Input-Output Analysis, Linear Programming and Modified Multipliers

output multiplier for service sector is given by 1.353 from the unrestricted IO model
(original multiplier) and 1.293 from the restricted IO model (modified multiplier). The
central government may calculate the amount of investment in service sector as $1,381 (=
$1,869/1.353) using the original multiplier, which in fact is not enough to recover the
loss. Government’s investment increases only $1,786 (= $1,381 × 1.293) in economy and
the economy is still losing $83. Actually, the final demand in service sector should rise
by $1,445 (= $1,869/1.293) to recover all of economic loss, which is $64 more
investment comparing to amount of expenditure based on the original multiplier. Net
benefit to use the modified multiplier is $19 (= $83 - $64). If the economy is relatively
large, say millions of dollars, the difference might be substantial. Clearly the
conventional way underestimates the economic impact after imposing exogenous
production restriction.

Empirical Analysis

As shown in above sections, the IO analysis deals with final demand changes and
rippling effects on the regional economy. However, when exogenous capacity limitation
on production is imposed, the multipliers are changing as in equation (10) and the
difference might be substantial as illustrated above numerical example. For the real
example, the US input-output table is formulated using IMPLAN 2006 data and linear
programming model accordingly. IMPLAN sectors are aggregated into 21 sectors which
is 2 digit NAICS with power generation and supply sector (MIG, Inc, 2004). See Table 2
for sectoral aggregation. As in equations (8), the LP model is run and the output
multipliers are obtained, which are reported in the second column in Table 3.

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