phenomenology of household consumption patterns ...introduction motivations goals data income...

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. [email protected]

https://mail.sssup.it/∼fagiolo

Sant’Anna School of Advanced Studies, Pisa, Italy

Max-Planck-Institute of EconomicsJena, April 2007


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


My Homepage

https://mail.sssup.it/∼fagiolo/welcome.html


Motivations


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?


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)


“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


“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, . . . )


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


Goals


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?


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?


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


Data


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


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


Results: Income


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


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)


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)


Results: Consumption


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



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




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




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




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


0.0

5.1

.15

.2.2

5K

erne

l den

sity

0 10 20 30 40Food

1989 1991 1993 19951998 2000 2002 2004


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


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


16


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


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


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


Results:Income and Consumption


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



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)



Income-Consumption: Functional formAppears to be linearRobustly across timeFor majority of categories (but not all!)

Aggregate Consumption



Income-Consumption: Functional formAppears to be linearRobustly across timeFor majority of categories (but not all!)

Food Non Durable


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


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


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?


Results: Budget Shares


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



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



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


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


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


b

Figure 8: Time evolution of parameter b (Log-scale on vertical axis).

14

a-Parameter b-Parameter



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



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.



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.


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


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


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


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


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


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


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


That’s all

Thanks!

phenomenology of household consumption patterns ...introduction motivations goals data income...

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