Post on 07-Nov-2020
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Phenomenology of HouseholdConsumption Patterns:
Stylized Facts in Search of Explanations
L. Alessi M. Barigozzi M. Capasso G. Fagiologiorgio.fagiolo@sssup.it
https://mail.sssup.it/∼fagiolo
Sant’Anna School of Advanced Studies, Pisa, Italy
Max-Planck-Institute of EconomicsJena, April 2007
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Research Areas
Agent-Based Computational Economics (ACE)Methodology: Empirical validation in ACE modelsApplications: ACE models and policy
NetworksGame-theoretic models of strategic network formationEmpirical properties of economic networks
Industrial dynamics: models and empirical evidenceFirm locational choices and the geography of industrial agglomerationFirm size and growth dynamics: the role of financial constraints
Statistical properties of micro/macro dynamicsStatistical properties of household consumption patternsStatistical properties of country-output growth
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Research Areas
Agent-Based Computational Economics (ACE)Methodology: Empirical validation in ACE modelsApplications: ACE models and policy
NetworksGame-theoretic models of strategic network formationEmpirical properties of economic networks
Industrial dynamics: models and empirical evidenceFirm locational choices and the geography of industrial agglomerationFirm size and growth dynamics: the role of financial constraints
Statistical properties of micro/macro dynamicsStatistical properties of household consumption patternsStatistical properties of country-output growth
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Research Areas
Agent-Based Computational Economics (ACE)Methodology: Empirical validation in ACE modelsApplications: ACE models and policy
NetworksGame-theoretic models of strategic network formationEmpirical properties of economic networks
Industrial dynamics: models and empirical evidenceFirm locational choices and the geography of industrial agglomerationFirm size and growth dynamics: the role of financial constraints
Statistical properties of micro/macro dynamicsStatistical properties of household consumption patternsStatistical properties of country-output growth
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Research Areas
Agent-Based Computational Economics (ACE)Methodology: Empirical validation in ACE modelsApplications: ACE models and policy
NetworksGame-theoretic models of strategic network formationEmpirical properties of economic networks
Industrial dynamics: models and empirical evidenceFirm locational choices and the geography of industrial agglomerationFirm size and growth dynamics: the role of financial constraints
Statistical properties of micro/macro dynamicsStatistical properties of household consumption patternsStatistical properties of country-output growth
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
My Homepage
https://mail.sssup.it/∼fagiolo/welcome.html
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Motivations
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Demand and Economic Theory
Understanding “demand side” of the marketHow does individual demand for different commodities getformed?How does market demand behave?How and why do individual and aggregate consumptionpatterns change across time?Crucial for industrial and macroeconomics dynamicsPositive and normative aspects
Traditional approach in economicsGeneral equilibrium model (GEM)A long list of problematic issuesRationality, interactions, stability vs. dynamics, . . .An instrumentalist perspective?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Demand and Economic Theory
Understanding “demand side” of the marketHow does individual demand for different commodities getformed?How does market demand behave?How and why do individual and aggregate consumptionpatterns change across time?Crucial for industrial and macroeconomics dynamicsPositive and normative aspects
Traditional approach in economicsGeneral equilibrium model (GEM)A long list of problematic issuesRationality, interactions, stability vs. dynamics, . . .An instrumentalist perspective?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Neoclassical Demand Theory and Empirics
Neoclassical approach vs. testable implicationsWhat testable implications?Two classes
Direct implicationsIndirect implications
“Direct” implicationsLaw of demandWald’s axiom
“Indirect” implicationsEstimating econometric specifications consistent withmodels of household expenditure behavior based onstandard neoclassical assumptionsDemand systems (Deaton and Muellbauer)
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Neoclassical Demand Theory and Empirics
Neoclassical approach vs. testable implicationsWhat testable implications?Two classes
Direct implicationsIndirect implications
“Direct” implicationsLaw of demandWald’s axiom
“Indirect” implicationsEstimating econometric specifications consistent withmodels of household expenditure behavior based onstandard neoclassical assumptionsDemand systems (Deaton and Muellbauer)
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Neoclassical Demand Theory and Empirics
Neoclassical approach vs. testable implicationsWhat testable implications?Two classes
Direct implicationsIndirect implications
“Direct” implicationsLaw of demandWald’s axiom
“Indirect” implicationsEstimating econometric specifications consistent withmodels of household expenditure behavior based onstandard neoclassical assumptionsDemand systems (Deaton and Muellbauer)
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
“Direct” implications
Across-household heterogeneity becomes crucialLaw of demand and Wald’s axiom can be obtained as theoutcome of aggregation of not-necessarily-rationalbehaviors (Hildenbrand, 1994)Aggregate well-behaved demand schedules as theoutcome of badly-behaved individual demand schedules
Empirical work on fish markets (Kirman, Gallegati, . . . )
Micro GEM machinery not necessary after all. . .
