21.2 Input-Output Modeling
Therefore, the simplest way to view multipliers
is that
T
I
1 · l' _ direct effect + indirect effect
ype mu tip ler -
d'
f"
lrect elect
and
Type II multiplier =
direct effect + indirect effect + induced effect
direct effect
Explanations of the different multipliers are
rather straightforward. "An output multiplier for
sector j is defined as the total value of production
in all sectors of the economy that is necessary in
order to satisfy a dollar's worth of final demand for
sector j's output" (Miller and Blair, 1985, p. 102).
In contrast, income multipliers, "translate an initial
$1.00 output estimate (which comes from an initial $1.00 final-demand change) into an expanded
... estimate of the value of resulting employment
(household income) (Miller and Blair, 1985, p.
105). "The direct income change for each sector is
given by the household row entry of the regional
1-0 table when expressed in input coefficient form
(i.e., the direct coefficients table)" (Richardson,
1972, p. 32). As before, "The Type II multiplier
takes into account the repercussionary effects of
secondary rounds of consumer spending in addition to the direct and indirect interindustry effects"
(Richardson, 1972, p. 33).
Following the same argument as was presented
for Types I and II income multipliers, we may wish
to relate the total employment effect to an initial
change in employment, not final demand (and output) in monetary terms. That is, a dollar's worth of
new output by sector j means additional jobs in sector j in the amount of the physical labor coefficient
(Miller and Blair, 1985, p. 112). The employment
multiplier is simply the expanded employment effect divided by the direct employment change, as
before. Equations for these multipliers can be found
in Miller and Blair (1985, pp. 103-112).
Note that the Type II multiplier is larger than the
Type I by the addition of the induced effect to the
numerator. The induced effect is the increased consumption of all goods and services, directly and indirectly, as households have increased income, due
to increased production (i.e., considering the labor
share of increased income). The household sector
is taken as an exogenous sector for the Type I multiplier, but as endogenous for the Type II. Blair
(1991, p. 180) discusses the question as to whether
households should be considered endogenous:
311
Should households be included with the endogenous sectors? In calculating ... [the augmented Leontief inverted
matrix], household consumption was considered to be
determined by the amount of spending within the system. Thus, household spending was endogenous. Such a
treatment was consistent with the export-base theory of
growth, which claims that all local economic activity is
supported by exports. However, some input-output
analyses have treated household consumption as independent of the level of exports; in other words, household spending has been treated as exogenous. Clearly,
some consumption would occur even if households had
no income. The consumption could be financed from past
savings. Thus, to some extent, household consumption
is exogenous.
When household consumption is treated as independent of the level of exports, the size of the multiplier is
smaller than when household consumption is considered
to be induced by the level of exports. When consumption is induced by exports, an increase in exports will not
only stimulate industry trade, but also local consumption; hence, the multiplier will be larger when household
consumption is considered to be dependent upon exports.
[T]he sales multiplier for each sector can be calculated directly from the inverted Leontief matrix .... This
calculation is accomplished by simply adding coefficients in a given column of this matrix for the processing sector. This multiplier indicates the amount of economic activity generated in the economy by an additional
dollar of final demand for the products of the specific
sector. Higher output multipliers indicate a higher degree
of interdependence among sectors of the economy. (p. 4)
For our hypothetical regional economy, the output
multipliers are 2.40, 2.22, and 2.47 for sectors 1,
2, and 3, respectively (see Table 21.3).
In general, prevailing opinion among analysts is
that Type I multipliers underestimate impacts,
whereas Type II multipliers overestimate impacts.
Some analysts maintain that Type III multipliers
are the most realistic, because they recognize the
fact that the household consumption function
changes as income level changes. These are the
same in concept as Type II (i.e., the numerator is
the direct effect + indirect effect + induced effect), but the induced effect is modified to reflect
changes in average per capita consumption as income changes. Essentially the consumption function is changed as income changes. This is in contrast to the fixed consumption function used to
derive Type II multipliers. Unfortunately, there are
a number of different formulations of Type III, so
it is not possible to generalize this type. For an example, see the IMPLAN models (Section 21.3.1).
Techniques for deriving other multipliers may be
found in Richardson (1972, Chapter 3) and, at a
more advanced level, in Miller and Blair (1985,
Chapter 4).
