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REGIONAL ECONOMIC ISSUES
Working Paper Series
Sensitivity o f the Chicago Region Econom etric Input-O utput M odel
[CREIM ] to A lternative Sources of Interindustry Relationships
Philip R. Israilevich, Geoffrey J. D. Hewings,
Graham R. Schindler and Ramamohan Mahidhara
FEDERAL RESERVE BANK
OF CHICAGO
WP- 1995/ 16
Sensitivity of the Chicago region econometric inputoutput model [CREIM] to alternative sources of
interindustry relationships1
Philip R. Israilevich, Geoffrey J.D. Hewings, Graham R. Schindler and
Ramamohan Mahidhara
Abstract
In this paper, we investigate the role of input-output data sources in regional
econometric input-output models. While there has been a great deal of
experimentation focused on the accuracy of alternative methods for estimating
regional input-output coefficients, little attention has been directed to the role
of accuracy when the input-output system is nested within a broader accounting
framework.
The issues of accuracy were considered in two contexts,
forecasting and impact analysis focusing on a model developed for the Chicago
region. We experimented with three input-output data sources: observed
regional data, national input-output, and randomly generated input-output
coefficients. The effects of different sources of input-output data on regional
econometric input-output models revealed that there are significant differences
in results obtained in both forecast and impact analyses. The adjustment
processes inherent in the econometric input-output system did not mask the
differences imbedded in input-output tables derived from different data sources.
Since applications of these types of models involve both impact and forecasting
exercises, there should be strong motivation for basing the system on the most
accurate set of input-output accounts.
Introduction
In the early development of regional input-output tables, discussion centered on
the costs of survey versus nonsurvey data collection (see Hewings and Jensen
1986; Round 1983 for a thorough discussion). These debates, enjoined in
earnest in the 1960s, continued for almost two decades without any apparent
resolution; Jensen's (1980) distinction between holistic and partitive accuracy
seems to have produced a sense of agreement about the ways in which input-
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output tables produced under a variety of different procedures could be
compared.
However, this discussion did not address the issue of survey versus nonsurvey
methods (or any combination) in the context of the development of models in
which the input-output tables were nested within a broader framework. In this
context, one could consider the imbedding of input-output tables in social
accounting systems (a modest extension of the simple input-output model) or
within general equilibrium models. These possibilities raise a fundamental
question: does the source of the input-output data matter when the nuvfeling
system is more extensive? The purpose of this paper is to contribute to this new
perspective by examining the implications on model output when three
different input-output tables are embedded in a regional econometric inputoutput model (REIM). This study can be considered as one of few studies
investigating the role of input-output embedded in the system of simultaneous
equations. This system of simultaneous equations is comprised of different
blocks such as input-output, demographic, consumption and so forth. In this
paper, attention will be directed to only one block -- input-output. The purpose
of this analysis is to determine if differently constructed input-output tables
would have a significant effect on the input-output block as determined in the
Chicago Regional Econometric Input-Output Model (CREIM ). It is important
to distinguish that the input-output block in CREIM is not a traditional inputoutput system; it has a stochastic and dynamic nature that facilitates the
adjustment of the observed input-output table to time-series variations in the
output vector and the final demand matrix. While future research can explore
the impact of including additional blocks (generating a more extensive closure
of the simultaneous system), it was considered important to determine whether
differently constructed input-output tables have a significant impact on the
input-output block, prior to the inclusion of other blocks into the analysis.
Hence, we focus specifically on the behavior of the input-output block, which
we detach from the rest of the model.2 Empirical results are drawn from the
Chicago input-output table constructed for 1982. The paper is organized as
follows. In section 2 we discuss the effect of the choice of data sources for
input-output tables on regional static input-output models. Section 3 is devoted
to measuring the effect of incorporating these different input-output tables on
the results obtained with regional econometric input-output models. Section 4
describes experiments conducted for three input-output tables constructed using
different techniques and data sources. [An appendix provides a description of
the Chicago-observed input-output table (CIO)]. Section 5 concludes the paper.
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Effect of the choice of input-output tables on regional static inputoutput models
Input-output tables can be constructed by using a variety of methods and data
sources; with limited funds available for survey-based table construction,
general attention has been focused on appropriate hybrid methods. In this
context, the analyst is faced with the problem of allocating scarce resources to
those components of the table that are deemed analytically important. Now
assume that the input-output table is but one part of a broader modeling system;
would the decision-rules adopted in the allocation of survey resources for the
construction of an input-output table alone also apply for the case of a more
complete modeling system? With the exception of some work by Harrigan e t
a l. (1991) in comparing simple input-output and CG E systems, these issues
have not been addressed formally. Even in the Harrigan e t a l. (1991) paper,
the explicit focus was not on the accuracy of the input-output tables (since the
same tables were used for the comparison). Coomes, et. a l. (1991) tested
regional versus national input-output specification in an effort to determine
differences in models of regional employment. Using interindustry linkages
(input coefficients) expressed in employment terms, the authors were able to
link quarterly employment of one industry to employment in other industries.
