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WP 6 Methodological researchrelated 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 inter-

industry 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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• B = input coefficient per unit of industry output

• C = share of industry output stemming from producing one commodity

• D = commodity output proportions (market shares)

U f q

VT x

hT w p

qT xT p

Domestic supply and use table

1ˆ xUB

1ˆ qVD TT

TT VxC 1ˆ

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qDx T Cxq

M1 = Industry technology assumption for product by product tablesM6 = Product technology assumption for product by product tables M2 = Fixed product sales structure for industry by industry tablesM5 = Fixed industry sales structure for industry by industry tables

M3 = DT · M1          (industry by product)M4 = C-1 · M6 (industry by product)

M7 = D-T · M2          (product by industry)M8 = C · M5 (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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Randomization of V

eVq ii eVx Tii )(

Randomization of u, f, h, w i

jkjkijk εvv 0 )][;0(~ 200

jkijk vρNε i

jkjkijk δuu 0 )][;0(~ 200

jkijk uρNδ

)][;0(~ 200j

ij fρNφi

jjij φff 0

ikk

ik θhh 0 )][;0(~ 200

kik hρNθ

ii ωww 0 )][;0(~ 200 wρNω i

iii qfeU TiTiiT )()( xhUe

Reconciliation h, f, piTTi feeh )(

iiTTii wp ])[(21 feeh

RAS-based Solution

iii qfeU TiTiiT )()( xhUe iiTi pw eh )(iiiT pw fe

SUPPLY-SIDE APPROACH

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Randomization of V

eVq ii eVx Tii )(

Randomization of u, f, h, w i

jkjkijk εvv 0 )][;0(~ 200

jkijk vρNε i

jkjkijk δuu 0 )][;0(~ 200

jkijk uρNδ

)][;0(~ 200j

ij fρNφi

jjij φff 0

ikk

ik θhh 0 )][;0(~ 200

kik hρNθ

ii ωww 0 )][;0(~ 200wρNωi

RAS-based Solution

USE-SIDE APPROACH

])/()[(~ ehhh Tiiiii wp ]/)[(~ iTiiii wp feff

iii feUq ~ TiiTTi )~()( hUex

ii qeV ~ iTi xeV )~(

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00 )(: jk

ijk mmEH

0jkm is obtained by using the observed values ( 00000 ,,,, qhfVU , 0x , and 0w ).

Each run i (= 1, …, N) thus generates a value ijkm (for which we have 12 candidates)

Ns

mmt

jk

jkjkjk /

0

ijk

Nijk mm 1Σ )1/()(Σ 2

12 Nmms jk

ijk

Nijk

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Results. Supply-side approach 1,000 simulations M1 M2 M3 M4 M5 M6 Bias 0.0006 0.0002 0.0002 0.0007 0.0007 0.0007 Standard deviation 0.0044 0.0018 0.0015 0.0066 0.0055 0.0062 Average t-statistic 6.0139 5.3763 11.0997 4.8217 5.2223 5.6144 % Cells significant bias 96.99 97.25 95.16 94.99 96.74 91.98

Results. Use-side approach 1,000 simulations

M1 M2 M3 M4 M5 M6

Bias 0.0000 0.0000 0.0001 0.0019 0.0009 0.0026 Standard deviation 0.0034 0.0018 0.0017 0.0157 0.0070 0.0153 Average t-statistic 2.3823 1.3341 -0.9567 5.3359 5.2241 3.6351 % Cells significant bias 75.19 64.82 79.06 97.74 98.50 94.74

ITMC X C FPSI X I ITMI X C PTMI X C FISI X I PTMC X C

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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!

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