Neoclassical approach vs. heterogeneityGEM as an heterogeneous-agent model?Heterogeneity is completely irrelevant in the model butappears to be
a persistent feature of real-world patternscrucial to understand demand patterns
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
“Direct” implications
Across-household heterogeneity becomes crucialLaw of demand and Wald’s axiom can be obtained as theoutcome of aggregation of not-necessarily-rationalbehaviors (Hildenbrand, 1994)Aggregate well-behaved demand schedules as theoutcome of badly-behaved individual demand schedules
Empirical work on fish markets (Kirman, Gallegati, . . . )
Micro GEM machinery not necessary after all. . .
Neoclassical approach vs. heterogeneityGEM as an heterogeneous-agent model?Heterogeneity is completely irrelevant in the model butappears to be
a persistent feature of real-world patternscrucial to understand demand patterns
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
“Indirect” implications
A falsification of neoclassical demand theory?Econometric specifications heavily rely on (mathematical)restrictions with poor economic contentSome of them are typically rejected (symmetry,homogeneity)Implications of rational choice theory are to some extentmisspecified
Alternative models?Standard theory is not considered falsified because thereare no rival theories (Gilbert, 1991)Alternatives:
Prospect theory and beyond (Kahneman, Tversky, Thaler)“Evolutionary Theories” (Saviotti, Witt, Brenner, . . . )
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
“Indirect” implications
A falsification of neoclassical demand theory?Econometric specifications heavily rely on (mathematical)restrictions with poor economic contentSome of them are typically rejected (symmetry,homogeneity)Implications of rational choice theory are to some extentmisspecified
Alternative models?Standard theory is not considered falsified because thereare no rival theories (Gilbert, 1991)Alternatives:
Prospect theory and beyond (Kahneman, Tversky, Thaler)“Evolutionary Theories” (Saviotti, Witt, Brenner, . . . )
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Alternative Demand Theories vs. Empirical Data
Empirically testable implicationsNot always able to deliver fresh stylized factsExample: Aversi et al. (1999)
Agent-based model with imitation and innovation inconsumption patternsAble to replicate several stylized facts (demand law, Wald’saxiom, Engel-type dynamics of budget shares, etc.)
General problem with ABM: empirical validation?
A paradoxical situationMost of empirics is (standard) theory-drivenStandard theory is not really as good as desiredExisting alternatives often tackling testable implications ofstandard modelsLack of robust alternative theories delivering fresh stylizedfacts and/or facing with theory-free facts
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Alternative Demand Theories vs. Empirical Data
Empirically testable implicationsNot always able to deliver fresh stylized factsExample: Aversi et al. (1999)
Agent-based model with imitation and innovation inconsumption patternsAble to replicate several stylized facts (demand law, Wald’saxiom, Engel-type dynamics of budget shares, etc.)
General problem with ABM: empirical validation?
A paradoxical situationMost of empirics is (standard) theory-drivenStandard theory is not really as good as desiredExisting alternatives often tackling testable implications ofstandard modelsLack of robust alternative theories delivering fresh stylizedfacts and/or facing with theory-free facts
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Goals
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Phenomenology of demand dynamics
Looking for stylized factsGoing back to the dataAttempt to pursue a theory-free explorationSingle out robust statistical properties of householddemand dynamicsLevels of disaggregation: commodities, households,geography, etc.
