A presentation by José Marín Arcas (Independent Authority for Fiscal Responsibility, Spain) at the Workshop on Public Finances in Riga on 21 June 2016

1. REDISTRIBUTION AND STABILIZATION
OF PER CAPITA INCOME OF
HOUSEHOLDS BY REGIONS
José Marín

2. THE ISSUE
2
Primary income is redistributed through the tax and transfer system:
Primary income - Income taxes + transfers = Disposable income
 Is disposable income per capita of households by regions more
equally distributed and more stable than primary income?

3. 3
REVIEW OF THE LITERATURE
• Methodological approach: data driven econometric
analysis of panel data:
 Redistributive effects, variables in levels, cross-section dimension
 Stabilizing effects, variables in changes, time series dimension
• Main result: the estimated effects are very different
 In size, redistributive effects are higher and more precisely
estimated than stabilizing effects
 In composition, there are puzzling differences:
 In the same country, some operation may contribute negatively to
redistribution and positively to stabilization
 The same operation may contribute in one direction to redistribution
or stabilization in one country and in the contrary direction in
another country
• No explanations for these differences

4. 4
MAIN FINDING OF THIS PAPER
The redistributive and stabilising effects of the existing tax and
transfers systems can be replicated by equivalent linear taxes
Three implications
• Simplify estimation method and interpretation of the results
• Compare estimated with observed redistributive effects
• Explain stabilisation effects as a combination of fiscal
impulses (not always stabilising) and drag effects (always
stabilising)

5. 𝑇 𝑦𝑖 = 𝜏 ∙ 𝑦𝑖 − 𝐼 → 𝑑𝑖= 𝑦𝑖 − 𝑇 𝑦𝑖 = 1 − 𝜏 ∙ 𝑦𝑖 +𝐼
The constant of contraction:
1. is independent from primary income distribution
2. is the ratio of the coefficients of variation of
disposable income to primary income
3. is the elasticity of disposable to primary income
𝑑
T
y
y
UNDERSTANDING THE EFFECTS OF THE LINEAR TAX
450 line
The distribution of disposable income is a linear
contraction of the distribution of primary income
𝑑 𝑖−𝑑 𝑚
𝑑 𝑚
= 𝜂 ∙
𝑦 𝑖−𝑦 𝑚
𝑦 𝑚
→ 𝜂 =
1 − 𝜏
1 − 𝑡 𝑚
Redistribution and stabilization effect =1 − 𝜂
-I
I
2  Observed redistribution =1 − 𝜂 = 1 −
𝐶𝑉 𝑑
𝐶𝑉 𝑦
1  Estimated redistribution =1 − 𝜂 = 1 −
1−𝜏
1−𝑡 𝑚
=
𝜏−𝑡 𝑚
1−𝑡 𝑚
=
𝐼
𝑑 𝑚
3  Estimated stabilisation =1 − 𝜂 = 1 −
Δ𝑑
Δ𝑦
𝑑 𝑚
𝑦 𝑚
𝜏𝑦 − 𝐼
1 − 𝜏 𝑦 + 𝐼

6. UNITED STATES EQUIVALENT LINEAR TAX 2012
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New York
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Utah
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y = 0,8122x + 9823
R² = 0,9805
24000
29000
34000
39000
44000
49000
54000
59000
24000 29000 34000 39000 44000 49000 54000 59000
DISPOSABLEINCOME
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Maine
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New York
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Utah
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Alaska
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Maine
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y = 0,1829x - 2111
R² = 0,8251
y = -0,0049x + 7712
R² = 0,0015
2000
3000
4000
5000
6000
7000
8000
9000
10000
24000 29000 34000 39000 44000 49000 54000 59000
INCOME TAX PERSONAL TRANSFERS
6
𝑑𝑖 = 𝑦𝑖 − 𝑇 𝑦𝑖 + 𝑇𝑅 𝑦𝑖 =
= 1 − 𝜏1 − 𝜏2 ∙ 𝑦𝑖 + 𝐼1 + 𝐼2
𝑑𝑖 = 1 − 0.1829 − −0.049 ∙ 𝑦𝑖 + 2111 + 7112
Estimated redistributive effect: 24.9%
(9823/39397) = 24.9%
Income tax contribution:
(2111/39397) = 5.4 pp
Current transfers contribution:
(7712/39397) = 19.6 pp
Observed redistributive effect: 24.2%
Coefficient of variation CV(y) = 20.7%
Coefficient of variation CV(d) = 15.7%
Ratio 15.7/20.7 = 0.758
 Observed effect is 1- 0.758 = 24.2%45 degrees
𝑑𝑖 = 1 − 𝜏 ∙ 𝑦𝑖 +𝐼
SIMPLE ESTIMATION METHOD: LINEAR REGRESIONS
24.9% ≈ 24.2%
T 𝑦𝑖 = 𝜏1 ∙ 𝑦𝑖 − 𝐼1
TR 𝑦𝑖 = 𝜏2 ∙ 𝑦𝑖 + 𝐼2