Some earlier work by Hewings (1977; 1984) provided the basis for the type of
assessment adopted in this paper. In one case, two sets of regional input
coefficients obtained from two survey based tables for two states were
exchanged under a variety of assumptions; a further set of input coefficients
was obtained from a random number generator. The results indicated that no
matter what the source of the coefficients, it would be possible to approximate
the observed regional column multipliers given appropriate margin
information. However, when attention was focused on the separate, partial
multipliers (i.e., the individual elements of the Leontief inverse), the exchange
procedures produced very unsatisfactory results. Hewings (1984) reviewed
research which identified analytically important coefficients (the set of
coefficients whose correct estimation is deemed critical in generating accurate
results) and the issue of analytical importance in more extensive, social
accounting systems. The general conclusions were that (i) as economies
evolve, the set of analytically important coefficients changes, and (ii) the
importance of interindustry transactions seems to decrease when the inputoutput tables are embedded in social accounting systems. Can these findings be
generalized to modeling systems of the REIM type?
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Regional input-output tables have even wider potential for variation with
respect to sources and methods of construction. Analysts often compare inputoutput multipliers as a measure of differences between methods and data
sources. In general, input-output tables generated by different methods with
column sums being constrained to the same vector will produce veiy similar
multipliers (Katz and Burford 1985; Phibbs and Holsman 1981). However,
coefficients for both the input-output tables and the Leontief inverse will vary
with each method of construction. This distinction can be expressed as follows,
by noting that the input-output multiplier is a total derivative composed of a
sum of the Leontief inverse elements:
dx
Y'
(i)
where tttj is a multiplier, and TntJ are Leontief inverse elements,
X = [x, ]
is the output vector,
x =J'
1
X,,
y = [>*; ] is the final demand vector, y = y
.
i
Earlier studies would argue, correctly, that m i are largely independent of the
input-output table components and determined mostly by the column-sum of
input-output coefficients.
For example, Drake (1976) proposed an
approximation for the multiplier based entirely on the column-sum of the inputoutput table:
mj =\ +
where
atJ
a.
1- a
are regional input-output coefficients,
(2)
a%j = y
qiV and a
is a
mean value of a y .
Therefore, if the purpose of a study is to determine multipliers only, then it
makes little difference how regional input-output tables are constructed, as long
as the coefficient column-sum is determined correctly. In other words, in order
to predict output for a given vector Y , methods of regional input-output table
construction play no significant role. However, in order to answer questions
related to the decomposition of multipliers, we have to look at the detailed
input-output table. For example, if a single component of the final HamanH
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vector (say, food consumption) increases, then the multiplier for the food
industry will provide the change in overall economic output. In order to
determine the change in demand for intermediate products, we would need a
hill input-output table.3 In the next section we show that REIM-type models
require information from a lull input-output table, and thus, the column sums
of a table ( a i ) are not sufficient.
Effect of choice of input-output tables on regional econometric inputoutput models
In the recent literature on CGE models (see Kraybill 1991) and regional
econometric input-output models (see Conway, 1990; Treyz and Stevens, 1985;
Treyz, 1993), there has been limited discussion about how differently
constructed input-output tables affect model outcomes. In this paper, we
address this issue by analyzing the two roles that input-output tables play in
such models, namely, when these models are used for (1) forecasting and (2)
for policy impact analysis.
To illustrate, we concentrate on regional
econometric input-output models, REIM (see for example, Conway, 1990;
Israilevich and Mahidhara 1991).
Input-output tables are used in REIM as a deterministic linear predictor of
output:
(3)
where f tJ is a normalized regional purchase coefficient in the final demand
matrix,
Y = |^ .J is the final demand vector consisting of the following components:
personal consumption elements, investment, government expenditures, and net
exports,
* = [»,] is a vector of variables exogenous to the regional economy (such as
GNP, national industrial production indices and other national data),
E = [ei ] is a vector of normalized regional gross export coefficients,
FRB CHICAGO Working Paper
December 1995, WP-1995-16
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Z = [z, ]
are predicted output values (as opposed to x t which are observed
values of output) and
t indicates year. For brevity we omit this superscript in the rest of this paper.
Exports, derived as a residual in the base year, are assumed to be proportional
to the corresponding national variable (equation 3); however, this relationship
is modified through the process described in equation (17), generating a
nonlinear relationship between regional and national exports.
The crucial difference between traditional input-output approaches and
equation (3) are the weights assigned by (3) to each of the input coefficients.
These weights are expressed as o b se rv e d outputs, X , for each time period. In
order to formalize the difference between the traditional input-output approach
and equation (3), we can rewrite (3) in matrix form:
Z rEIM = A X + Y '
^
where A is the input-output matrix and Y is a vector of aggregate) final
demand; all variables change in time, but we omit the time parameter to
simplify exposition. However, the adjustment process takes place in (17) and it
is an adjustment of the base year values of the input coefficients and the exports
coefficients from (3). Denote the difference between the observed and
estimated outputs as A = ZREIM— X . Then equation (3) can be presented as:
Zm
=S*X=AX+Y^
(J)
If the usual input-output (IM) approach is used then:
zm
= {i -
a )-' y
'
From (5), we have:
A + X - A X = A + (I - A) X = Y
Expression (6) then can be rewritten as:
^ im —{ I A ) Y —(I —A ) & + X
^
Now, we can determine the difference between the IM and REIM estimation of
outputs as:
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[ ( / - ^ ) ',A + ^ r] - ( A + jr ) =
[ ( / - ^ - '- / J a ,
(9 )
and, by using the power series decomposition of the Leontief inverse, we have:
Z a , - Z l a m = ( A + A 1+ ...+ A ')&
(10)
From this expression, it is clear that the difference between the traditional
input-output estimates (IM) and those generated by equation (3) (these being
the output estimates from REIM ), will be amplified by the structure of the A
matrix. Hence, the differences between the two estimates will be directly
related to the nature of the linkages between industries, measured by the
indirect multiplier effects. It is not unreasonable to expect that the use of the
input-output system in (3) as opposed to the traditional input-output
formulation may amplify the effect of differently constructed input-output tables
on the prediction of total output, Z.
