Sevilla May 2011, WIOD 2nd Consortium Meeting
WP 6 Methodological research
related to the database
WP 6.4 Multiplier bias from Supply and Use Tables
José M. Rueda-Cantuche (JRC-IPTS)
Erik Dietzenbacher (RUG, NL)
Esteban Fernández (University of Oviedo, ES)
Antonio F. de Amores (Pablo de Olavide University, ES)
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Rationale
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Following Dietzenbacher (2006):
• Leontief inverse, L, plays a relevant role in interindustry economics
• L captures direct + indirect effects of an
exogenous shock on industry/commodity output
• L can also describes the inter-industry core of a
CGE model
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•As far as, typically, L = (I – A)-1, it is subject to the
many sources of measurements errors that are
very well known for IOT, A and SUT.
•Hence, it seems plausible assuming A stochastic,
which leads to L is biased, with input coefficients:
– totally independent (Simonovits, 1975)
– biproportionally stochastic (Lahiri, 1983)
– moment-associated (Flam and Thorlund-Petersen, 1985).
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• More recently, stochastics was alternatively
imposed on the intermediate transactions of an
input-output table rather than on its technical
coefficients (e.g. Dietzenbacher, 2006).
• The findings of these experiments turned out
that the bias tends to be rather small and needs
a large sample size to get significant relevance.
• Complementary to Roland-Holst (1989).
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• This work however shifts the attention to
supply and use tables, which really
constitute the basic units of the elements
of an input-output table and therefore, of
the technical coefficients.
• Six kind of multipliers discussed in the
form of multiplier matrices
• Supply-use based Monte Carlo
experiment
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Multiplier matrices
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Domestic supply and use table
U
f
q
VT
qT
x
hT
w
xT
p
p
•
B = input coefficient per unit of
industry output
•
C = share of industry output
stemming from producing one
commodity
1 T
ˆ
C x V
•
D = commodity output
proportions (market shares)
D  V qˆ
B  Uxˆ
1
T
T
T
1
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xD q
T
q  Cx
M1 = Industry technology assumption for product by product tables
M6 = Product technology assumption for product by product tables
M2 = Fixed product sales structure for industry by industry tables
M5 = Fixed industry sales structure for industry by industry tables
M3 = DT · M1
M4 = C-1 · M6
(industry by product)
(industry by product)
M7 = D-T · M2
M8 = C · M5
(product by industry)
(product by industry)
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Monte Carlo experiment
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Empirical application for Spain (2006):
Monte Carlo experiment
1. Data sources: SUT (basic prices), 59 ind. x 59
prod. (Eurostat and INE).
2. Two approaches:
• Supply-side
• Use-side
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SUPPLY-SIDE APPROACH
Randomization of V
v ijk  v 0jk  ε ijk
qi  V ie
Randomization of u, f, h, w
ε ijk ~ N (0;[ ρ 0 v 0jk ]2 )
x i  (V i ) T e
u ijk  u 0jk  δ ijk
δ ijk ~ N (0;[ ρ 0 u 0jk ]2 )
f ji  f j0  φij
φij ~ N (0;[ ρ 0 f j0 ]2 )
hki  hk0  θ ki
θ ki ~ N (0; [ ρ 0 hk0 ]2 )
wi  w0  ωi
ωi ~ N (0;[ ρ 0 w0 ]2 )
Uie  f i  qi
eT U i  (h i )T  (x i )T
Reconciliation h, f, p
(h i ) T e  e T f i
p i  12 [(h i ) T e  e T f i ]  w i
RAS-based Solution
Uie  f i  qi
eT f i  w i  p i
e T U i  ( h i ) T  (x i ) T
(h i ) T e  w i  p i
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USE-SIDE APPROACH
Randomization of V
v ijk  v 0jk  ε ijk
Randomization of u, f, h, w
ε ijk ~ N (0;[ ρ 0 v 0jk ]2 )
u ijk  u 0jk  δ ijk
δ ijk ~ N (0;[ ρ 0 u 0jk ]2 )
f ji  f j0  φij
φij ~ N (0;[ ρ 0 f j0 ]2 )
hki  hk0  θ ki
θ ki ~ N (0; [ ρ 0 hk0 ]2 )
wi  w0  ωi
ωi ~ N (0;[ ρ 0 w0 ]2 )
~i
f  f i [( p i  w i ) / e T f i ]
qi  V ie
x i  (V i ) T e
~
qi  Uie  f i
RAS-based Solution
~
~
V i e  q i (V i ) T e  x i
~
h i  h i [( p i  w i ) /(h i ) T e]
~
( x i ) T  e T U i  (h i ) T
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H 0 : E (m )  m
i
jk
0
jk
m 0jk is obtained by using the observed values ( U 0 , V 0 , f 0 , h 0 , q 0 , x 0 , and w 0 ).
Each run i (= 1, …, N) thus generates a value m ijk (for which we have 12 candidates)
t jk 
m jk  Σ m
N
i 1
i
jk
m jk  m
0
jk
s jk / N
s  Σ (m  m jk ) /( N  1)
2
jk
N
i 1
i
jk
2
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Results. Supply-side approach 1,000 simulations
Bias
Standard deviation
Average t-statistic
% Cells significant bias
M1
M2
M3
M4
M5
M6
0.0006
0.0044
6.0139
96.99
0.0002
0.0018
5.3763
97.25
0.0002
0.0015
11.0997
95.16
0.0007
0.0066
4.8217
94.99
0.0007
0.0055
5.2223
96.74
0.0007
0.0062
5.6144
91.98
ITMC X C
FPSI X I
ITMI X C
PTMI X C
FISI X I
PTMC X C
Results. Use-side approach 1,000 simulations
Bias
Standard deviation
Average t-statistic
% Cells significant bias
M1
M2
M3
M4
M5
M6
0.0000
0.0034
2.3823
75.19
0.0000
0.0018
1.3341
64.82
0.0001
0.0017
-0.9567
79.06
0.0019
0.0157
5.3359
97.74
0.0009
0.0070
5.2241
98.50
0.0026
0.0153
3.6351
94.74
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CONCLUSIONS:
1. The absolute average values of the bias in all
cases are not very significant and may
probably be considered negligible as in
Roland-Holst (1989) and Dietzenbacher
(2006).
2. This is just an almost definite answer that
deserves further research for a bigger number
of iterations (say, 10,000); more countries
and/or years and different levels of variability
in the randomized supply and use values.
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Thank you!
http://ipts.jrc.ec.europa.eu