7. 7
INCOME INEQUALITY
Observed effect = 1 −
𝐶𝑉 𝑑
𝐶𝑉 𝑦
Estimated effect =
𝐼
𝑑 𝑚
REDISTRIBUTION EFFECT
COMPARING OBSERVED AND ESTIMATED REDISTRIBUTION

8. 8
COMPARING REDISTRIBUTION EFFECTS ACROSS COUNTRIES

9. 9
UNDERSTANDING STABILISING EFFECTS
Need to separate changes in income from changes in the equivalent linear tax

10. 10
DEFINING FISCAL IMPULSE AND DRAG EFFECTS
Observed
Estimated
E2
E1
D2
D1
Automatic change
Fiscal impulse
Y1 Y2
Δ Disposable income ≡ Δ Primary income – Fiscal drag + Fiscal impulse + Residual
Estimated change: 𝐸2 𝑌2 − 𝐸1 𝑌1 = 𝐼2 + 1 − 𝜏2 ∙ 𝑌2 − 𝐼1 + 1 − 𝜏1 ∙ 𝑌1
𝐸2 𝑌1 − 𝐸1 𝑌1 = 𝐼2 − 𝐼1 − 𝜏2 − 𝜏1 ∙ 𝑌1
𝐸2 𝑌2 − 𝐸2 𝑌1 = 1 − 𝜏2 ∙ 𝑌2 − 𝑌1
 Primary income change: 𝑌2 − 𝑌1
 Fiscal drag: 𝜏2 ∙ 𝑌2 − 𝑌1
Automatic change:
Observed change ≡ Estimated change + Residual

11. 11
Primary income growth
P&E
C&E
P&R
C&R
Automatic change line
Disposable
Income
Growth
EXPLAINING STABILISING EFFECTS
450 line => elasticity = 1
Average
Is the elasticity of disposable to primary income less than one?
Primary
drag
Impulse
Disposable

12. 12
STYLISED FACTS:
• Expansionary fiscal effects on average (growth of disposable income higher than primary)
• Comparatively small fiscal drag (22.7%, slope of automatic changes line 0.773)
• Countercyclical effects in all years (all points are in the countercyclical regions)
• Restrictive fiscal impulses only in 2011 (only point below the automatic change line)
• Fiscal impulses always stabilizing (overriding the drag only when primary growth weak)
• Very systematic effects (relatively high correlation coefficient on observed effects: 0.83)
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 AVERAGES
Primary income 2,3 0,0 2,6 5,0 4,4 6,4 4,1 1,7 -6,6 1,2 6,5 5,3 2,7
Disposable income 3,7 3,5 3,8 5,1 3,5 5,7 3,8 3,6 -1,4 1,8 4,2 4,4 3,5
Difference: 1,4 3,5 1,3 0,1 -1,0 -0,7 -0,4 2,0 5,2 0,6 -2,3 -0,9 0,7
Impulse 1,9 3,4 1,8 1,2 0,2 0,8 0,8 2,6 3,5 1,0 -0,4 0,4 1,4
Drag -0,5 0,0 -0,5 -1,1 -1,1 -1,5 -1,0 -0,4 1,3 -0,3 -1,7 -1,3 -0,7
UNITED STATES. STABILISING EFFECTS
-7
-5
-3
-1
1
3
5
7
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Drag Impulse
Residual Primary income
Disposable income Automatic change
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
y = 0,4559x + 2,23
R² = 0,8279
y = 0,773x - 0,06
R² = 0,9992
-6
-4
-2
0
2
4
6
8
-7 -5 -3 -1 1 3 5 7

13. 13
Observed Estimated Drag Impulse Estimated
United States 24 24 23 32 54
United Kingdom 25 25 25 39 64
Germany 41 42 40 3 43
France 44 48 47 -34 13
Italy 17 18 16 -5 11
Spain 17 19 17 6 23
REDISTRIBUTIVE STABILISING
AVERAGE REDISTRIBUTIVE AND STABILISING EFFECTS (%) 2000-2012
INTERNATIONAL COMPARISONS OF AVERAGE EFFECTS
CONCLUSIONS
• Estimated redistributive effects are very close to the observed ones
• Stabilising effects are a combination of fiscal impulses and drag effects
• Drag effects are automatic stabilisers and very close to redistribution effects
• Fiscal impulses can be stabilizing or destabilizing
• Estimated stabilizing effects can diverge from redistributive effects due to
discretionary fiscal impulses