A phenomenological approach ?Extremely fruitful perspective
Kaldor in macroeconomicsEconophysics of financial marketsIndustrial dynamics
From facts to theory (and not the other way around)Does a theory-free fact really exist?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Phenomenology of demand dynamics
Looking for stylized factsGoing back to the dataAttempt to pursue a theory-free explorationSingle out robust statistical properties of householddemand dynamicsLevels of disaggregation: commodities, households,geography, etc.
A phenomenological approach ?Extremely fruitful perspective
Kaldor in macroeconomicsEconophysics of financial marketsIndustrial dynamics
From facts to theory (and not the other way around)Does a theory-free fact really exist?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Characterizing heterogeneity: Research Questions
1 Cross-Section Distributions of ConsumptionExpenditure
Fitting distributions with known density familiesStability of shape/parameters over
Time periodsCommodity classesIncome classesGeographical areas
2 Cross-Section Consumption/Income DistributionsHow does the double distribution look like?Shape of the income density over years, etc.Are the two distributions drawn from the same density?What statistical properties of C-distribution are explained byY-distribution?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Characterizing heterogeneity: Research Questions
1 Cross-Section Distributions of ConsumptionExpenditure
Fitting distributions with known density familiesStability of shape/parameters over
Time periodsCommodity classesIncome classesGeographical areas
2 Cross-Section Consumption/Income DistributionsHow does the double distribution look like?Shape of the income density over years, etc.Are the two distributions drawn from the same density?What statistical properties of C-distribution are explained byY-distribution?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Characterizing heterogeneity: Research Questions
3 Budget Shares (BS)How do budget shares change through time?Fitting distributions with known density families (Beta?)Any evidence in favor of multimodality?Stability of shape/parameters over
Time periodsCommodity classesGeographical areas
4 Budget Shares vs. IncomeHow do BS distributions change across different incomeclasses?How does BS-income relation change across time?Towards an analysis of Engel’s curves
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Characterizing heterogeneity: Research Questions
3 Budget Shares (BS)How do budget shares change through time?Fitting distributions with known density families (Beta?)Any evidence in favor of multimodality?Stability of shape/parameters over
Time periodsCommodity classesGeographical areas
4 Budget Shares vs. IncomeHow do BS distributions change across different incomeclasses?How does BS-income relation change across time?Towards an analysis of Engel’s curves
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Data
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Data
Survey of Italian Households’ Income and WealthProvided by Bank of ItalyHousehold data8 waves from 1989 to 2004About H = 8000 households in each waveRepresentative of the Italian populationSub-sample of about 4000 panel households
Data StructureDemographicsDisposable income, expenditures, savings, wealthConversion to Euros (for 1989-2000)Deflated and weighted
Sample weights provided by Bank of Italy
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Data
Survey of Italian Households’ Income and WealthProvided by Bank of ItalyHousehold data8 waves from 1989 to 2004About H = 8000 households in each waveRepresentative of the Italian populationSub-sample of about 4000 panel households
Data StructureDemographicsDisposable income, expenditures, savings, wealthConversion to Euros (for 1989-2000)Deflated and weighted
Sample weights provided by Bank of Italy
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Data
Disaggregation: Expenditure categoriesData disaggregated among several expenditure categoriesTraditional consumption aggregates available
Expenditure categories1 Nondurable goods
Food
2 Durable goods3 Insurance premia
Life insuranceHealth insurancePrivate pensions
Casualty insurance
4 House rent5 Real estate extraordinary maintenance6 Mortgage repayments7 Down payments for real estate
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Data
Disaggregation: Expenditure categoriesData disaggregated among several expenditure categoriesTraditional consumption aggregates available
Expenditure categories1 Nondurable goods
Food
2 Durable goods3 Insurance premia
Life insuranceHealth insurancePrivate pensions
Casualty insurance
4 House rent5 Real estate extraordinary maintenance6 Mortgage repayments7 Down payments for real estate
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results: Income
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of real income (1/3)
Moments vs. YearsMoments very stable across wavesDistributions are quite skewedSome evidence for fat tails
10000
15000
20000
25000
30000
35000
1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Waves
Rea
l Inc
ome
Mean StdDev
0
2
4
6
8
10
12
14
1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
WavesSkewness Kurtosis
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of Real Income (2/3)
Fitting income distributionsReal income is lognormal in the bodyPower law in the tail?
