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I/O MULTIPLIERS

(http://faculty.washington.edu/krumme/systems/multp.html)


Supporting Pages:

Gross Output
Multiplier
Income Coefficient
(Type A & B Multipliers)
Income Multiplier
Type I & II Multipliers
Direct & Indirect Effects
Type I and Type A Multipliers
Mjx =
n
S
i=1
bij
MjA =
n
S
i=1
vibij
MjI =
n
S
i=1
vibij
---
vj
Direct, Indirect & Induced Effects
Type II and Type B Multipliers
M'jx =
n
S
i=1
b'ij
MjB =
n+1
S
i=1
vib'ij
MjII =
n+1
S
i=1
vib'ij
---
vj


Employment Multiplier
Direct & Indirect Effects
Type I Multiplier
ME =
n
S
i=1
eibij
---
ej
Direct, Indirect & Induced Effects
Type II Multiplier
M'E =
n+1
S
i=1
eib'ij
---
ej


M = Multiplier

bij = Leontief coefficient identifying the direct and indirect (inter-industry) effects on the demand for the output of industry i as a result of changes in the demand (and thereby the input requirements) of industry j.

b'ij = Leontief coefficient identifying the direct, indirect (inter-industry) and induced (by household expenditures) effects on the demand for the output of industry i as a result of changes in the demand (and thereby the input requirements) of industry j.

vi or j = value added (mainly including labor incomes) of industry i (or j) per $1 of total inputs (or output/sales) of that industry. Often used as the quasi labor coefficient in the direct coefficient table.

i = the supplying industry

j = the receiving industry

e = Employment per $1 of total inputs or output/sales


Misunderstandings, Misconceptions, Caveats, and Limitations of Multipliers:

  1. "Large multipliers" are NOT the same as "large multiplier impacts". The impacts or effects depend on BOTH the size of the multiplier and the magnitude of the "exogenous" stimulus by which the multiplier is multiplied. Thus, given multiplier effects can be alternatively the result of
    1. large multipliers associated with minimal "exports" or
    2. small multipliers and substantial exports.

  2. Multipliers can be expressed in many different forms, both for whole regions and for individual industries. Modeling specifications which affect the multiplier include:
    • the range of effects which are permitted ("endogenized") by the model, over
      1. space (size of region etc.)
      2. time (short- vs. long-run effects)
      3. "structural inclusion" or "scope" of the multiplier (i.e. which linkages to which components of the economy have been included, e.g. have households ("induced" effects) or local government activities been made part of the model?)
    • the variable considered (e.g. income or employment)
    • the denominator unit of the multiplier ratio: What is created per unit of what? Total jobs created per export job will be smaller than total jobs created per million dollars of exports

  3. Multipliers developed for a region or an industry within a region are representing the region or industry as a whole but not individual sub-regions or establishhments with an industry.

  4. Multiplier effects are based on assumptions about the availability of un- or under-utilized resources and people to accomodate the effects (migration, unemployment etc.). Since many resources are already utilized in a full-employment economy, multiplier effects tend to ignore or mask (negative) displacement effects. Thus, positive multiplier effects will -- presumably in a highly differentiated way -- include hidden opportunity costs and substitution effects.

  5. What applies to production (above) also applies to consumption. Household money spent on Mariner Baseball ticket and hot dogs enhances the appearance of baseball's economic impact on Seattle but is presumably not spent on other consumption goods or services with a higher or lower local impact.

  6. Empirically derived multipliers represent the period for which the underlying relationships have been quantified. Such relationships do not just change ("structurally") over the long-haul but are sensitive to cyclical variations. Particular reference should be made to the tendency that during boom periods (when the region may run out of local resources) multipliers tend to decrease, while spatial efficiencies and local loyalties may enhance the multiplier during downturns.

  7. Multiplier effects are not necessarily occurring after the specified exogenous stimulus. Thus, in addition to the difference between short- and long-run multipliers, one may have to consider that multiplier-related behaviors can be based on expectations and may thus occur in advance of the actual stimulus. In general, moving the (comparative-) static multiplier concept into a (e.g. forecasting) context where time is more explicitly considered can be tricky. (Based on a variety of sources; see: I/O Bibliography)


    Stability of Input-Output Derived Coefficients & Multipliers:

    Potential Causes for Changes of Multipliers over Time:

    1. Technological change (affecting the technical facets of regional coefficients)

    2. Increasing (or decreasing) benefits from scale of production ("scale economies")

    3. Variations in product mix (within industrial sectors) including entirely new products (or loss of products); same applies to the coming and going of entire branches of industries or sectors.

    4. Relative price changes (as such; given that coefficients have a monetary foundation)

    5. Input substitutions (in response, e.g. to price changes or technological change)

    6. Changes in trade patterns (affecting the "regional" in regional input coefficients; including import "substitution" and "outsourcing" beyond regional boundaries)

    Source and suggested further reading: Conway (1977)


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