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Consumption patterns of Polish households – cross-sectional analysis The 26th INFORUM World Conference Katarzyna Walerysiak-Grzechowska Faculty of Economics and Sociology Chair of Public Finances University of Lodz Poland

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Page 1: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

Consumption patterns of Polishhouseholds – cross-sectional analysis

The 26th INFORUM World ConferenceKatarzyna Walerysiak-GrzechowskaFaculty of Economics and Sociology

Chair of Public FinancesUniversity of Lodz

Poland

Page 2: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Outline

1. Background: aging population in Poland2. Data: demographic factors3. A cross-section consumption function4. Methods5. Results6. Further work

Page 3: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Aging population in Poland

Main reasons :• low birth rates: Polish woman has 1.3 children (on average). It would take

2.1 to replace generations.• lengthening the average life expectancy: from almost 68 in 1960 to above

78 (last year).• emigration: over the last two decades, a number of Poles have left their

country.

Page 4: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Aging population in Poland• In 2050, half of the population in Poland will be over the age of 50.• The share of the population above 65 is expected to almost double by 2030. With the current retirement age,

the working-age population would shrink by more than 15 percent by 2035.• As the population is aging, it has also started to decline: from about 38.6 million in 1995, to 38 million in 2010,

to an expected 32 million in 2050.

39,141,9

48,652,5

2013 2020 2035 2050

year

Median age of population*

*Source: Central Statistic Office of Poland

Impact of demographic changes:labor supply, demand for educational and medical services, revenues and expenses of the social security system and consumption.

0

20

40

60

80

100

2013 2014 2015 2020 2025 2030 2035 2040 2045 2050

Dependency ratio

Non-working Pre-working Post-working

Page 5: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Purpose

How demografic factors and age influence on the patterns of Polish

households consumption?

The objective of this research is to identify households consumption

patterns in Poland.

Page 6: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

The HBS is a cross-section survey of Polish household data conducted by the Central Statistical Office (CSO) of Poland.Since 1957, the CSO has been conducting a budget survey based on the representative method.Since 1992 the HBS is based on territorial approach with monthly rotation of households.

The data have rich information about household i.e.:• expenditures by categories,• sources of income,• household characteristics such as type of residence, area of residence,

characteristics of household members.

Data: Household budget survey (HBS)

Page 7: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

0

50

100

150

200

250

300

350

400

450

village city

place of residenceFood

Beverages

Alcoholic beverages &CigarettesClothes & Footwear

House & Utilities

Health

Transportation&CommounicationRecreation

Education

Others

0

100

200

300

400

500

600

700

1 2 3-4 5+

household size

Average monthly households expenditures per capita in PLN by:

*Source: Central Statistic Office of Poland, HBS 2013

Page 8: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

0

50

100

150

200

250

300

350

400

450

500

<35 35-55 >55

age of household head

Food

Beverages

Alcoholic beverages

Cigarettes

Clothes & Footwear

House & Utilities

Health

Transportation&CommounicationRecreation

Education

Others

0

100

200

300

400

500

600

<hight hight >hight

education of household head

Average monthly households expenditures per capita in PLN by:

*Source: Central Statistic Office of Poland, HBS 2013

Page 9: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

0

50

100

150

200

250

300

350

400

450

500

emp

loye

e

farm

er

seff

-em

plo

yed

pen

sio

ner

livin

g o

n u

ne

arn

ed s

ou

rces

socio-economic group of household head

Food

Beverages

Alcoholic beverages & Cigarettes

Clothes & Footwear

House & Utilities

Health

Transportation&CommounicationRecreation

Education

Others

0

100

200

300

400

500

600

1 2 >2

income earners

Average monthly households expenditures per capita in PLN by:

*Source: Central Statistic Office of Poland, HBS 2013

Page 10: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

𝐶𝑖ℎ = (𝛼𝑖0 +

𝑗=1

5

𝛼𝑖𝑗𝑌𝑗ℎ +

𝑘=1

14

𝛽𝑖𝑘𝐷𝑘ℎ) (

𝑔=1

8

𝑤𝑔𝑛𝑔ℎ) + 𝑢𝑖 ,

𝐶𝑖ℎ - household h’s consumption of good i,

𝑌𝑗ℎ - amount of household h’s per capita income within jth income bracket,

𝐷𝑘ℎ - kth demographic dummy variable in household h, represented by a zero-one,

𝑛𝑔ℎ - number of family members in age group g in household h,

𝑢𝑖 - disturbance term with assumption of independently and identically distributed acrosshouseholds for the good i,

𝛼𝑖0, 𝛼𝑖𝑗, 𝛽𝑖𝑘, 𝑤𝑔 - coefficients to be estimated, they represent marginal propensity to consume in

each income bracket, demographic effects, and Adult Equivalency Weights (AEW), respectively.