This confirms previous results for ItalyCastaldi and Dosi (2004), Clementi and Gallegati (2005)
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of real income (3/3)
Fitting income distributionsReal income is lognormal in the bodyPower law in the tail?
This confirms previous results for ItalyCastaldi and Dosi (2004), Clementi and Gallegati (2005)
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results: Consumption
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of Consumption Levels (1/5)
Moments vs. YearsAlmost all moments are fairly stableWeakly increasing mean and std devEuro did not heavily impact on shapesDistributions are highly skewed
0
1
10
100
1000
1987 1989 1991 1993 1995 1997 1999 2001 2003 2005
Waves
Logs
of T
otal
Con
sum
ptio
n
Mean Std. Dev. Min Max Skewness Kurtosis
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of Consumption Levels (2/5)
Fitting consumption distributionsConsumption distributions can be well approximated by alognormal density
in the aggregate for all waves
1990 1992 1994 1996 1998 2000 2002 20046
8
10x 10
−4 Mean
1990 1992 1994 1996 1998 2000 2002 20041.4
1.6
1.8
2x 10
−6 Variance
1990 1992 1994 1996 1998 2000 2002 20042
2.5
3Skewness
1990 1992 1994 1996 1998 2000 2002 20046
8
10
12Kurtosis
1990 1992 1994 1996 1998 2000 2002 20040
0.5
1x 10
−5 Min
1990 1992 1994 1996 1998 2000 2002 20045
6
7x 10
−3 Max
Figure 1: Evolution of moments1, min and max of kernel density.
0.0
02.0
04.0
06K
erne
l den
sity
0 500 1000 1500Consumption
1989 1991 1993 19951998 2000 2002 2004
Figure 2: Evolution of kernel density.
3
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of Consumption Levels (3/5)
Fitting consumption distributionsConsumption distributions can be well approximated by alognormal density
in the aggregate for all waves−
10−
8−
6−
4−
20
2 4 6 8lnc
emp lognorm
(a) 1989−
10−
8−
6−
4−
20
0 2 4 6 8lnc
emp lognorm
(b) 1991
−10
−8
−6
−4
−2
0
2 4 6 8lnc
emp lognorm
(c) 1993
−10
−8
−6
−4
−2
0
0 2 4 6 8lnc
emp lognorm
(d) 1995
−10
−8
−6
−4
−2
0
2 4 6 8 10lnc
emp lognorm
(e) 1998
−10
−8
−6
−4
−2
0
0 2 4 6 8lnc
emp lognorm
(f) 2000
−10
−8
−6
−4
−2
0
0 2 4 6 8lnc
emp lognorm
(g) 2002
−10
−8
−6
−4
−2
0
2 4 6 8lnc
emp lognorm
(h) 2004
Figure 4: Zipf plots.
5
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of Consumption Levels (4/5)
Fitting consumption distributionsConsumption distributions can be well approximated by alognormal density
in the aggregate for all waves−
10−
8−
6−
4−
20
−2 0 2 4 6lncons
emp lognorm
(a) 1989
−10
−8
−6
−4
−2
0
−2 0 2 4 6lncons
emp lognorm
(b) 1991
−10
−8
−6
−4
−2
0
−2 0 2 4 6lncons
emp lognorm
(c) 1993
−10
−8
−6
−4
−2
0
−2 0 2 4 6lncons
emp lognorm
(d) 1995
−10
−8
−6
−4
−2
0
−2 0 2 4 6lncons
emp lognorm
(e) 1998−
10−
8−
6−
4−
20
−2 0 2 4 6lncons
emp lognorm
(f) 2000
−10
−8
−6
−4
−2
0
−2 0 2 4 6lncons
emp lognorm
(g) 2002
−10
−8
−6
−4
−2
0
−2 0 2 4 6lncons
emp lognorm
(h) 2004
Figure 8: Zipf plots.
