INPUT OUTPUT ANALYSIS II

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INPUT OUTPUT ANALYSIS II

• Wednesday, January 25

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Industry Sector Flow Diagram
Steel
Natural Gas
Electric Power
Metal pipes
Cement
Water
Plumbing
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Relationships Between All Industry Sectors
Steel
Natural Gas
Electric Power
Metal pipes
Cement
Water
Plumbing
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Input-Output Matrix
A matrix is a table with rows and columns. In an
IO matrix, each column represents a single
industry sector. Each row represents a single
industry sector. A column shows the amount of
each input that is used by a single sector. A
row shows the amount of input a single sector
provides to all the other sectors.
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Example of an IO Matrix
Outputs
Inputs
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Relationships in an IO Matrix
Outputs
Inputs
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Industry Sector Flow Diagram
Steel
Natural Gas
Electric Power
Metal pipes
Cement
Water
Plumbing
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Quantitative Relationships in an IO Matrix
Outputs
Inputs
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Relationships Between All Industry Sectors
Steel
Natural Gas
Electric Power
Metal pipes
Cement
Water
Plumbing
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More Complex IO Matrix
Outputs
Inputs
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Deriving Cell Entries for the Direct Requirements
Table
The cell entries are obtained by dividing the
total sales of inputs (from rows) by the total
sales of outputs (from columns). The next three
slides show these calculations for a hypothetical
example.
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Deriving Cell Entries for the Direct Requirements
Table
Outputs
Inputs
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Divide Inputs by Total Output
Outputs
Inputs
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Calculate Input-Output Direct Requirement
Coefficients (in dollars)
Outputs
Inputs
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Direct Requirement Matrix

• An entry Aij, at the intersection of the ith row
  and jth column shows the value of input i
  required directly to produce 1 worth of output
  of sector j
• Available at 8585 sector detail or at 500500
  detail

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Total requirement matrix

• What is the total output of different sectors
  needed to meet a new electricity demand of 1?
• Consider the simple two sector direct requirement
  matrix
• Electricity Water
• Electricity 0.333 0.167
• Water 0.286 0.375

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1 Electricity
Direct Requirement
0.333 Electricity 0.286 Water
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1 Electricity
Direct Requirement
0.333 Electricity 0.286 Water
0.3330.333Elec. 0.3330.286 Water
0.2860.167Elec. 0.2860.375 Water
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1 Electricity
Direct Requirement
0.333 Electricity 0.286 Water
0.3330.333Elec. 0.3330.286 Water
0.2860.167Elec. 0.2860.375 Water
Total Elec. 1 0.333 (0.3330.333
0.2860.167) 1.694
Total Water 0.286 (0.3330.286
0.2860.375) 0.778
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1 Water
Direct Requirement
0.167 Electricity 0.375 Water
0.1670.333Elec. 0.1670.286 Water
0.3750.167Elec. 0.3750.375 Water
Total Electricity 0.167 (0.1670.333
0.3750.167) 0.452
Total Water 1 0.375 (0.1670.286
0.3750.375) 1.807
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Algebraic Method

• Total output new final demand intermediate
  demand
• Let X1 be total output of electricity
• Let X2 be total output of water
• Let Y1 and Y2 be changes in final demand for
  electricity and water respectively

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Algebraic Method

• X1Y10.333X10.167X2
• X2Y20.286X10.375X2
• Now what are X1 and X2 if
• Y11 a 1 change in final demand of
  electricity? and
• Y20

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Algebraic Method solve for X1

• X1Y10.333X10.167X2
• X2Y20.286X10.375X2
• X110.333X10.167X2
• X20.286X10.375X2

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Algebraic Method solve for X1

• X110.333X10.167X2
• X20.286X10.375X2
• X110.333X10.167(0.286X10.375X2)
• X11.333X1.048X1.063X2
• X1-.333X1-.048X1 1.063X2
• .619X11.063X2
• X1(1.063X2)/.619

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Algebraic Method

• X2 .286X1 .375X2
• X2 .286(1.063X2)/.619.375X2
• X2.286.018X2/.619 .375X2
• X2.286/.619 .018X2/.619 .375X2
• X2-.029X2-.375X2.462
• .596X2.462
• X2.775
• X1(1.063.775)/.619
• X11.694

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Algebraic Method

• X11.694, X20.775
• These represent total requirements to meet 1 new
  electricity demand
• Similarly, we can solve when Y10, Y21 (to meet
  1 increased final demand of water)
• 0.452 electricity
• 1.807 water

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A Total Requirements Table (in dollars)
Direct Requirements Matrix
Total Requirements Matrix
Outputs
Outputs
Inputs
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Total Requirements matrix

• An entry Lij, at the intersection of the ith row
  and jth column shows the value of input i
  required directly and indirectly to meet a final
  demand for 1 worth of output of sector j

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Three Sector Model (again)
Outputs
Inputs
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Three sector Model

• X1, X2, X3 are outputs of steel, electricity and
  water
• Y1,Y2,Y3 are new final demands for steel,
  electricity and water
• X1 Y1 0.387X1 0.381X2 0.458X3
• X2Y2 0.322X1 0.333X2 0.167X3
• X3 Y3 0.290X1 0.286X2 0.375X3

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Multiplier (Ripple) Effects (in dollars)
Outputs
Inputs
Total Requirements Matrix
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Multiplier (Ripple) Effects

• When total direct and indirect effects are
  considered, one dollar increase in the final
  demand for a industry output results in an
  increase of more than a dollar in the total
  output of the economy. This is called the
  multiplier effect. The quantitative estimate is
  the sector multiplier.

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U.S. IO Tables
The U.S. Bureau of Economic Analysis (BEA)
calculates total requirements tables for the U.S.
using the industrial sector codes described in
the chapter on industry sectors. This is done
once every five years. http//www.bea.doc.gov/bea/
an/1297io/tab4-1.htm
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Using IO Tables

• IO tables for an economy can be used to estimate
  the direct and indirect impacts on all industry
  sectors of an increase or decrease in demand in a
  single sector. Both businesses and government
  use them for this purpose.
• IO tables can also be used to describe the
  complex interrelationships of industry sectors.
  For example, a business can see which sectors it
  relies on the most, both directly and indirectly.

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Further uses

• If you calculate direct employment per output,
  total requirement matrix can be used to estimate
  economy-wide direct and indirect employment
  impacts
• If you calculate emissions per output, total
  requirement matrix can be used to estimate
  economy-wide direct and indirect emission impacts