Input-Output Economics Essay

This essay has a total of 7416 words and 43 pages.

Input-Output Economics

Table of Contents
I Aim of the study/paper
II Introduction
III The Beginning of Input-Output Economics
IV The Leontief Paradox
V The Input-Output Model Today
VI Calculation of the Input-Output Table Multipliers
VII Computer Program for the Inverse of a Matrix
VIII Regional Input-Output Analysis
VIIII The Use of Input-Output Analysis with Regard to the Environment
IX Conclusion
X Bibliography


List of Illustrative Material

I Input-Output Table for the US Economy in 1947
II Table: Labour and Capital needed to reduce exports and increase i
mport substitutes by $1 million in the United States in 1947
III Transaction Table
IV Direct Requirements Table
V Total Requirements Table
VI Output, Income and Employment Measures from Input-Output Analysis, an example
VII Example Questionnaire used in the Survey Approach to Input-Output Analysis


Abstract
The aim of this study, and thereby this paper, is to discover the field of input-output
economics as an integral component of the wider trade theory.


We start therefore, with an introduction to the discipline, its history and its place
today within the global economic context.


We move on to explain in detail the calculation of an input-output table as it is used for
the total output calculations of a national as well as a regional economy. The concept of
the multiplier will also be discussed here.


To conclude, we will present an example of the application of input- output economics to a
specific, current issue namely, the environment.



An Introduction
The wider discipline of trade theory within which we find the field of input-output
economics consists of four broader areas. Input-output economics, based on the
Heckscher-Ohlin theory and defined by the findings of Wassily Leontief forms the biggest
most well known part. However, there are other areas which deserve to be mentioned in
order to round out the discussion. These other areas are the Ricardian model of
comparative advantage, Posner's technological-gap theory and Vernon's product life-cycle
theory.


The Ricardian model, which is the next most important model to that on which input-output
economics is based, will be described in some depth for the sake of comparison and to give
an alternative insight into the discipline of trade theory.


The Ricardian model then, suggests that labour costs will be the determinant of trade: the
country with the lower labour cost in the production of a good will be the exporter of
that commodity. This theory was tested in 1952 by MacDougall who used data on 25 products
from 1937 to compare labour productivity and exports for the United States and Great
Britain. In this way, MacDougall tested whether their relative exports to third countries
were connected with their labour productivities. The results which MacDougall found were
inconsistent with the simple Ricardian model. However, they are generally interpreted as
supporting a more general "Ricardian" argument that differences in relative labour
productivities are the determinant of comparative advantage. As long as these differences
are due to technology, the model exists as an alternative to the model described
previously.


MacDougall found that wage rates in the manufacturing sector were roughly twice as high in
the United States as in Britain. Therefore, the United States should be the dominant
exporter in markets where her labour productivity was more than twice as high as in
Britain. Britain, on the other hand, should be the dominant supplier in any line of
production where her labour productivity was more than 50% of the American. Whenever
labour productivity in US industry was twice that of its British counterpart, we should
expect export shares of the two countries to be roughly equal in third markets.


In most cases, the ratio of US to British exports was higher whenever her ratio of labour
productivity was higher. However the dividing line between British and US exporters in
third markets was not where American productivity was twice as high as in Britain. In
these markets, Britain still had a comparative advantage. The American markets needed a
productivity advantage of roughly 2.4 to be even with the British in third markets. The
basic explanation MacDougall suggested for this phenomenon was that imperial preferences
and other tariff advantages that were enjoyed by countries which were close to her
politically could be possible explanations for the advantage that Britain at the time
enjoyed in her export markets. Other reasons put forward were that Britain had been the
pioneering industrial nation and that her dominance in international finance and her
commercial reputation still gave her certain advantages which were difficult to measure
but which were still important.1



The Beginning of Input-Output Economics
Although the French economist Francois Quesney had formulated a "tableau economique" in
1958 which depicted the workings of a farm and Leon Walras and other classical economists
formulated general equilibrium models of the economy, none could employ their findings to
the solution of problems. Therefore, the beginnings of the discipline of input-output
economics are most often referred to as a 1951 paper written by Wassily Leontief.


In this paper, Leontief made a relatively simple point. The boom time after the second
world war had brought with it an indigestible amount of facts. To this Leontief said "we
have in economics today a high concentration of theory without fact on the one hand, and a
mounting accumulation of fact without theory on the other"2 . He went on to state that the
collusion of the two was the most important task at hand for economists of the day. He
made this collusion possible through the analytical method which he called interindustry
or input-output analysis.


