico

The input-output matrix represents an indispensable tool in The input-output matrix represents an indispensable tool in Mexico and the INEGI Institute develops input output Mexico and the INEGI Institute develops input output projects through the System of National Accounts of projects through the System of National Accounts of Mexico, since it represents the starting point and frame of Mexico, since it represents the starting point and frame of reference of the products obtained. reference of the products obtained.

It reflects and updates the formal relationships that carry It reflects and updates the formal relationships that carry out the various sectors and economic agents involved in all out the various sectors and economic agents involved in all phases of the cycle (production, consumption and phases of the cycle (production, consumption and accumulation), and also provides detailed logs that serve accumulation), and also provides detailed logs that serve basis for modifying the base years of the calculations are basis for modifying the base years of the calculations are carried out.carried out.

Input-Output Analysis in MexicoInput-Output Analysis in MexicoMexico has six input-output matrices referring to the years Mexico has six input-output matrices referring to the years 1950, 1960, 1970, 1975, 1978 and 1980. Also, for this last 1950, 1960, 1970, 1975, 1978 and 1980. Also, for this last year, Mexico has a matrix for the agriculture and forestry year, Mexico has a matrix for the agriculture and forestry sector. In regards to the matrices of 1950 and 1960, they sector. In regards to the matrices of 1950 and 1960, they were developed by the Bank of Mexico and were allowed to were 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 of while the following matrices were made by the Department of Statistics (DGE) of National Institute of Statistics, Geography Statistics (DGE) of National Institute of Statistics, Geography and Informatics (INEGI). and Informatics (INEGI).

The matrix of 1970, which was first developed by the DGE, The matrix of 1970, which was first developed by the DGE, introduced substantial improvements in relation to the introduced substantial improvements in relation to the previous ones, in both the conceptual framework and data previous ones, in both the conceptual framework and data processing, and the level of detail of the matrix. It also processing, and the level of detail of the matrix. It also established the methodological basis for the development of established the methodological basis for the development of further matrices prepared in Mexico. The matrices for 1975 further matrices prepared in Mexico. The matrices for 1975 and 1978 were part of an upgrade of 1970, while the matrix of and 1978 were part of an upgrade of 1970, while the matrix of 1980 introduced innovative features in relation to the 1980 introduced innovative features in relation to the preceding matrix.preceding matrix.


The input-output matrices in Mexico are considered as The input-output matrices in Mexico are considered as pictures of intersectoral transactions valued at producer pictures of intersectoral transactions valued at producer prices, in millions of pesos, from which other tables are prices, in millions of pesos, from which other tables are derived. The technical coefficients, direct and indirect derived. The technical coefficients, direct and indirect requirements and import matrices, in millions of dollars, requirements and import matrices, in millions of dollars, with corresponding technical coefficients. The breakdown with corresponding technical coefficients. The breakdown that occurs with different matrices corresponds to 32 that occurs with different matrices corresponds to 32 sectors in 1950 and 45 sectors in 1960. Since 1970, the sectors in 1950 and 45 sectors in 1960. Since 1970, the breakdown is expanded to 73 branches of economic breakdown is expanded to 73 branches of economic activity. activity.

The matrices follow the International Standard Industrial The matrices follow the International Standard Industrial Classification (ISIC) of all Economic Activities, Series M Classification (ISIC) of all Economic Activities, Series M prepared by the United Nations Organization (UN) and the prepared by the United Nations Organization (UN) and the Mexican Classification of Activities and Products (CMAP) in Mexican Classification of Activities and Products (CMAP) in 1994. 1994.


The estimates of the components of final demand were based on the The estimates of the components of final demand were based on the income-expenditure surveys of households, government administrative income-expenditure surveys of households, government administrative records, the balance of payments and specific research in the area, records, the balance of payments and specific research in the area, which have enabled the estimation of private consumption, government which have enabled the estimation of private consumption, government consumption, gross capital formation and exports. Special mention consumption, gross capital formation and exports. Special mention should be made for the use of the data presented in the current 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 account of the balance of payments, as well as allowing estimates for exports that make possible to construct the arrays of imports.exports that make possible to construct the arrays of imports.