Therefore, the simplest way to view multipliers
is that
T
I
1 · l' _ direct effect + indirect effect
ype mu tip ler -
d'
f"
lrect elect
and
Type II multiplier =
direct effect + indirect effect + induced effect
direct effect
Explanations of the different multipliers are
rather straightforward. "An output multiplier for
sector j is defined as the total value of production
in all sectors of the economy that is necessary in
order to satisfy a dollar's worth of final demand for
sector j's output" (Miller and Blair, 1985, p. 102).
In contrast, income multipliers, "translate an initial
$1.00 output estimate (which comes from an initial $1.00 final-demand change) into an expanded
... estimate of the value of resulting employment
(household income) (Miller and Blair, 1985, p.
105). "The direct income change for each sector is
given by the household row entry of the regional
1-0 table when expressed in input coefficient form
(i.e., the direct coefficients table)" (Richardson,
1972, p. 32). As before, "The Type II multiplier
takes into account the repercussionary effects of
secondary rounds of consumer spending in addition to the direct and indirect interindustry effects"
(Richardson, 1972, p. 33).
Following the same argument as was presented
for Types I and II income multipliers, we may wish
to relate the total employment effect to an initial
change in employment, not final demand (and output) in monetary terms. That is, a dollar's worth of
new output by sector j means additional jobs in sector j in the amount of the physical labor coefficient
(Miller and Blair, 1985, p. 112). The employment
multiplier is simply the expanded employment effect divided by the direct employment change, as
before. Equations for these multipliers can be found
in Miller and Blair (1985, pp. 103-112).
Note that the Type II multiplier is larger than the
Type I by the addition of the induced effect to the
numerator. The induced effect is the increased consumption of all goods and services, directly and indirectly, as households have increased income, due
to increased production (i.e., considering the labor
share of increased income). The household sector
is taken as an exogenous sector for the Type I multiplier, but as endogenous for the Type II. Blair
(1991, p. 180) discusses the question as to whether
households should be considered endogenous:
311
Should households be included with the endogenous sectors? In calculating ... [the augmented Leontief inverted
matrix], household consumption was considered to be
determined by the amount of spending within the system. Thus, household spending was endogenous. Such a
treatment was consistent with the export-base theory of
growth, which claims that all local economic activity is
supported by exports. However, some input-output
analyses have treated household consumption as independent of the level of exports; in other words, household spending has been treated as exogenous. Clearly,
some consumption would occur even if households had
no income. The consumption could be financed from past
savings. Thus, to some extent, household consumption
is exogenous.
When household consumption is treated as independent of the level of exports, the size of the multiplier is
smaller than when household consumption is considered
to be induced by the level of exports. When consumption is induced by exports, an increase in exports will not
only stimulate industry trade, but also local consumption; hence, the multiplier will be larger when household
consumption is considered to be dependent upon exports.
[T]he sales multiplier for each sector can be calculated directly from the inverted Leontief matrix .... This
calculation is accomplished by simply adding coefficients in a given column of this matrix for the processing sector. This multiplier indicates the amount of economic activity generated in the economy by an additional
dollar of final demand for the products of the specific
sector. Higher output multipliers indicate a higher degree
of interdependence among sectors of the economy. (p. 4)
For our hypothetical regional economy, the output
multipliers are 2.40, 2.22, and 2.47 for sectors 1,
2, and 3, respectively (see Table 21.3).
In general, prevailing opinion among analysts is
that Type I multipliers underestimate impacts,
whereas Type II multipliers overestimate impacts.
Some analysts maintain that Type III multipliers
are the most realistic, because they recognize the
fact that the household consumption function
changes as income level changes. These are the
same in concept as Type II (i.e., the numerator is
the direct effect + indirect effect + induced effect), but the induced effect is modified to reflect
changes in average per capita consumption as income changes. Essentially the consumption function is changed as income changes. This is in contrast to the fixed consumption function used to
derive Type II multipliers. Unfortunately, there are
a number of different formulations of Type III, so
it is not possible to generalize this type. For an example, see the IMPLAN models (Section 21.3.1).
Techniques for deriving other multipliers may be
found in Richardson (1972, Chapter 3) and, at a
more advanced level, in Miller and Blair (1985,
Chapter 4).