Leontief's findings were revolutionary in many ways, however most importantly because they
cast doubt on the Heckscher-Ohlin theory. Under the Heckscher-Ohlin theory, "productive
factors are assumed to move from areas of low remuneration to areas of high remuneration,
lowering their supply in the first region and raising it in the latter. The workings of
the market then raise the earnings of the migrating factor in the land of departure and
lower it in the land of arrival, thus tending to equalize factor rewards the world over"3
. The doubt which was cast over this theory became known as the Leontief Paradox.



The Leontief Paradox
Leontief argued that the Heckscher-Ohlin theory predicts that a country will tend to
export those commodities which use its abundant factor of production intensively and
import those which use its scarce factor intensively. However, when taking a
representative basket of American exports, he discovered that they embodied more labour
and less capital than a representative basket of American imports.


Leontief presented the first working model of input-output economics on the US economy in
1919. for this, he constructed a 46 x 46 sector table. Each sector having both a vertical
and a horizontal column. In 1932 the third table for the US economy was constructed with
the use of a computer. It comprised only 42 sectors but required 56 computer hours to do
the necessary computations.


This 42 sector model is depicted on the following pages. This is a national model which
today has 512 sectors. This type of national model is the most advanced form of the
input-output model. Generally, however, the type of input-output approach which will be
described further on in this writing is adapted to regions. These regional input-output
tables describe how regional industries interact with each other and with the outside
world, through imports and exports.


There was no doubt that the United States was the country most highly endowed with capital
in 1947, so according to the Heckscher-Ohlin theory, it should have been exporting
capital-intensive products and importing labour intensive goods. In constructing his
table, Leontief was unable to obtain information on the factor intensity of the actual
imports to the United States.


However, the Heckscher-Ohlin theory predicts that under free trade and with consequent
factor-price equalization, the capital-labour ratio in US import competing goods should be
the same as in its imports. Leontief was able to obtain information on the capital-labour
ratio in US import-competing goods. He went on to estimate the consequences for the use of
factors of production of the United States decreasing its exports and increasing its
import substitutes by US$1 million. He took only two factors explicitly into account,
capital and labour. When exports are decrease, both capital and labour are released. When
production of import-competing goods is increased, both more labour and capital are
needed. According to Leontief's hypothesis, we would expect relatively more capital to be
released from the export industries and relatively more labour to be needed by the
import-competing industries . 4



Capital and labour needed to reduce exports and increase import-substitutes by $1 million
in the United States in 1947. 5


Exports Import-substitutes
Capital ($,000 at 1947 prices) 2,551 3,091
Labour (men years) 182 170
Capital-Labour ratio 13.99 18.18

In 1947, the United States was exporting labour-intensive goods. Therefore, how can this
paradox possibly be explained ? Several proposals have been put forward. The following is
a summary of these proposals.


1. Buchanan argued that Leontief's capital coefficients were "investment requirement
coefficients" which did not take into account the durability of capital.


2. Loeb argued that the differences in capital-intensity between the export sector and the
import-competing sector were not statistically significant.


3. Swerling argued that 1947 was an atypical year.

4. Leamer argued that the Leotief paradox is the consequence of an incorrect
interpretation of the Heckscher-Ohlin theory when trade is not balanced. That is, when a
capital rich country is experiencing unbalanced trade then we cannot conclude from the
Heckscher-Ohlin model that its exports will be relatively capital-intensive. He
demonstrated that when a country has a trade surplus (as was the case of the United States
in 1947) the appropriate test is to compare the capital-labour ratio in either the
country's net exports or its production with the capital-labour ratio in the country's
consumption. Using these tests, there was no evidence of the Leontief paradox on US trade
in 1947.


5. Labour must be differentiated by level of skill. It was argued that American skill
could not really be compared with labour in other countries, because the productivity of
the American worker was substantially higher. Several tests were carried out to prove
this, however, the paradox that the US was importing capital-intensive goods continued to
prevail.


6. Vanek found that over the period 1870-1955, the United States became a net importer of
goods that were intensive in natural resources (products of the extractive industries such
as agriculture and mining). He also found that natural resources and capital were
complementary inputs, and argued that the finding that the United States imported
labour-intensive goods in fact reflected their imports of goods that were intensive in
their use of natural resources. If natural resources were taken into account, a solution
might be found. Subsequently, it has been proven that the Leotief paradox disappears when
resource-based industries are excluded when the Heckscher-Ohlin theory is being tested.



The input-output model today.
Today, sound economic development decisions require information about the impacts of
economic growth and/or decline and the relative benefits and costs of alternative
development strategies. So, typical issues confronted by the economist using the
input-output model would be: what will be the impact of a manufacturing plant closure or
what resources does the community have to offer to potential industries seeking a plant
location ? 6


The fundamental underlying relationship of input-output analysis is that the amount of a
product (good or service) produced by a given sector in the economy is determined by the
amount of that product that is purchased by all the users of the product, has not changed
since Leotief. However, today input-output analysis has become important to all the
highly-industrialized countries in economic planning and decision making because of this
flow of goods and services that it traces through and between different industries.
Input-output tables are capable of simulating almost any conceivable economic impact.