At the regional and state levels, several input output matrices have At the regional and state levels, several input output matrices have been constructed in recent years by universities and research centers been constructed in recent years by universities and research centers in Mexico. The results of input-output matrices are used especially as a 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 basis for structural studies of the economy and for analyses of the direct and indirect impact of changes in demand, prices and wages on 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 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 basis that can flexibly be used for model and simulation calculations as well as forecasts. well as forecasts.

ConclusionsConclusionsThe input output (IO) model gives an overview of the structure of an 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 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 useful in viewing the world economy as an integrated system. The input output method is now being used as a basic analytical tool by input output method is now being used as a basic analytical tool by government agencies in a large number of countries around the government agencies in a large number of countries around the world. world.

The structure of the input output model has been incorporated into The structure of the input output model has been incorporated into national accounting in many developed and developing countries, and national accounting in many developed and developing countries, and as such forms an important part of measures such as GDP. as such forms an important part of measures such as GDP.

In addition to studying the structure of national economies, input In addition to studying the structure of national economies, input output economics has been used to study regional economies within output 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 the Indeed a main use of input-output analysis is for measuring the economic impacts of events and projects as well as public economic impacts of events and projects as well as public investments or economic programs. Input output models are also investments or economic programs. Input output models are also used to identify economically related industry clusters and key used to identify economically related industry clusters and key industries that are most likely to enhance the internal structure of a industries that are most likely to enhance the internal structure of a specified economy. specified economy.

INFORUM ModelsINFORUM Models

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

The input output equation model system is the following: The input output equation model system is the following:

Z = B(I - A)-1Y is the common equation system of input-output Z = B(I - A)-1Y is the common equation system of input-output analysis.analysis.

wherewhere

B = matrix of input coefficients for specific variable in economic B = 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 requirements Z = 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 under Matrix 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 goods The diagonal matrix Y denotes exogenous final demand for goods and services. and services.

The matrix Z incorporates the results for the direct and indirect The matrix Z incorporates the results for the direct and indirect requirements (intermediates, labor, capital, energy) or joint products requirements (intermediates, labor, capital, energy) or joint products (emissions) for the produced goods and services. (emissions) for the produced goods and services.

The Model of Dynamic Input-Output Analysis.The Model of Dynamic Input-Output Analysis.

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

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 for X = 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 the This 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.

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 the 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.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 same bivariate 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 typical 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 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 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 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 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. 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 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 inputs 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 to The 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 mathematical However, many economists view the RAS procedure as a purely mathematical procedure hardly capable of tracing the complex phenomenon of technological procedure hardly capable of tracing the complex phenomenon of technological change.change.

INPUT OUTPUT INTERNATIONAL CONFERENCESINPUT OUTPUT INTERNATIONAL CONFERENCES

The first international Input Output conference met in Driebergen, Holland The first international Input Output conference met in Driebergen, Holland in 1951, it brought together economists interested in the theoretical, the in 1951, it brought together economists interested in the theoretical, the statistical, and the computational problems of interindustry analysis.statistical, and the computational problems of interindustry analysis.

A second conference was held between June 27 and July 10, 1954, at A second conference was held between June 27 and July 10, 1954, at Varenna, Italy. Varenna, Italy.

A third international conference was held in September 1961 in Geneva. A third international conference was held in September 1961 in Geneva. Economists and statisticians from more than 41 different countries Economists and statisticians from more than 41 different countries participated in this conference. For the first time, representatives of the participated in this conference. For the first time, representatives of the Soviet Union and of other socialist countries, as well as planners from Soviet Union and of other socialist countries, as well as planners from underdeveloped countries, participated in the international input-output underdeveloped countries, participated in the international input-output conference.conference.

““Input Output Economics: Empirical Applications in Mexico Input Output Economics: Empirical Applications in Mexico and International Experience in the Development of Input and International Experience in the Development of Input Output AnalysisOutput Analysis""

Dr. Alejandro Díaz-BautistaDr. Alejandro Díaz-BautistaCatedrático y Profesor Investigador en Catedrático y Profesor Investigador en Economía, ColefEconomía, Colef

Professor of Economics at Colef Professor of Economics at Colef

[email protected]

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

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Professor Alejandro Diaz Bautista, Input Output Conference, June 2012