10
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Distributions of Consumption Levels (5/5)
Fitting consumption distributionsConsumption distributions can be well approximated by alognormal density
for almost all categories
1990 1992 1994 1996 1998 2000 2002 20040.02
0.03
0.04Mean
1990 1992 1994 1996 1998 2000 2002 20041
2
3
4x 10
−3 Variance
1990 1992 1994 1996 1998 2000 2002 20041.5
2
2.5
3Skewness
1990 1992 1994 1996 1998 2000 2002 20044
6
8
10Kurtosis
1990 1992 1994 1996 1998 2000 2002 20040
2
4
6x 10
−4 Min
1990 1992 1994 1996 1998 2000 2002 20040.1
0.2
0.3Max
Figure 9: Evolution of moments1, min and max of kernel density.
0.0
5.1
.15
.2.2
5K
erne
l den
sity
0 10 20 30 40Food
1989 1991 1993 19951998 2000 2002 2004
Figure 10: Evolution of kernel density.
12
1990 1992 1994 1996 1998 2000 2002 20041
1.5
2
2.5x 10
−3 Mean
1990 1992 1994 1996 1998 2000 2002 20041
2
3
4x 10
−5 Variance
1990 1992 1994 1996 1998 2000 2002 20043.5
4
4.5
5Skewness
1990 1992 1994 1996 1998 2000 2002 200415
20
25
30Kurtosis
1990 1992 1994 1996 1998 2000 2002 20040
1
2x 10
−5 Min
1990 1992 1994 1996 1998 2000 2002 20040.02
0.03
0.04Max
Figure 13: Evolution of moments1, min and max of kernel density.
0.0
1.0
2.0
3.0
4K
erne
l den
sity
0 200 400 600 800Durable Goods
1989 1991 1993 19951998 2000 2002 2004
Figure 14: Evolution of kernel density.
16
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income vs. Consumption Distribution Tails
Tail behaviorIncome seems to have tails much fatter than consumption
010
0000
2000
0030
0000
Tot
al C
onsu
mpt
ion
0 100000 200000 300000Real Income
Quantile−Quantile plot 1989
010
0000
2000
0030
0000
4000
00T
otal
Con
sum
ptio
n
0 100000 200000 300000 400000Real Income
Quantile−Quantile plot 2004
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
North-South differences in consumption patterns
Aggregate consumption distributionsSo far: stability vs. time, heterogeneity vs. categoriesWhat happens when we study consumption distributions for northern,central and southern Italy?Sensible differences across Italian macro-regions, somewhat shrinkingacross time
1990 1995 2000100
150
200
250Mean
1990 1995 20000
2
4
6
8x 10
4 Variance
1990 1995 20001.5
2
2.5
3
3.5Skewness
1990 1995 20005
10
15
20Kurtosis
Figure 6: Blue line: North Italy, red line: Central Italy, green line: South Italy.
10
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income and Consumption: Some Remarks (1)
Persistent heterogeneityHousehold consumption behaviors are heavilyheterogeneousAverage behavior is not appropriate to describe entiredistributionConsumption distribution driven by income distribution?
Univariate distributionsConsumption and income seem to be drawn from differentdistributions, at least in their right tailHow can one explain the different behavior in the tail?
Aggregation effectsModeling univariate processesModeling bivariate process
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income and Consumption: Some Remarks (1)
Persistent heterogeneityHousehold consumption behaviors are heavilyheterogeneousAverage behavior is not appropriate to describe entiredistributionConsumption distribution driven by income distribution?
Univariate distributionsConsumption and income seem to be drawn from differentdistributions, at least in their right tailHow can one explain the different behavior in the tail?
Aggregation effectsModeling univariate processesModeling bivariate process
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results:Income and Consumption
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income-Consumption (Double) Distribution
Well-Shaped Double DensityRelatively stable over timeVery skewed on both dimensions (logs scale!)
log(C) log(Y
)
Density
log(C) log(Y
)
Density
1989 2004
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income-Consumption (Double) Distribution
Correlation Income-ConsumptionPositive, strong, but weakly declining
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Waves
Cor
r(C
,Y)
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income-Consumption (Double) Distribution
Income-Consumption: Functional formAppears to be linearRobustly across timeFor majority of categories (but not all!)
Aggregate Consumption
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income-Consumption (Double) Distribution
Income-Consumption: Functional formAppears to be linearRobustly across timeFor majority of categories (but not all!)