Stochastic equation fo r the input-output components
To turn this model into an econometric forecasting model, vector Z has to be
stochastically related to the observed vector, X . In REIM , this is accomplished
through a set of regression equations:4
(11)
where
zi t_x is a lagged input-output-generated predicted output, and g(
is the
set of exogenous variables selected by the modeler [there are ( T x N )
equations in (11)]. The lag structure shown in (11) varies by sector; in some
cases, the lag will be zero, while in other cases a first-order or even secondorder nonlinear difference equation will be appropriate. Equation (11) is
estimated separately for each industry i with the vector of random errors, et .
Equations are estimated using EG LS, assuming autocorrelation, otherwise an
OLS procedure is adopted.
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Equation (11) assigns a set of regression coefficients to each row of the inputoutput table, weighted by annually observed outputs, in a nonlinear fashion.
This means that the input-output column sums would not provide enough
information for the system (11) and, hence, Drake’s (1976) short-cut method
could not be employed in KEIM .
In a fully specified REIM system, the final demand matrix is itself endogenous
within the whole model. However, for the presentation in this section, we
break the link with the rest of the REIM by assuming that vector Y is
exogenously determined. As a result, system (11) can be represented in the
following fashion to illustrate the relationship to traditional input-output
computations. First, denote the right-hand side of (11) as:5
X
II
>
f
( zZi,t-1}
a 0 + a z log
+ <Xggit
V/ =
(12)
)
Vt = \,...,T
Then (11) can be rewritten (dropping the time subscript) as:
X ,= M
V/ =
V/ = i ,...,r
(13)
By diagonalizing /?, as a diagonal matrix, /?, , and utilizing (3), the system
(11) can be presented as:
X = fiAX + fiY
Vf = l ,...,r
>
(14)
or, finally, as:
Y
\/t = \,...,T
(15)
It is important to stress that the matrix, (5 is a nonlinear first-difference
operator that modifies the static Leontief inverse into a dynamic one. This
modified inverse,
L=
changes with the choice of the input-
output table in two respects. First, if ^4 is modified, then the estimates in (11)
will change (i.e., /? is a function of A ) and secondly, the matrix A itself will be
different.
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The system of equations (IS) provides a forecasting or impact capability,
assuming that Y is determined exogenously. However, in REIM only the vector
of exports within final demand Y is a function of exogenous variables (such as
national indices of industrial production, GDP etc.). A ll other components of
final demand are linked to other submodules within REIM . Hence, (IS) does
not represent a full REIM-based solution but provides insight into how the
input-output component plays a different role from standard input-output
analysis.
Shock specification in REIM
In the standard IM system, a shock is usually introduced through a change in
an element of the final demand vector. Similarly, the system (IS) can be
shocked exogenously by adding a vector of change to the output, X . Therefore,
the impact on all outputs, X , is measured as:
X = fAX+fiY+s
V/ = l ,...,r
(16)
where s is a vector with positive (negative) shock, 5( , and zeroes elsewhere,
and thus represents a positive (negative) shock to sector i 6 The closed form
solution for the impact analysis is:
(17)
However, recall that Y is part of a larger system within REIM and therefore the
closed form solution would involve interactions with other equations from other
modules within REIM. In both forecasting and impact analysis (equations IS
A
and 17), the differences in A can be compensated by the estimated f i . In other
words, P compensates for differences in input-output table' «o that the final fit
to the observed output is achieved by minimizing random error. As a result,
one may argue that survey-based input-output tables within REIM would yield
the same results for impact analyses and forecasts as those generated with
nonsurvey tables. If this is the case, then the efforts expended on estimating the
input-output coefficients should be minimized. The implications from this
assertion are that the debates initiated by Drake (1976) may have applicability
in REIM systems. In the next section, we attempt to test this assertion with
empirical analysis.
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Three input-output table experiments
Input-output models (IM), social accounting matrices (SAM), and regional
econometric input-output models (REIM) differ in the information they use in
calculating output. The IMs treat final demand as an exogenous vector, while
the SAMs endogenize many of the final demand components. Neither
modeling system, however, uses information on national variables in the sense
that the multipliers of these two systems would not change with a change in
national variables. The REIMs, on the other hand, utilize all the information
present in the detailed final demand matrix, including national variables;
therefore, the REIM multipliers will change with different values of » ,. All
three approaches (IM, SAM, and REIM ) incorporate direct and indirect effects.
However REIM does not calculate the Leontief inverse explicitly; instead it
runs a system of simultaneous equations [including (3.1) and (3.2)] in a timerecursive fashion, thereby measuring impact in a dynamic sense.
In REIM , there is only one input-output table on which all historical estimates
and forecasting values are based. For the year (base year) corresponding to the
input-output table:
z ^ jr,
for all other years, this identity does not hold. This base year identity is
achieved by either assuming export as a residual or allowing some adjustment
procedure to balance rows only of the input-output table. For all other
periods, P adjusts the rows of the input-output table through equation (17).