Economists using input-output analysis today generally adopt an eclectic approach. They
classify the goods in the tables into three classes which broadly match the three fields
of trade theory outlined above.


1. Heckscher-Ohlin goods, which have generally known and relatively stable technologies,
with comparative advantage resting largely on factor endowments, and which are not tied
down to the availability of specific factors. Textiles are often stated as typical
Heckscher-Ohlin goods. Comparative advantage may shift around among countries in response
to changes in factor prices and factor availabilities, so that the so-called
³foot-loose² industries would come in this group.


2. Technological goods for which the production process is sophisticated and subject to
frequent change, with the most recent technology probably specific to certain countries,
and with proximity to large high- income markets an important factor. Computers and
pharmaceutical products are examples of such goods. It is argued that the countries which
have, and will keep, the comparative advantage in this group are the most developed
nations.


3. Ricardo goods, where comparative advantage depends largely on production conditions.
These usually include extraction industries (agriculture, mining as mentioned previously)
and industries which carry out the processing of raw materials. Comparative advantage here
may lie with the developing countries. 7


The ensuing relationships of goods between industries reflect the state of technology of a
particular region. Technology then is an essential feature of the input-output analysis.
The investigation seeks to determine what can be produced, and quantity of each
intermediate product which must be used up in the production process, given the quantities
of available resources and the state of technology. 8 Growth in a particular industry may
be induced by growth in others and input-output methods allow the effects of such
interlinkages to be unraveled and the components of growth to be identified consistently.
9


One of the interests in the field of input-output economics lies with the fact that it is
very concrete in its use of empirical data and also very compact. All changes in the
endogenous sectors of an input-output table are results of changes in the exogenous
sectors.


In the static model, one deals solely with the production or "current account side" of an
economy which provides a sound example of the compactness of the model. However,
investment or capital account activities are not included. These are then generally
included in final demand rather than in the part of the input-output matrix representing
flows between individual industries. This then becomes a serious limitation of the static
model because the changes in the structure of an industry's capital stock, and the changes
in its pattern of capital equipment sourcing, are one of the most important manifestations
of technological change and may have a direct impact on its output growth.


Economies are dynamic so it may be argued that dynamic input- output models should be used
because after all, input-output tables give the stance at a particular point in time,
which will be outdated extremely quickly. However, they are much less efficient and are
generally passed over in favour of the static model.


Further in this discussion, we will outline the process of defining the matrices involved
in an analysis of the static type. The types of matrices shown may then be used to attain
goals such as increasing employment within a region, or to compare output figures of one
economy to another.


Input-output tables have three advantages that make them particularly well suited to analysing structural change.

1. The data are usually comprehensive and consistent. By their nature, input-output tables
encompass all the formal market place activity that occurs in an economy, including the
service sector which is frequently poorly represented. For some countries, over a hundred
different data sources are used to ensure the completeness and internal consistency of the
data, making it probably the single most comprehensive and complete source for economic
data for most countries. Consequently, input-output tables frequently play a fundamental
role in the construction of the national accounts. This role means that the data are
thoroughly checked for their accuracy, and that the tables are intrinsically linked with
many of the traditional indicators of economic performance such as production and GNP.


2. The nature of input-output analysis makes it possible to analyse the economy as an
interconnected system of industries that directly and indirectly affect one another,
tracing structural changes back through industrial interconnections. This is especially
important as production processes become increasingly complex, requiring the interaction
of many different businesses at the various stages of a product's processing. Input-output
techniques trace these linkages from the raw material stage to the sale of the product as
a final, finished good. This allows the decomposition analysis to account for the fact
that a decline in domestic demand for autos not only affects the auto industry, but also
its suppliers like the steel industry and the steel suppliers like the coal industry and
so on. In analysing an economy's reaction to changes in the economic environment, the
ability to capture the indirect effects of a change is a unique strength of input-output
analysis.


3. The design of input-output tables allows a decomposition of structural change which
identifies the sources of change as well as the direction and magnitude of change. Most
importantly, an input- output based analysis of structural change allows the introduction
of a variable which describes changes in producer's recipes - that is, the way in which
industries are linked to one another, in input-output language, called the "technology" of
the economy. It enables changes in output to be linked with underlying changes in factors
such as exports, imports, domestic final demand as well as technology. This permits a
consistent estimation of the relative importance of these factors in generating output and
employment growth. In a general sense, the input-output technique allows insight into how
macroeconomic phenomena such as shifts in trade or changes in domestic demand correspond
to microeconomic changes as industries respond to changing economic conditions.