Food Non Durable
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conditioning on income levels
Consumption conditional distributionsC|Y -distributions are very heterogeneousPoor (1st decile) vs. Rich (10th decile)
For exampleVariance: Poor=low, Rich=highSkewness: Poor=high, Rich=lowShape: Power-law, bimodality, etc. across poor/rich andconsumption categories
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conditioning on income levels
Consumption conditional distributionsC|Y -distributions are very heterogeneousPoor (1st decile) vs. Rich (10th decile)
For exampleVariance: Poor=low, Rich=highSkewness: Poor=high, Rich=lowShape: Power-law, bimodality, etc. across poor/rich andconsumption categories
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conditioning on income levels
Moments of consumption conditional distributionsMean of C|Y increases with Y more than linearlyStd dev of C|Y increases with Y more than linearly
2.5 3 3.5 4 4.5 5 5.5 6 6.50
50
100
150
200
250
300
350
400
450Average consumption conditioned on income classes
2.5 3 3.5 4 4.5 5 5.5 6 6.50
20
40
60
80
100
120
140
160
180
200Consumption standard deviation conditioned on income classes
1989 1991 1993 1995 1998 2000 2002 2004
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Income and Consumption: Some Remarks (2)
(Y,C) Double distributionWell-shapedDisplays interesting structureMoments of consumption are very heterogeneous acrossincome classes and across categoriesWhat are the determinants of this heterogeneity?
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results: Budget Shares
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Budget share of household h for good i
ωi,h =ci,h
yh0 < ωi,h < 1
RemarksDividing by total consumption does not change resultsDeflated aggregates
Fitting BS with Beta distribution
f (ω) =ωa−1(1− ω)b−1
β(a, b)
β is the Beta(a,b) function
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Budget share of household h for good i
ωi,h =ci,h
yh0 < ωi,h < 1
RemarksDividing by total consumption does not change resultsDeflated aggregates
Fitting BS with Beta distribution
f (ω) =ωa−1(1− ω)b−1
β(a, b)
β is the Beta(a,b) function
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Budget share of household h for good i
ωi,h =ci,h
yh0 < ωi,h < 1
RemarksDividing by total consumption does not change resultsDeflated aggregates
Fitting BS with Beta distribution
f (ω) =ωa−1(1− ω)b−1
β(a, b)
β is the Beta(a,b) function
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Beta fitsGenerally good (exception: durable goods)High across-households heterogeneityHeterogeneity not a consequence of income
Year μ σ2 s κ1989 0.75979 0.027062 -0.81569 3.19771991 0.75288 0.02507 -0.75862 3.13481993 0.71413 0.034225 -0.66473 2.82631995 0.73963 0.031236 -0.75692 3.01931998 0.68262 0.038045 -0.55943 2.62872000 0.69919 0.036047 -0.61401 2.72752002 0.70378 0.036269 -0.63428 2.75122004 0.72686 0.033778 -0.71791 2.9133
Table 3: Estimated Moments.
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3
Budget shares
19891991199319951998200020022004Beta
Figure 1: Kernel density of budget shares. The dotted line represents the betadistribution with as parameters the time average of the estimated a and b.
4
Year μ σ2 s κ1989 0.14203 0.020923 1.4507 4.98631991 0.16358 0.0257 1.3274 4.46271993 0.14841 0.026417 1.4959 4.97751995 0.18172 0.03585 1.3062 4.16691998 0.17897 0.03471 1.317 4.22192000 0.18103 0.034866 1.301 4.1732002 0.17162 0.033796 1.3723 4.4032004 0.15821 0.030083 1.4524 4.7383
Table 12: Estimated Moments.
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
7
8
9
Budget shares
19891991199319951998200020022004Beta
Figure 4: Kernel density of budget shares. The dotted line represents the betadistribution with as parameters the time average of the estimated a and b.
10
Aggregate Durable
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Beta fits vs. timeBS distributions fairly stable across time
1989 1991 1993 1995 1998 2000 2002 2004
100
101
year
tot consumptionnondurablesfooddurablesinsurances
a
Figure 7: Time evolution of parameter a (Log-scale on vertical axis).
1989 1991 1993 1995 1998 2000 2002 200410
0
101
102
103
year
tot consumptionnondurablesfooddurablesinsurances
b
Figure 8: Time evolution of parameter b (Log-scale on vertical axis).