Since (17) is derived from (11), in which there is a random error term, X on the
left-hand side of (11) is estimated, not observed. This balancing procedure is
different from the co lu m n s a n d ro w s adjustment approaches used in more
traditional input-output and social accounting systems. Although this is a
potential limitation, in our experience the procedure did not produce
coefficients that violate the Hawkins-Simon conditions. In macro national
models, such as the one developed by Hudson and Jorgenson (1974), the input
coefficients are estimated through a derivation using Shepard’s Lemma. In this
type of approach, analysts balance derived input coefficients with columnconstrained adjustments. As shown by Israilevich (1991), this procedure may
cause imbalances.
In designing experiments to address the issue of the importance of the choice of
input-output tables, we noted that REIM s are used for two purposes: forecast
and impact analyses. Accordingly, in our investigation we analyze the
forecasting ability of the input-output model and its impact analysis features.
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While the forecasting ability of input-output is not of great interest in itself, we
investigate it as it is a building block in REIM-type models. We thus analyze
how differently constructed input-output tables affect its forecasting ability. A
second aspect of REIM is in its role in impact analysis; in this respect, REIM is
similar to IM. Both models lack an observed figure against which the
performance of the model can be judged, since no one knows what the "true"
impact is. In the following two subsections, we test both the forecasting
performance and the impact performance of input-output.
For the tests, we consider the input-output portion of the Chicago REIM
(CREIM ). We consider three tables which are balanced for 1982, according to
equation (3). The Chicago-observed input-output table (CIO) is constructed
from observed (Manufacturing Census) data combined with regionalized data
from the national input-output table and other sources.7 The second table is
referred to as the Chicago-national input-output table (NIO) and is constructed
directly from the national input-output table using location quotients for the
regionalization procedure. Finally, in the spirit of earlier work by Hewings
(1977), a third table is constructed; the Chicago-random input-output (RIO)
table consists of randomly generated input-output coefficients. All three tables
have the same normalized final demand matrix f is; some variations in this
final demand matrix are the result of construction procedures explained in the
appendix. All three tables are balanced to the same total outputs. The export
vector is determined as a residual and, therefore, varies for each of the inputoutput tables. Since the purpose of this study is to explore the effects of
changes in the input-output table on the output vector specified in (17), all
changes due to simulations with different input-output tables will be recorded
as changes in A”.
Forecast Experiments
In order to estimate the Z variables of equation (3), we allow vectors X , Y, and
N to vary over the historical period (1983-92) using three different sets of
input-output coefficients: CIO, NIO, and RIO. Afterwards, we reestimate /?
coefficients for each of the three versions of Z. This completes the estimation
of coefficients necessaiy for the simulation of the system (14). The other REIM
modules are unchanged since the estimation of these modules is unaffected by
the changes in the input-output table. [The system (14) is endogenized within
REIM by making the final demand vector F endogenous. For example,
changes in personal income will affect personal consumption (part of F)].
Accordingly, we derive three versions of REIM that we simulate over the
historical period.
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Table 1
Average Absolute Percent Difference
Number of
Average Percent
Number of
Average Percent
occasions
Difference [NIO-
occasions
Difference [RIO-
CIO]
CIO]
\S NIo \> \S CIo\
\S RIo \> \S CJo\
R eso u rces
R eso u rces
3 out of 4
2.4
M a n u fa c tu r in g
2
out of 4
11.1
M a n u fa c tu r in g
16 out of 19
42.1
S e rv ic e s
13 out of 19
73
S e rv ic e s
10 out of 13
13.1
9 out of 13
12.4
In order to gauge the differences among the three simulations, we compare
estimated outputs with observed outputs in the following manner:
•
First, we accumulated absolute percent errors, over the simulation period
(1983-92). The results are presented in figure 1. In this figure, errors are
averaged over time and accumulated over industries. The best results were
obtained with the Chicago input-output model (CIO) while the national
table adjusted to Chicago totals produced forecasts that were superior to
those obtained from the randomly generated input-output table.
•
Second, we accumulated absolute percent errors for each individual
industry over the simulated period (see figure 2). In this figure, we
compare the results from NIO and CIO.8 It is clear that, for most
industries, CIO provides better estimates.
The comparisons are
summarized in table 1.
The first column of table 1 records the number of industries for which the
forecasting error derived with NIO exceeds the forecasting error with CIO.
Similar information is recorded in the third column for the comparison between
CIO and the randomly generated coefficients. In the second and fourth
columns, the averaged absolute percent differences are recorded for both sets of
paired comparisons.
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These results suggest that the differences in the construction of input-output
tables translates into differences over the forecast period. Within the sectors,
the manufacturing sector exhibits the greatest difference; here the survey-based
input-output table predicts better by 42 percent over the table constructed using
the national coefficients and over 73 percent in comparison to the randomly
generated tables. This is not surprising since the manufacturing component of
CIO was derived from aggregations of individual establishment-level data. On
the other hand, the differences in the nonmanufacturing sectors are smaller
than those observed in manufacturing.
Figure 1
Forecasted Output Average Absolute
Sector
— CHICAGO — NATIONAL— RANDOM
FRB CHICAGO Working Paper
December 1995, WP-1995-16
]3
Figure 2
25
Cumulative Absolute Percent Error by
Sector, 1983-1992
Res.
