Multiplier Decomposition in a SAM framework: an application to the Italian economic system

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Multiplier Decomposition in a SAM framework an
application to the Italian economic system
Marisa Civardi (University of Milan-Bicocca) Renat
a Targetti Lenti (University of Pavia)

• Monitoring Italy
• ISAE
• Rome, June 3th4th 2009

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Multiplier Decomposition and Inequality Analysis

• Aims of the research
• Analysing the linkages between the countrys
  productive structure and personal income
  distribution
• Studying the impact of alternative policies on
  personal income distribution and inequality
• Evaluating direct and indirect effects of
  exogenous income injections on household mean
  income and distribution
• Assessing the equalizing and unequalizing forces
  behind changes in the distribution of personal
  income

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Using a SAM as a Simulation Model for
Distributive Policy Analysis

• Structural Analysis of income generation from
  value added creation to redistribution of
  disposable households income
• Links between the structure of production and
  distribution of income to factors and to
  households
• Decomposition of direct and indirect effects of
  exogenous shocks to the economic system
• Analysis of transmission patterns of exogenous
  effects to different accounts of the SAM
  production activities, factors and institutions
• Framework valid at the macro and the meso level

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Using a SAM as a simulation model

• Methodology
• I step
• deriving the accounting fixed-price (global)
  multiplier matrix
• II step
• microscopic decomposition of the single element
  mij of the global multiplier matrix M

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The SAM-approach and the Decomposition of
Accounting Multipliers

• Multiplicative Decompostion of Global Multiplier
  Matrix Pyatt-Round (1979) and Bottiroli Civardi
  (1988)
• Aggregate SAM distinction between an exogenous
  (Governement, Rest of the World, Capital) and
  four endogenous (Production Activities, Factors,
  Institutions and Commodities) accounts

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• Derivation of Sam-based multipliers (1)
• Distinguishing between endogenous and exogenous
  accounts, row and column totals constraints can
  be expressed
• t n x
• t5 l y
  
• with
• n row totals of endogenous accounts of matrix T
• x row totals of exogenous account
• l row total of leakages
• y column total of exogenous account

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• Derivation of Sam-based multipliers (2)
• Dividing each element of submatrices Ti,j for the
  correspondent element of the column total vector
  tj, we obtain Aij
• A T -1
• Matrix A Accounting Multipliers Matrix
• showing the average expenditure propensities of
  endogenous accounts
• Substituting we obtain
• t At x

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• Global Multipliers Matrix (M)
• Solving for t we obtain
• t (I-A)-1 x Mx
• with M (I-A)-1
• Matrix M Accounting fixed-price Global
  Multipliers Matrix
• representing the average responses of
  endogenous accounts (t) to exogenous injections
  (x).
• Each element of M (mij) captures the direct and
  indirect effect of a unit exogenous injection to
  account j on account i.

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• Decomposition of Matrix M
• A multiplicative decomposition of M in three
  submatrices
• dt Mdx M3M2M1dx
• with
• M1 (within block transfer effects)
• M2 (across block open-loop effects)
• M3 (between block closed-loop effects)

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• Following Stone (1985) it is possible to rewrite
• t Mx M3 M2M1x in the additive form
• as the sum of four non-negative matrices.
• M I( M1- I)(M2-I) M1 (M3 - I) M2M1

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The decomposition of the single component mij of M

• Pyatt-Round (2006) e Bottiroli Civardi-Targetti
  Lenti (2007) decomposition in microscopic
  detail of the single element mij of global
  multiplier matrix M
• where
• mij di M dj di M3 M2 M1 dj
• i unit vector
• rdi M3 DM2 s M1 dj
• The single element mij is obtained bordering
  matrix M2 with row i of matrix M3 (vector r)
  and column j of matrix M1 (vector s)

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Analysis of an exogenous shock on Activities
accounts to Households accounts

• Considering HAmij as an element of the
  sub-matrix MHA of M where
• j is a Production Activity
• i is a Households group
• HAmij (di 3MHH 2MHA 1MAA dj)
• Or
• r di 3MHH D 2MHA s1MAA dj

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Analysis of an exogenous shock

• Example
• j A1 (Agriculture), A4 (Food Processing), A14
  (Building) and A21 (Education).
• i H1 and H5
• A unit exogenous change in income of Activity j
• generates
• a multiplicative effect on block of Activities
• (within group effect, captured by element s)
• this effect is transmitted to Institutions
• (open-loop effect, captured by 2MHA)
• finally, due to circular flow of income, the
  effect is transferred to Household i (closed-loop
  effect, captured by element r)

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Further decomposition of mij

• Row and column totals of the
  transformation of HAmij allow distinguishing four
  distinct effects
• Direct-Direct
• (from Aj on Hi)
• Indirect-Direct
• (from each Aj on Hi, with j?j)
• Direct-Indirect
• (from Aj on each Hi with i?i)
• Indirect-Indirect
• (from each Aj on each Hi with j?j and i?i)
• These four effects allow reconstructing the
  entire path of transmission of a exogenous
  injection to the endogenous account income Aj on
  the income of the endogenous account Hi

Ds
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the SAM for Italy (year 2002)
Application to the ITALIAN Economy

• Structure of the SAM
• 23 production sectors
• 22 commodities (12 private consumptions, 10
  collective consumptions)
• 5 factors of production
• 13 Institutions (5 household groups 3 domestic
  Enterprises 5 government branches)
• 7 exogenous accounts

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• The matrix of the Households incomes has been
  obtained from the HIWS biannual survey of the
  Bank of Italy (Banca dItalia, 1999, 2001, 2003)
  adjusted (reestimated by IRPET) combining the
  surveys of 1998, 2000, and 2002.
• The vector of the primary incomes has been
  obtained from disposable income running a fiscal
  micro simulation model (MIRTO) which allows
  calculating the fiscal debt for each household
  unit.