Although the field is widely practiced today, problems such as those Leontief encountered,
still exist. The limitations of the input-output approach, according to the OECD document,
Structural Change and Industrial Performance are:


1. The basic input-output analysis assumes constant returns to scale. The input-output
model assumes that the same relative mix of inputs will be used by an industry to create
output regardless of quantity.


2. Each industry is assumed to produce only one type of product. For example, the
automobile industry produces only cars. The distribution and sale of this product is
fixed.


3. Each product within the industry is assumed to be the same. Also, there is no
substitution between inputs. The output of each sector is produced with a unique set of
inputs.


4. Technical coefficients are assumed to be fixed: that is, the amount of each input
necessary to produce one unit of each output is constant. The amount of input purchased by
a sector is determined solely on the level of output. No consideration is made to price
effects, changing technology or economies of scale.


5. It is assumed that there are no constraints on resources. Supply is infinite and perfectly elastic.

6. It is assumed that all local resources are efficiently employed. There is l no underemployment of resources.

. 7. Timeliness of input-output data. There is a long time lag between the collection of
data and the availability of the input-output tables. The sporadic nature of input-output
tables means that continuous time series are impossible to construct without estimating
input-output tables for the years between benchmarks. In effect, input-output tables
provide a snapshot of the complete economy and all of its industrial interconnections at
one time.



Calculation of the input-output table
As will become clear, input-output analysis emphasizes general equilibrium phenomena. It
seeks to take account of production plans and activities of many industries which
constitute an economy. This interdependence arises out of the fact that each industry
employs the outputs of other industries as its raw material. Its output, in turn, is used
by other industries as a productive factor.


Each row of the input-output table shows, in detail, the receipts of an industry from
other sectors of the economy (ref: Leontief's tables on p 7-8). This table is known as the
transactions table. As we move across the table, we move from the sales to processing
sectors and shipments to the final far right hand cell of final demand sectors such as
consumers, investors, governments or foreign countries. It is assumed that this flow
across the sectors is a fixed and constant proportion of the amount of the product being
produced. Input-output tables used in practice are generally constructed in dollar terms.
However, in theory they can be expressed in any physical unity. The first step of this
calculation will allow the user to convert the dollar values into technical coefficients
in order to come up with the total final output for each industry.


The following is a step-by-step analysis of the processes involved in the calculations of the input-output economist.


Step One
Just as Leontief did for the first time in 1919, the first step in the input-output
analysis process is to systematically define all the transactions of each industry in the
economy. In order to do this, a transactions table is required. The transaction table
which will form the basis of these calculations is shown below.


Purchasing Sector Final Demand10
From Into Agriculture Manfct Trade Service Househ Other Total Output
Agriculture 202 182 10 47 100 200 741
Manufacturing 34 68 2 26 39 298 467
Trade 47 35 991 440 1200 66 2779
Service 86 59 565 510 1500 313 3033
Households 200 40 205 1250 200 1494 3389
Imports 172 83 1006 760 350 1053 3424
Total 741 467 2779 3033 3389 3424


Reading down, the entries typically show first the purchases from other sectors of goods
and services required by an industry to carry on its activities. With some minor
adjustments, the GNP from the product side can be compiled from these right hand final
demand sectors.11



Step Two
The direct requirements table follows from the transactions table. There is however, some
confusion in the title of direct requirements because this table deals solely with local
inputs, imported goods are not represented. Nonetheless, rather than showing actual dollar
transactions, this table shows, for the sector named at the top, what fraction of total
expenditures was made to purchase inputs (what was required) from the sector named at the
left. The technical co-efficients are found by the simple formula:



aij = xij / xj
where, the quantity of the output of sector i absorbed by sector j per unit of its total
output j is described by the symbol aij and is called the input co-efficient of product of
sector i into sector j.12 The technical coefficients allow us the determine how large the
annual outputs of each sector must be in order to "satisfy not only given direct demand by
the final users, the households, but also the intermediate demand depending in its turn on
the total level of output in each of the two productive sectors.


Using the following direct requirements table, we can follow the steps and determine a
technology matrix which will enable us to find out the final output required by each
industry to meet both internal and final demands.



Purchasing Sectors13
FromInto Agriculture Manufacturing Trade Service Households
Agriculture 0.27 0.39 0 0.02 0.03
Manufacturing 0.05 0.15 0 0.01 0.01
Trade 0.06 0.07 0.36 0.15 0.35
Continues for 22 more pages >>




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