Manufacturing
Services
20
c 15
2
£10
5
0
1 1 1 1 1 M T11
1 4 7 10 13 16 19 22 25 28 31 34
Sector
M i l -H--H M
1 111 1 1 1 1 1 1 1 1 1 ■f M
— CHICAGO
NATIONAL
Impact Analysis
The second set of experiments is devoted to impact analysis. In the forecast
analysis, we allowed the entire set of exogenous variables to vary over time. In
the impact analysis, we fix all exogenous variables for the year in which the
shock is implemented. Then, we change one exogenous variable, in this case,
the export of a given industry, to represent a shock to that sector. Once this
shock is entered in the model, changes in the outputs of all other industries are
recorded. The information derived from these changes is similar in form to
that of a column of the traditional Leontief inverse as specified in equation (1).
Each of the 36 sectors was shocked for 1990, representing a 10 percent change
over the base case output (see Israilevich e t a t. 1994 for details), and the
average effect on all other sectors was recorded. While the choice of 1990 was
arbitrary, other benchmark years would have yielded the same qualitative
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ordering in the pattern of results. Since REIM has a recursive structure of
equations, we had to simulate the model for several years; a shock to the model
would eventually lose its effect but there is a minimum number of years that
should be considered for tracking the effects. In this case, it was decided to use
6 years, but for any greater number of years, the derived multipliers would be
practically the same (see Israilevich e t a l. 1994). In essence, the impact from a
shock is largely independent of a chosen number of years beyond some
minimum value. Of course, with a REIM , the impact is considered to be more
diffused in time in contrast to the comparative static nature of the usual
Leontief system in which the time path of the shock through the system is not
considered (for modifications, see Romanoff and Levine, 1986; McGregor e t a l.
1995).
In this part of the analysis, there is no observed forecast against which we can
compare derived results (as it was the case in the forecasting section). Hence,
our analysis compares results derived from each of the three tables. For
comparison, we form two pairs: the first pair is NIO and CIO, and the second
pair is RIO and CIO.
To enable a concise comparison among the three models, we regress the
changes in all sectors induced by a shock in one experiment on the comparable
changes found in the other experiments. For example, in comparing the
simulation results from NIO and CIO, we form the regression:
A X N,0 = a + b A X la0 -
(18)
The results are recorded in tables 2 and 3.
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T a b le 2
Pairwise Regressions of Partial Multipliers
National vs. Chicago
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Regression
a
b
0.022
1.031
0.035
1.093
0.012
1.005
0.020
1.034
0.014
1.020
0.008
1.006
0.024
1.018
0.026
0.979
0.026
1.006
0.019
1.094
0.021
1.094
0.023
1.097
0.006
1.053
0.021
1.017
0.019
1.044
0.024
1.021
0.023
1.209
0.034
1.049
0.020
1.081
0.025
1.055
0.014
1.017
0.023
1.021
0.024
1.022
0.020
1.031
0.015
1.009
0.011
1.008
0.020
1.055
0.024
1.031
0.005
1.082
0.025
1.059
0.023
1.062
0.019
1.015
0.025
1.033
0.027
1.048
0.034
1.045
0.023
0.992
Ave
0.021
Sector
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
1.043
Standard Errors
a
b
0.006
0.034
0.012
0.055
0.003
0.020
0.005
0.026
0.003
0.013
0.008
0.007
0.005
0.008
0.009
0.009
0.006
0.015
0.028
0.028
0.007
0.035
0.034
0.027
0.040
0.044
0.047
0.028
R-Squared
0.964
0.919
0.987
0.979
0.995
0.997
0.966
0.976
0.968
0.986
0.970
0.982
0.998
0.982
0.976
0.972
0.982
0.934
0.980
0.976
0.988
0.974
0.970
0.983
0.986
0.993
0.977
0.975
0.999
0.964
0.966
0.976
0.952
0.943
0.935
0.974
0.005
0.028
0.973
0.002
0.010
0.006
0.005
0.005
0.005
0.006
0.006
0.033
0.026
0.031
0.023
0.033
0.026
0.008
0.024
0.028
0.030
0.028
0.048
0.026
0.028
0.019
0.029
0.031
0.023
0.001
0.005
0.005
0.005
0.005
0.008
0.005
0.006
0.004
0.005
0.006
0.005
0.004
0.003
0.006
0.006
0.001
0.021
F-Stat [0,11*
9.325
11.543
7.593
12.663
16.702
11.786
9.834
14.603
13.240
26.668
16.290
24.296
41.680
11.495
10.665
12.891
56.023
11.332
19.662
16.646
11.102
12.929
12.112
10.835
9.157
8.706
11.674
10.142
108.387
11.440
11.862
9.785
9.026
9.359
11.517
9.364
* F-Stat indicates rejection of null hypothesis at the 95% level in all
cases.
Note: Nation = a + £*Chicago.