14. 14
RESERVE SLIDES

15. 15
ELT RESIDUALS ARE PERSISTENT

16. 16
CONTRIBUTIONS TO THE RESIDUALS ARE ALSO PERSISTENT

17. 17

18. 18

19. 19

20. 20
• Expansionary fiscal effects on average (0.5 pp)
• There are no observations of points in the procyclical regions (NE and SW)
• The fiscal drag is small, like in the US, and much smaller tan in FR and GE
• Stabilising effects have been determined by prudent fiscal impulses in six years (2003-2007 and 2010)
• Fiscal impulses have strengthened substantially the automatic effects on average (0.75 vs. 0.36 slopes)
• Not very systematic effects (Low correlation coefficient)
• Very strong response to the Great Recession, with delayed effects in 2010
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 AVERAGE
Primary income -- 4,8 2,5 4,3 4,1 4,7 4,1 5,5 0,7 -1,3 5,0 0,3 0,6 2,9
Disposable income -- 5,0 3,2 3,7 2,9 3,7 3,8 4,5 2,4 3,1 4,5 0,6 3,0 3,4
Difference: -- 0,1 0,7 -0,6 -1,2 -1,0 -0,3 -1,0 1,7 4,4 -0,5 0,3 2,4 0,4
Drag -- -1,1 -0,6 -1,0 -1,0 -1,2 -1,0 -1,5 -0,2 0,3 -1,4 -0,1 -0,2 -0,7
Impulse -- 1,2 1,4 0,4 -0,3 0,2 0,8 0,4 1,9 4,1 0,9 0,5 2,6 1,2
17. UNITED KINGDOM. STABILISING EFFECTS
2001
2002
2003
2004
2005
2006 2007
2008
2009
2010
2011
2012
y = 0,3612x + 2,2996
R² = 0,5141
y = 0,7493x + 0,0077
R² = 0,9987
-2
-1
0
1
2
3
4
5
6
-2 -1 0 1 2 3 4 5 6
POLICYSTANCE
-2
-1
0
1
2
3
4
5
6
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Drag Impulse Residual
Primary income growth Dispsable income growth Automatic change

21. 21
• Neutral fiscal effects on average
• Procyclical impulses overriding the fiscal drag in 2001 and 2010
• Second highest fiscal drag, after France
• Fiscal impulses less stabilising than in the UK and the US
• Less systematic effects (lower correlation coefficient) than in the US, but more than in the UK
• Very small fiscal impulses in 2006-2008
• Timid response to the Great Recession in 2009, with delayed procyclical effects in 2010
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 AVERAGE
Primary income -- 2,7 -0,6 1,9 0,7 1,7 3,8 3,1 3,9 -2,0 2,4 5,0 2,7 2,1
Disposable income -- 4,4 0,3 2,7 1,6 1,9 2,3 1,7 2,4 -0,9 2,8 3,8 1,8 2,1
Difference: -- 1,7 0,9 0,9 0,9 0,2 -1,5 -1,4 -1,5 1,2 0,4 -1,2 -0,9 0,0
Drag -- -1,1 0,2 -0,8 -0,3 -0,6 -1,5 -1,2 -1,5 0,9 -1,0 -2,0 -1,1 -0,8
Impulse -- 3,0 0,6 1,7 1,2 1,2 -0,1 -0,2 -0,2 0,4 1,3 0,7 0,1 0,8
22. GERMANY. STABILISING EFFECTS
2001
2002
2003
2004 2005
20062007
2008
2009
2010
2011
2012
y = 0,5684x + 0,8748
R² = 0,6434
y = 0,5816x + 0,021
R² = 0,9992
-1
0
1
2
3
4
5
-3 -2 -1 0 1 2 3 4 5
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
5,0
6,0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Drag Impulse Residual
Primary income growth Dispsable income growth Automatic change

22. 22
• Marginally expansionary effects on average
• Procyclical effects (or close) in almost every year, except 2009
• Highest fiscal drag of all countries
• Fiscal impulses neutralising or overriding the fiscal drag in most years
• Very systematic effects (Highest correlation coefficient)
• Timid response to the Great Recession (0.5 pp), with delayed effects in 2010
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 AVERAGE
Primary income 4,2 2,6 1,9 3,2 2,4 3,9 4,1 2,7 -2,0 1,6 2,2 0,9 2,3
Disposable income 4,4 3,3 1,8 3,7 2,1 3,8 4,6 2,5 -0,5 1,8 1,5 0,1 2,4
Difference: 0,3 0,7 0,0 0,5 -0,3 -0,2 0,5 -0,1 1,6 0,2 -0,7 -0,8 0,1
Impulse 2,0 1,7 0,7 1,8 0,7 1,8 2,5 1,4 0,5 1,0 0,5 -0,4 1,2
Drag -1,7 -1,0 -0,8 -1,3 -1,0 -2,0 -2,0 -1,4 1,0 -0,8 -1,1 -0,5 -1,0
8. FRANCE. STABILISING EFFECTS
-3
-2
-1
0
1
2
3
4
5
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Drag Impulse Residual
Primary income Disposable income Automatic change
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
y = 0,8737x + 0,418
R² = 0,8546
y = 0,5334x + 0,0302
R² = 0,9771
-1
0
1
2
3
4
5
-3 -2 -1 0 1 2 3 4 5

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25. 25

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28. 28
Poghosyan, T., Senhadji, A., and Cottarelli, C. (2015): “The role of fiscal transfers in smoothing regional
shocks”, chapter 2 of Carlo Cottarelli and Martine Guerguil (Eds.): “Designing a European Fiscal Union.
Lessons from the experience of fiscal federations”, International Monetary Fund. Published by Routledge

29. 29

30. 30
LINEAR INCOME TAX REDISTRIBUTION

31. 31
GINI INDEX AND ITS IMPLICIT INDIFFERENCE CURVES

32. 32

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