Estimation equation

PLEC- Piecewise Linear Engel Curve weighted size of household h for each good

Page 11: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Income brackets (each contains 20% of total households):B1 = [0 – 612,8] PLN, B2 = [612,81 – 846,83] PLN, B3 = [846,84 – 1124,42] PLN, B4 = [1124,43 – 1558,36] PLN, B5 = [1558,37 – ∞) PLN.

Demographic factors:• place of residence: village, city;• household size: 1, 2, 3-4, 5 and above;• age of household head: <35, 35-55, > 55;• education of household head: lower than high school, high school, higher than high school;• socio-economic group of household head: employee, farmer, self-employed, retiree or pensioner,

living on unearned sources;• number of income earners: 1, 2, >2.

Age groups: 0-5, 6-15, 16-20, 21-30, 31-40, 41-50, 51-65, 66+

Independent variables

Page 12: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Percentage of zero observationGrains, cereals and cereal products 2,82%Tools and equipment for the garden 73,50%

Bread 0,15%Cleaners and services related to running a household 5,66%

Meet 13,49%Pharmaceutical and medical products, therapeutic equipment 23,58%

Poultry and offal 6,03%Out-patient services 62,63%

Cold meats 0,74%Hospital services 98,93%

Fish and seafood 23,98%Purchase of vehicles 98,38%

Milk and dairy products 0,80%Operation of personal transport equipment 41,79%

Cheese and eggs 0,66%Transport services 64,74%

Butter and other animal fats 20,48%Postal services 93,62%

Vegetable fats 10,05%Telephone equipment 98,10%

Citrus fruits and bananas 15,81%Telephone and telefax services 3,03%

Other fruits and processed fruit 6,89%Audio-visual, photographic and information processing equipment 87,75%

Potatoes 23,77%Other major durables for recreational and culture 99,49%

Other vegetables and mushrooms 0,38%Games, toys, sports equipment 45,30%

Flour, sugar, bakery and confectionery 0,59%Recreational and cultural services 28,67%

Baby foods 92,68%Newspapers, books and stationery 34,05%

Other food products 2,82%Package holidays 91,22%

Non-alcoholic beverages 1,24%Pre-primary and primary education 93,64%

Alcoholic beverages 39,44%Secondary and post-secondary non-tertiary education 97,82%

Tobacco 92,45%Tertiary education 98,58%

Clothes 33,83%Education not definable by level 98,10%

Men's footwear 86,19%Catering services 65,65%

Women's footwear 80,87%Accommodation services 95,90%

Children's footwear 94,80%Hairdressing services 99,66%

Shoe repairs 99,23%Cosmetics, hygiene products and personal care appliances 5,20%

Actual rentals for housing 93,02%Silverware, jewelry, other personal effects 63,09%

Maintenance and repair of the dwelling 79,10%Articles for children 99,61%

Water supply and miscellaneus services relating to the dwelling 6,96%Care for children and the elderly 99,40%

Electricity, gas and other fuels 4,95%Insurance 72,83%

Furniture and furnishing, carpets and other floor covering 88,49%Financial services 75,34%

Household textiles 82,00%Funeral services 99,80%

Household appliances 91,97%Prostitution and other services 97,20%

Glassware, tableware and household utensils 70,10%

Page 13: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

According to Bardazzi, Barnabani (1998), Ding (2006), choices of estimation this nonlinear equation could be carried out with:• nonlinear least square (NLS),• tobit model,• Cragg-Double-Hurdle model,• „probit” model (nonlinear probability model).

Methods

>50% of zeros

<=50% of zeros „PROBIT”

NLS

Page 14: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

PLEC (selected categories)

-0,10

9,27

11,14

12,98

15,93 16,29

-2

0

2

4

6

8

10

12

14

16

18

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

1. Cereals and cereal products

-2,90

16,46

20,0522,66

28,91 29,31

-5

0

5

10

15

20

25

30

35

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

3. Meet

2,44

15,69

17,44

20,24

23,07 23,26

0

5

10

15

20

25

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

7. Milk and dairy products

3,75

17,1819,24

21,97

27,15 27,93

0

5

10

15

20

25

30

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

8. Cheese and eggs

-2,12

24,37

30,65

37,35

48,73 50,25

-10

0

10

20

30

40

50

60

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

15. Flour, sugar, bakery and confectionery

0,88

4,59 4,72

5,35

5,94 6,00

0

1

2

3

4

5

6

7

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

14. Potatoes

Page 15: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

PLEC (selected categories)