FRB CHICAGO Working Paper
December 1995, WP-1995-16
16
T a b le 3
Pairwise Regressions of Partial Multipliers
Random vs. Chicago
Sector
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Ave
Regression
a
b
0.004
0.919
0.002
0.878
0.015
1.252
-0.001
0.950
0.010
0.841
0.019
0.973
0.013
0.745
0.011
0.910
0.007
1.382
0.009
0.854
-0.001
0.958
0.006
0.467
0.016
0.974
0.006
1.483
0.006
0.886
0.007
0.940
0.016
1.419
0.009
0.988
0.010
0.957
0.008
0.899
0.010
0.944
0.001
0.991
0.003
0.991
0.006
0.806
0.009
0.977
0.012
0.851
0.010
0.917
0.011
0.796
0.013
0.983
0.013
0.883
0.001
0.878
0.003
2.106
0.004
0.881
0.007
0.941
0.008
0.978
-0.005
0.785
0.008
0.983
Standard Errors
a
b
0.005
0.030
0.010
0.045
0.005
0.027
0.006
0.033
0.003
0.013
0.003
0.017
0.003
0.017
0.004
0.019
0.006
0.035
0.004
0.022
0.006
0.033
0.014
0.006
0.006
0.006
0.014
0.019
0.049
0.076
0.031
0.029
0.031
0.065
R-Squared
0.966
0.918
0.984
0.960
0.992
0.989
0.982
0.985
0.979
0.978
0.961
0.984
0.990
0.911
0.957
0.970
0.984
0.983
0.986
0.982
0.984
0.977
0.960
0.978
0.984
0.981
0.977
0.975
0.986
0.985
0.905
0.957
0.960
0.969
0.966
0.809
0.006
0.029
0.967
0.002
0.010
0.003
0.017
0.006
0.005
0.006
0.004
0.004
0.004
0.004
0.005
0.006
0.005
0.004
0.004
0.005
0.005
0.004
0.004
0.017
0.079
0.032
0.028
0.031
0.010
0.022
0.019
0.021
0.020
0.026
0.035
0.021
0.022
0.020
0.024
0.022
0.020
F-Stat fO, 11**
3.838**
4.884
63.664
1.507*
80.322
19.746
108.565
11.970
74.008
22.575
1.078*
1449.599
14.231
22.268
6.375
2.363*
124.116
2.681*
4.775
11.770
5.569
0.060*
0.105*
46.249
2.700*
26.926
6.267
44.103
5.684
19.618
3.715*
125.953
8.389
2.156*
0.971*
7.540
* Failed to reject the null hypothesis at the 95% level.
** F-Stat indicates rejection of null hypothesis in 25 of 36 cases.
Note: Random = a + b*Chicago.
FRB CHICAGO Working Paper
December 1995, WP-1995-16
17
The maintained hypothesis,
H0, namely that a=0 and b=l, implies that there
are no differences between the partial multipliers derived from both
experiments; a similar hypothesis is formed for the comparisons between RIO
and CIO. To test the null hypothesis of
B0 = [0,l] ,
we use an F-statistic,
calculated as:
[(£°“ - B ^ X 'X (B ous - B ^
F = ------------------2-----------------SSEU
d .f .
SSEUis the sum of squared errors from the pairwise regression and d.f.
are the degrees of freedom. For both experiments, H0 was strongly rejected.
where
In essence, the choice of tables provides significantly different results;
however, unlike the case of the forecast experiment, no preference ordering can
be provided in terms of which set of tables provides the better fit. A ll we are
able to state is that the observed differences are not due to chance.
Finally, we should note that Coomes e t. a l. (1991) show that employment
adjusted by input-output coefficients have significant regression coefficients for
10 out of 28 industries. We show, similarly, that input-output coefficients
matter for forecasting purposes. Coomes e t a l. (1991) show that the substitution
of national coefficients instead of regional coefficients changes regression
coefficients for input-output adjusted employment figures in small increments,
which, however, “...result in rather large differences in impact multipliers
between models.” Again, these results are similar to our impact analysis
differences. In the present study, the majority of industries have significant
intercept but insignificant slope; this result may be due to the deficiencies of
the location quotient methodology. The results indicates that the overall level
of output prediction by NIO is higher (lower) than the corresponding value
predicted by CIO (table 2). Obviously, alternative methodologies, such as the
estimation of input coefficients using regional purchase coefficients, could have
different results. The sensitivity of the model for impact analysis to changes in
input-output coefficients is clearly demonstrated by tables 2 and 3.
FRB CHICAGO Working Paper
December 1995, WP-J995-16
18
Conclusions
In this paper, we have attempted to extend some of the earlier discussions on
the role of input-output coefficient estimation in the applications of the
underlying model. Our work uses a regional econometric input-output model
as the basis for the comparison; in this model, the input-output tables are nested
within a larger analytical framework. Three alternative specifications of the
input-output tables are used; one contains the most survey-based information,
one uses adjusted national coefficients and one uses no local information at all
(relying on random numbers).
The results indicate that when the system is used in a forecast mode, the
differences appear to be pronounced. Since only the set of coefficients for the
manufacturing sectors are fully observed in Chicago, the corresponding inputoutput coefficients are more independent of those derived from adjustments of
the corresponding national coefficients. As a result, the forecast for these
sectors were shown to be particularly sensitive to the choice of input-output
tables.
In essence, the results provide a different perspective to the one
advanced by Drake (1976) and Katz and Burford (1985). However, a word of
caution should be interjected here.
The differences in the partial, static multipliers associated with impact analysis
reveal significant variations as well. In this regard, the results parallel most
strongly the earlier experiments by Hewings (1977). The next step would be to
promote a similar inquiry in a full forecasting context and to link this work
with some of the new developments proposed by Sonis and Hewings (1989,
1992) in the context of the specification of a field of influence of change. Here
attention would be focused on the sources of error or change generated by
individual coefficients rather than on the source of differences generated by
differently constructed tables in t o t o . Finally, the analysis needs to be extended
to test the sensitivity to alternative closures and alternative national variable
forecasts.