14
1989 1991 1993 1995 1998 2000 2002 2004
100
101
year
tot consumptionnondurablesfooddurablesinsurances
a
Figure 7: Time evolution of parameter a (Log-scale on vertical axis).
1989 1991 1993 1995 1998 2000 2002 200410
0
101
102
103
year
tot consumptionnondurablesfooddurablesinsurances
b
Figure 8: Time evolution of parameter b (Log-scale on vertical axis).
14
a-Parameter b-Parameter
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
BS moments vs. time: Some interesting trendsFood: Average BS decreasing since 1993Insurance: Average BS increasingTotal Consumption: Variance increasing
1990 1992 1994 1996 1998 2000 2002 200410
−2
10−1
100
Total ConsumptionNondurablesFoodDurablesInsurances
Figure 9: Time evolution of mean of budget shares. Note that the vertical axis is inlog scale.
15
1990 1992 1994 1996 1998 2000 2002 20040
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Total ConsumptionNondurablesFoodDurablesInsurances
Figure 10: Time evolution of standard deviation of budget shares.
16
Mean Std Dev
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Heterogeneity of BS distributionsBS distributions are fairly stable over time. . .. . . but they are profoundly heterogeneous acrosscategoriesA taxonomy of BS distributions?
HIGH a LOW aHIGH b Nondurables Insurances
FoodLOW b Aggregate Durables
Consumption
Table: Classification of goods according to their BS beta distribution.
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Unconditional Budget Shares
Heterogeneity of BS distributionsMapping the (a,b) taxonomy into momentsTaxonomy in terms of
high/low mean (µ) and std dev (σ)high/low skewness (s) and kurtosis (κ)
LOW (s, κ) HIGH (s, κ)
LOW (µ, σ) Nondurables InsurancesFood
HIGH (µ, σ) Agg.Cons.Durables
Table: Classification of goods according to BS moments.
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conditional Budget Shares
Conditioning BS on income: Total ConsumptionMoments of propensity to consume
Mean and Kurtosis decreaseStd dev and Skewness increase
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5
0.65
0.7
0.75
0.8
0.85Total Consumption: Average BS conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 11 11.50.12
0.14
0.16
0.18
0.2
0.22Total Consumption: BS standard deviation conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5−1.5
−1
−0.5
0Total Consumption: BS skewness conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 11 11.51
2
3
4
5
6Total Consumption: BS kurtosis conditioned on income classes
1989 1991 1993 1995 1998 2000 2002 2004
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conditional Budget Shares
Conditioning BS on income: Total ConsumptionMoments of propensity to consume
Mean and Kurtosis decreaseStd dev and Skewness increase
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5
0.65
0.7
0.75
0.8
0.85Total Consumption: Average BS conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 11 11.50.12
0.14
0.16
0.18
0.2
0.22Total Consumption: BS standard deviation conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 11 11.5−1.5
−1
−0.5
0Total Consumption: BS skewness conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 11 11.51
2
3
4
5
6Total Consumption: BS kurtosis conditioned on income classes
1989 1991 1993 1995 1998 2000 2002 2004
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conditional Budget Shares
Conditioning BS on income: Good CategoriesFood: Moments of propensity to consume
Mean and std dev decreaseSame result for non durable goodsHeterogeneous findings for other categories
7 7.5 8 8.5 9 9.5 10 10.5 110.01
0.02
0.03
0.04
0.05
0.06Food: Average BS conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 110
0.02
0.04
0.06
0.08
0.1Food: BS standard deviation conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 110
5
10
15Food: BS skewness conditioned on income classes
7 7.5 8 8.5 9 9.5 10 10.5 110
50
100
150
200Food: BS kurtosis conditioned on income classes
1989 1991 1993 1995 1998 2000 2002 2004
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Conclusions
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Summary
A preliminary statistical explorationData from Bank of Italy survey (8 waves)Looking for stylized facts on household consumption behaviorsStatistical properties of interesting distributionsObjects of analysis: consumption, income and budget sharesCross-section (households) vs. dynamic (waves) perspectiveAggregate consumption vs. good categoriesGeographical breakdown
A characterization ofUnivariate income and consumption distributionsDouble (Y,C) distributionConditional consumption distributionBudget shares
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Summary