6,62

21,23

25,79

31,14

41,2243,03

0

5

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

18_19. Non-alcoholic beverages

-6,75

15,58

26,53

40,32

77,19

87,44

-20,0

0,0

20,0

40,0

60,0

80,0

100,0

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

22. Cigarettes

-13,12

7,29

17,60

25,25

34,35

57,32

-20

-10

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

31. Actual rentals for housing

-7,34

2,67

10,06

20,40

36,17

61,17

-20

-10

0

10

20

30

40

50

60

70

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

35. Furniture and furnishing, carpets and other floor covering

-0,71

1,51

3,30

4,49

11,62

12,95

-2

0

2

4

6

8

10

12

14

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

38. Glassware, tableware and household utensils

-0,86

12,39

19,29

24,36

39,4341,98

-5

0

5

10

15

20

25

30

35

40

45

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

20_21. Alcoholic beverages

Page 16: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

PLEC (selected categories)

-0,120,07

0,170,31

1,35

2,21

-1

0

1

1

2

2

3

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

42. Out-patient services

-84,84

9,81

75,09

181,80

26,53

411,93

-200

-100

0

100

200

300

400

500

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

44. Purchase of vehicles

8,9812,29 13,65

20,43

39,02

50,76

0

10

20

30

40

50

60

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

55. Package holidays

-0,742,93 3,67

15,21

10,16

52,53

-10

0

10

20

30

40

50

60

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

60. Catering services

7,34

25,97

34,18

43,11

69,74

78,30

0

10

20

30

40

50

60

70

80

90

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

63. Cosmetics, hygiene products and personal care appliances

1,261,52

1,81 1,79

8,57

9,47

0

1

2

3

4

5

6

7

8

9

10

0 500 1000 1500 2000

Co

nsu

mti

on

Income per capita (PLN)

66_67. Care for children and the elderly

Page 17: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

AEW (selected categories)

0,59

0,90

1,121,04

1,00 0,990,91

0,81

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

1. Cereals and cereal products

0,39

0,630,75

0,83

1,00

1,41

1,63

1,39

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

3. Meet

1,41

1,13

0,87 0,84

1,001,08

1,17 1,19

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

7. Milk and dairy products

0,51

0,830,93 0,96 1,00

1,151,20

1,11

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

8. Cheese and eggs

0,74

1,161,23

0,941,00

1,40

1,691,60

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

14. Potatoes

1,08

1,32

0,85 0,82

1,001,10

1,26 1,30

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

15. Flour, sugar, bakery and confectionery

Page 18: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

AEW (selected categories)

0,87

1,02

0,93 0,931,00

0,82

0,62

0,44

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

23_26. Clothes

2,62

1,150,90 0,91 1,00

1,15 1,15 1,22

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

40. Cleaners and services related to running a household

1,67

0,700,45 0,56

1,001,14

1,79

3,32

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

41. Pharmaceutical and medical products. Therapeutic equipment

1,61

1,41

0,46

0,64

1,00

0,800,74

0,69

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

52. Games, toys, sports equipment

1,32

6,13

1,85

0,701,00 0,96 1,03

1,61

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

54. Books, textbooks, newspapers, magazines, stationery

1,15

0,42

0,67

0,83

1,000,91

0,700,60

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

63. Cosmetics, hygiene products and personal care appliances

Page 19: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

AEW (selected categories)

0,64

0,480,56

0,88

1,000,95

0,88

0,59

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

45. Operation of personal transport equipment

0,650,80

0,670,83

1,00

1,30

1,48

1,95

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

34. Electricity, gas and other fuels

2,87

2,52 2,45

1,72

1,00

1,44

1,711,54

0-5 6-15 16-20 21-30 31-40 31-40 41-50 51-65

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

44. Purchase of vehicles

0,11

0,89

0,62

0,97 1,00

0,43

0,57 0,60

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

35. Furniture and furnishing, carpets and other floor covering

0,24

0,53

0,79

0,941,00 1,01

0,90

0,73

0-5 6-15 16-20 21-30 31-40 31-40 41-50 51-65

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

49. Telephone and telefax services

0,64

1,47

0,75

0,97 1,00

0,810,75 0,76

0-5 6-15 16-20 21-30 31-40 41-50 51-65 66+

Ad

ult

eq

uiv

alen

cy w

eigh

t

Age group

53. Recreational and cultural services

Page 20: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Cross-section consumption items