References
Conway, R.S. 1990. The Washington Projection and Simulation Model: ten
years of experience with a regional interindustry econometric model.
I n t e r n a t i o n a l R e g i o n a l S c i e n c e R e v i e w 13: 141-165.
Coomes, P., Olson, D. and Glennon, D. (1991) The interindustry employment
demand variable: an extension of the I-SAMIS technique for linking inputoutput and econometric models. E n v i r o n m e n t a n d P l a n n i n g A 23: 1063-1068
FRB CHICAGO Working Paper
December 1995, WP-1995-16
19
Drake, R.L. 1976. A short-cut to estimates of regional input-output multipliers:
methodology and evaluation. In te rn a tio n a l R e g io n a l S c ie n c e R e v ie w 1:1-17.
Guccione, A., Gillen, W.J., Blair, P.D., and Miller, R.E. 1988. Interregional
feedbacks in input-output models: the least upper bound. Jo u rn a l o f R e g io n a l
S c ie n c e 28: 397-404.
Harrigan, F.J. 1982. The estimation of input-output type output multipliers
when no input-output model exists: a comment. Jo u rn a l o f R e g io n a l S c ie n c e
22: 375-381.
Harrigan, F., McGregor, P„ Dourmashkin, N„ Swales, K. and Yin, Y.P. 1991.
The sensitivity of output multipliers to alternative technology and factor market
assumptions: a computable general equilibrium analysis. In R e g io n a l In p u tO u tp u t M o d e lin g : N ew D evelo p m en ts a n d In te rp re ta tio n s, eds. J.H.L1.
Dewhurst, G.J.D. Hewings, R.C. Jensen, pp. 210-228. Aldershot: Avebury.
Hewings, G.J.D. 1977. Evaluating the possibilities for exchanging regional
input-output coefficients. E n v iro n m e n t a n d P la n n in g A 9: 927-944.
Hewings, G.J.D. 1984. The role of prior information in updating regional
input-output models. S o c io -E c o n o m ic P la n n in g S c ie n c e s 18: 319-336.
Hewings, G.J.D., and Jensen, R.C. 1986. Regional, interregional and
multiregional input-output analysis. In, H a n d b o o k o f R e g io n a l a n d U rb an
E c o n o m ic s, eds. P. Nijkamp and E.S. M ills, pp. 295-355. Amsterdam: NorthHolland.
Hudson, E.A ., and Jorgenson, D.W. 1974. US energy policy and economic
growth: 1975-2000. B e ll Jo u rn a l o f E c o n o m ic s 5: 461-514.
Israilevich, P.R. 1991. The construction of input-output coefficients with
flexible functional forms.
In R e g io n a l In p u t-O u tp u t M o d e lin g : N ew
D e ve lo p m e n ts a n d In te rp re ta tio n s, eds. J.H.L1. Dewhurst, G.J.D. Hewings,
R.C. Jensen, pj>. 9S-117. Aldershot: Avebury.
Israilevich P.R., and Mahidhara R. 1991. Hog butchers no longer: 20 years of
employment change in metropolitan Chicago. E co n o m ic P e rsp e c tiv e s (Federal
Reserve Bank of Chicago) 15: 2-13.
Israilevich, P.R., Hewings, G.J.D., Sonis, M., and Schindler, G.R. 1994.
Forecasting structural change with a regional econometric input-output model.
D isc u ssio n P a p e r 94-T-l Regional Economics Applications Laboratory,
Uibana, Illinois.
Jensen, R.C. 1980. The concept of accuracy in input-output. In te rn a tio n a l
R e g io n a l S c ie n c e R e v ie w 5: 139-154.
FRB CHICAGO Working Paper
December 1995, WP-1995-16
20
Katz J.L., and Burford R.L. 1985. Shortcut formulas for output, income and
employment multipliers. The A n n a ls o f R e g io n a l S c ie n c e 19:61-76.
Kraybill, D.S. 1991. Multiregional computable general equilibrium models: an
introduction and survey. Unpublished paper, Department of Agricultural and
Applied Economics, University of Georgia.
McGregor, P.G., Swales, J.K., and Yin, Y . Ping. 1995. Input-output analysis,
labour scarcity and relative price endogeneity: aggregate demand disturbances
in afle x - p r ic e Leontief system. E c o n o m ic System s R e se a rc h (forthcoming).
Miller, R.E. 1986. Upper bounds on the sizes of interregional feedbacks in
multiregional input-output models. Jo u rn a l o f R e g io n a l S c ie n c e 26: 285-306.
Phibbs P.J., and Holsman A.J. 1981. An evaluation of the Burford and Katz
short cut technique for deriving input-output multipliers. Th e A n n a ls o f
R e g io n a l S c ie n c e 15: 11-19.
Romanoff, E ., and Levine, S.H. 1986. Capacity limitations, inventory and timephased production in the sequential interindustry model. P a p e rs o f the
R e g io n a l S c ie n c e A sso c ia tio n 59: 73-91.
Round, J.I. 1983. Nonsurvey techniques: a critical review of the theory and the
evidence. In te rn a tio n a l R e g io n a l S c ie n c e R e v ie w 8: 189-212.
Sonis, M., and Hewings, G.J.D. 1989. Error and sensitivity input-output
analysis: a new approach. In F ro n tie rs o f In p u t-O u tp u t A n a ly s is , eds. R.E.