A preliminary statistical explorationData from Bank of Italy survey (8 waves)Looking for stylized facts on household consumption behaviorsStatistical properties of interesting distributionsObjects of analysis: consumption, income and budget sharesCross-section (households) vs. dynamic (waves) perspectiveAggregate consumption vs. good categoriesGeographical breakdown
A characterization ofUnivariate income and consumption distributionsDouble (Y,C) distributionConditional consumption distributionBudget shares
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results (1/2)
IncomeLognormal in the body, power law in the tail?Stable over time
ConsumptionWell-approximated by lognormal distributionsHousehold consumption patterns are persistently heterogeneousBoth in the aggregate and for the majority of categoriesStable over timeSensible geographical difference
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results (1/2)
IncomeLognormal in the body, power law in the tail?Stable over time
ConsumptionWell-approximated by lognormal distributionsHousehold consumption patterns are persistently heterogeneousBoth in the aggregate and for the majority of categoriesStable over timeSensible geographical difference
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results (2/2)
Income-ConsumptionDouble: Well-shaped, relatively stable over time(Y,C): Strong positive correlationLinear for almost all categoriesIncome has tails fatter than consumptionAs Y increases, average and standard deviation increase more thanlinearlyMoments of C|Y very heterogeneous across categories
Budget sharesWell-approximated by Beta distributionsFairly stable across time but with some weak trendsIt is possible to taxonomize categories with respect to moments of BSdistributions (and Beta parameters)Income-conditioned BS display interesting trends
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
Results (2/2)
Income-ConsumptionDouble: Well-shaped, relatively stable over time(Y,C): Strong positive correlationLinear for almost all categoriesIncome has tails fatter than consumptionAs Y increases, average and standard deviation increase more thanlinearlyMoments of C|Y very heterogeneous across categories
Budget sharesWell-approximated by Beta distributionsFairly stable across time but with some weak trendsIt is possible to taxonomize categories with respect to moments of BSdistributions (and Beta parameters)Income-conditioned BS display interesting trends
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
What’s next (1/2)
Stylized facts?Checking robustness of findings with respect to
Goodness of fit techniques vs. alternative distributionsExtreme-value theory and bi-modality testsAlternative (dis)aggregation of good categoriesCross-country comparisons
From facts to theoryWhich type of theory?Microfoundation of individual behaviors: How much?
Neoclassical vs. evolutionary vs. Hildenbrand
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
What’s next (1/2)
Stylized facts?Checking robustness of findings with respect to
Goodness of fit techniques vs. alternative distributionsExtreme-value theory and bi-modality testsAlternative (dis)aggregation of good categoriesCross-country comparisons
From facts to theoryWhich type of theory?Microfoundation of individual behaviors: How much?
Neoclassical vs. evolutionary vs. Hildenbrand
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
What’s next (2/2)
Replication vs. ExplanationTheory should jointly replicate stylized factsBrock’s critique: unconditional objectsReplicate many stylized facts is betterTrade off between replication and explanationReplication: finding the minimal model replicating stylized factsExplanation: finding causal relationships rooted in microeconomics
Inspiration: Simon’s theory of firm growth?Stochastic models of household income-consumption dynamicsAggregation across goods and householdsStylized facts explained by means of generic forces driving consumptionand income dynamicsInnovation, imitation, etc.Towards a reduced-form of Aversi et al. (1999) model
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
What’s next (2/2)
Replication vs. ExplanationTheory should jointly replicate stylized factsBrock’s critique: unconditional objectsReplicate many stylized facts is betterTrade off between replication and explanationReplication: finding the minimal model replicating stylized factsExplanation: finding causal relationships rooted in microeconomics
Inspiration: Simon’s theory of firm growth?Stochastic models of household income-consumption dynamicsAggregation across goods and householdsStylized facts explained by means of generic forces driving consumptionand income dynamicsInnovation, imitation, etc.Towards a reduced-form of Aversi et al. (1999) model
Introduction Motivations Goals Data Income Consumption Income and Consumption Budget Shares Conclusions
That’s all
Thanks!