place of residence

household sizeage of household

headeducation of household

headsocio-economic group of household head

number of income earners

village 1 25 and above

<35 >55lower than high school

higher than high school

farmer pensionerself-

employed

living on unearne

d sources

1 >2

Grains, cereals and cereal products + + + - - - +

Bread + + - + - + - -

Meet + - - + - + - + - -

Poultry and offal + - + - +

Cold meats + - - - + - - - - -

Fish and seafood + + - - - + + -

Milk and dairy products + + + - - + + -

Cheese and eggs + + + - - - + + - -

Butter and other animal fats + - - - + - + + + + - +

Vegetable fats + + + - + - + - +

Citrus fruits and bananas + + + - - - + - + - -

Other fruits and processed fruit + - - - + + + -

Potatoes + - + + - + + - +

Other vegetables and mushrooms + + + - + - + -

Flour, sugar, bakery and confectionery + - - - -

Baby foods + - - - + + + + - - - + - +

Other food products + + + - - - +

Non-alcoholic beverages - + + - - - + - - + - - +

Alcoholic beverages - + + - + + - - - - +

Tobacco - + + - + - - + + +

Demographics effects

Page 21: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Demographics effects

Cross-section consumption items

place of residence

household sizeage of household

headeducation of household

headsocio-economic group of household head

number of income earners

village 1 25 and above

<35 >55lower thanhigh school

higher than high school

farmer pensioner self-employedliving on

unearnedsources

1 >2

Clothes + - + + - + -

Men's footwear - + + - - - - - - - + - - +

Women's footwear - - - - - - + + - + + - -

Children's footwear - + - + - - + - - - -

Shoe repairs - + + - - - - + - - - - + +

Actual rentals for housing + + + + - + - - - - - - + +

Maintenance and repair of the dwelling + - - - + + + - + + + - + +

Water supply and miscellaneus services relating to the dwelling - + + - - + - + - - - - - +

Electricity, gas and other fuels + - - + + + + - - - - + +

Furniture and furnishing, carpets and other floor covering - - - + + - - + + - - + -

Household textiles + - - + - + + - - + - - + +

Household appliances

Glassware, tableware and household utensils - - + - + - + + + - - - +

Tools and equipment for the garden + + + - + + + + + - - - - -

Cleaners and services related to running a household + + + - - + + -

Pharmaceutical and medical products, therapeutic equipment - + - + + + - +

Out-patient services - + + + + + - - - + - - +

Hospital services + - - + - + - + + - -

Purchase of vehicles + - - + - + - + + - - + +

Operation of personal transport equipment + - - - - - + - - - -

Transport services - + + + + + - + + + - + +

Page 22: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Demographics effects

Cross-section consumption items

place of residence

household sizeage of household

headeducation of household

headsocio-economic group of household head

number of income earners

village 1 25 and above

<35 >55lower thanhigh school

higher than high school

farmer pensionerself-

employed

living on unearnedsources

1 >2

Postal services - - + + - - - - - - - + -

Telephone equipment - + + + - - + - - - - - + +

Telephone and telefax services - + + - - + - + - - + - - +

Audio-visual, photographic and information processing equipment - - + + - + -

Other major durables for recreational and culture

Games, toys, sports equipment + - + - + + - + - - + - + +

Recreational and cultural services + + - - + + -

Newspapers, books and stationery - - - + - - - + + - + - -

Package holidays - - + - + - - + - - + + -

Pre-primary and primary education - - - + - - - + - - + - -

Secondary and post-secondary non-tertiary education - - - + - - - - - - - - - +

Tertiary education - - - + - - + + + - -

Education not definable by level

Catering services - - - + - - + - - - -

Accommodation services + + + + + - + + - -

Hairdressing services - + + - + + - - + - - - + +

Cosmetics, hygiene products and personal care appliances - + + - + + - - + - +

Silverware, jewelry, other personal effects - - - + + - + + - + + + +

Articles for children

Care for children and the elderly - + - + + + + + - - -

Insurance + + + - - + - - + + - - +

Financial services

Funeral services - + + - + - + + + + - +

Prostitution and other services - - - + + - + - + - - - + -

Page 23: Consumption patterns of Polish households cross-sectional ... · 2013 2020 2035 2050 year Median age of population* *Source: Central Statistic Office of Poland Impact of demographic

11

Further works

Further purposes:• Improve result for cross-section estimation: more periods, alternative

estimation techniques?• Cohort analysis and the estimation of cohort effects.• Time-series aggregation and PADS (Perhaps Adequate Demand System)

estimation.