Miller, K.R. Polenske, A.Z. Rose, pp. 232-244. New York: Oxford University
Press.
Sonis, M., and Hewings, G.J.D. 1992. Coefficient change in input-output
models: theory and applications. E co n o m ic System s R e se a rc h 4: 110-121.
Stevens, B.H., and Trainer G.A. 1976. The generation of errors in regional
input-output impact models" W orking P a p e r. Regional Science Research
Institute, Peace Dale, Rhode Island.
Treyz, G.I. 1993. R e g io n a l E co n o m ic M o d e lin g . Boston: Kluwer.
Treyz, G.I., and Stevens, B.H. 1985. The TFS Modeling Methodology.
R e g io n a l S tu d ie s 19: 547-562.
FRB CHICAGO Working Paper
December 1995, WP-I995-I6
21
APPENDIX:
Chicago-observed input-output table (CIO)
The data employed in the construction of the Chicago input-output table (CIO)
draw on the US (BEA) Input-Output Tables for 1982 together with data derived
from the individual establishment-level files of the C e n su s o f M a n u fa c tu re s.
This latter source was used to construct the manufacturing sub block of the
technological matrix of the Chicago input-output table (SIC 20 through 39).
The Census collects information on a very disaggregated level and, at this level,
we were able to identify the lower bound of inflow of goods from the rest of the
world; the details are presented below. In the second part of the CIO
construction, we determine the regional purchase coefficients (RPC).9 By
matching observed purchases and observed production at a 6-digit level of
disaggregation, we were able to determine that a great number of items that
were consumed in Chicago were not produced there. This information enabled
us to determine a matrix of n o n co m p etitive im p o rts. Clearly, the matrix of
noncompetitive imports will enable the specification of an upper bound on the
RPC (see Miller 1986; Guccione e t a l. 1988). Using the non competitive
imports matrix, we construct a new type of RPC. Denote this matrix of
adjusted RPCs as
A rR which is constructed as follows:
a„ - m„ if mv > !v
a> rh
In this setting
A rR
if
(A l)
assumes noncompetitive import coefficients as a substitute
for LQ coefficients if the LQ coefficient ( l ^
had failed to exceed the
noncompetitive import coefficient {m ^ . The nonmanufacturing sub block of
CIO is adapted from the national input-output tables, but with further
modifications related to the treatment of net exports.
The most important feature of R E EM is its link of the output variables to the
available time series. The annual gross sate product series provides net export
figures on the annual basis; this Illinois series is first adapted to represent the
six-county Chicago metropolitan region. The Chicago REIM then adjusts
input-output data to be consistent with these export data through a proration
procedure for the base year as follows. First define net exports as:
FRB CHICAGO Working Paper
December 1995, WP-1995-16
22
n e -e -m -
* - ! ( * ; + n ')
K
K
+ O
*
.
(A2)
where ne, e, and m are scalars ofnet exports, exports and imports respectively,
X ' and Y ' are intermediate and final regional transaction flows, and
M l and M y
are intermediate and final import flows.
Equation A2 can be re-written as:
V
ij
(A3)
Therefore,
(A4)
As a result, the adjustments for the ne are made before regionalizing
transaction flows. This means that the matrix of intermediate and final
transaction flows ismultiplied by a scalar:
MM'*! ^ •
2 3
where
j isa matrix ofadjusted transaction flows. This adjustment was
applied to allthree matrices CIO, NIO, and RIO. After the n e adjustment, RPC
procedures were applied to the adjusted matrix, and a vector of gross exports
was computed as a residual.1
4
3
*
1SpecialthankstoRobertMcGuckinandstaffoftheCenterforEconomicStudies,US Bureauofthe
Census,forprovidingdataandadvicenecessaryforthecompletionofthisproject
Thisinput-outputblockdiffersfromconventionalinput-outputandCGE models, asexplainedlater
inSection3.
3 Intermediateproductconsumptionisdeterminedbytherow-sumoftheLeontiefinverse. Seealsothe
discussioninHarrigan(1982).
4 ThisspecificationwasadoptedfromConway(1990).
FRB CHICAGO Working Paper
December 1995, WP-1995-16
23
5
We specifyhereanequationestimatedbyOLS; theautoregressivecomponentforthe estimates
wouldservetomodifythisequation.
6 InConway(1990Xtheshockwasenteredthroughequation(11), whichisidenticalto(15). In
Conway,bysubstitutingX = ffZ + S forZin(4),onemayderive(16).
A briefdescriptionoftheCIOconstructionisprovidedintheappendix. Themanufacturingoutput
seriesareconstructedusingdatafromvarioussources. WagesfromBEAandoutputdeflatorsfromthe
BLSareused,valueadded,costofmaterials,andpayrolldatafromtheCensusofManufacturesand
AnnualSurveyofManufacturesarealsoincluded. We thentakeCensusProduct,costofmaterialsplus
valueadded,multipliedbytheratioofBEAwagestoCensuspayroll. Thisisthendeflatedusingthe
BLSdeflator.
8 A similarfigureforRIOwasomittedbecauseitdoesnotconveynewinformation; asummaryofthe
comparisonsisprovidedintable1.
9
FortheconventionalRFC estimationseeStevensandTrainer(1976).
FRB CHICAGO Working Paper
December 1995, WP-1995-16
24
@FedFRASER