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• Following the Stone decomposition method we
  determined the three additive components of M
• M1 (M1-I)
• M2 (M2-I)M1
• M3 (M3-I)M2M1
• Matrix M1 represent the immediate effect of dxi
  on dtj, M2 the cross effects and M3 the between
  effects.

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Additive components of M
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• In Italy the across effects dominate the
  between effects, as a consequence of an highly
  integrated productive system. In all cases and
  for each Household quintile the M2 values
  result higher than M3 values.
• The second interesting result refer to the so
  called invariance in income distribution. The
  ratios between the last quintile M3 value and
  the values for the others quintiles are
  approximately identical in any simulation.

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• The calculus of the multiplier blocks MH,A of
  matrix M allows quantifying the effects on the
  Households income from an exogenous injection of
  income directed to the Activity Sectors.
• A reading by columns shows the contribution of
  each Activity to the rise of the income of the
  Household sector as a whole. This contribution of
  different Activities is fairly differentiated.
• Some Activities (A1, A2, A20, A21) show a column
  total slightly higher than one. In particular, in
  the sectors A20 (Public Administration) and A21
  (Education) the impact on the Households income
  is larger probably because e the relatively
  higher share of the value added going to labour.

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Table A1 - Global Multiplier matrix M
Household/Activities block MH,A.
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• The calculus of the multiplier blocks MH,H of
  matrix M allows quantifying the effects on the
  Households income from an exogenous injection of
  income directed to the Households Sectors.
• The diagonal elements of the matrix blocks MH,H
  represent the immediate income multiplier within
  each Household group generated by an additional
  unit of disposable income exogenously attributed
  to the group itself. They are obviously all
  higher than one, and show a monotonically growing
  trend from the first to the last quintile.
• This means that, as a consequence of an exogenous
  injection of additional income equally done, the
  final effect within the poorest group is always
  weaker than within the richest.

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Table A2 - Multiplier matrix M3
Household/Household block.
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• A reading by columns shows the contribution of
  each Household group to the rise of the income of
  the Household sector as a whole. The contribution
  of different Household group is fairly
  differentiated and the lowest quintile
  contributing the most.
• A reading by row of MH,H multiplier blocks shows
  the different ability of Households to generate
  income for each Household group. These abilities
  are considerably differentiated over the various
  quintiles.

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• The row totals values show a monotonically upward
  trend. The value of the total multiplier for the
  first quintile is rather small it is equal to
  1,12217, instead for the last quintile the value
  is equal to 2,23985.
• These values indicate
• the reduced potential of the system to
  distribute income to the poorest.
• the degree of inequality in the income
  distribution over Endogenous Institution
  Households which can be considered structural.

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Table A3 First decomposition of mij
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• Table A3 shoes that the total direct effect is
  alternatively 0,0315 from A1 to H1 (81,36 of the
  total) and 0,0137 (85,88 of the total) from A4
  to H1.
• The share of this direct effect rises when the
  household group is H5 it is equal to 0,5415 (the
  85,88) of the total from A1 to H5 and equal to
  0,1354 (the 35,22 of the total) from A4 to H5.
• From A14 the capacity to stimulate directly the
  income of H1 or H5 is alternatively 0,0221 and
  0,0619. From A21 to H1 is 0,0619 while to H5 is
  0,3666.

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• The values in Table A3 show that the direct
  linkages of the first quintile, both with the
  Agriculture sector than with the other sectors
  result weaker than the linkages with the last
  quintile.
• The direct effect toward H5 from A1 is
  significantly higher than from A4. The opposite
  happens when we consider the group H1.
• These values explain the inequality in the
  personal income distribution depending on the
  inequality in the property of Factors,.

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Table A4 Second decomposition of mij
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• In each j-th column, the indirect effects are
  obtained as difference between the values of the
  column total of matrix and the values of
  corresponding direct effect.
• It is equal to 0,078 from A1 to H1 as the
  consequence of the level of activation of incomes
  of other households.
• This effect, instead, is equal to 0,0836 for H5.
  In the case of A4 the effect on H1 due to the
  activation of incomes of the other households is
  0,0195 while for H5 is 0,2597.
• It is worth to notice that, in the case of our
  exercise, the indirect effects are always
  significantly lower than the direct ones.

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Conclusions 1

• SAM-based Multiplier analysis allows studying the
  structural features of personal income
  distribution
• This approach offers a useful methodology to
  study the macro and the meso components of the
  distribution of personal income which should be
  complementary to the analysis of inequality at
  the micro level
• The Italian productive sector seems to have a
  very low power to generate income for the poorest
  groups.

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Conclusions 2

• The new decomposition of global multiplier
  matrix applied in this paper allows capturing
  direct and indirect effects of exogenous
  injections on household income
• Decomposing multipliers helps identifying
  equalizing and unequalizing forces behind policy
  interventions
• It is possible to reconstruct not only transfer,
  open and closed-loop effects but also all the
  path of transmissions of exogenous injection
  throughout the interdependent system.

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