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Labor Income EstimationLabor Income Estimation＆　＆　Smoothing Method Smoothing Method

bybyMaliki Maliki 真力真力

NTA Workshop INTA Workshop IOctober 2005October 2005

Organization

Labor Income AllocationSmoothing Method: LowessIntra-household Transfers (next week)

Labor Income Estimation

Labor Income Definition

All compensation that is return to work effort

Labor earningsEmployer-provided benefitsTaxes paid to the government on behalf of the employeesPart of entrepreneurial income (return to labor)

Labor Income Definition

i i i i iYL YLE YLF YLX YLS= + + +

YLi labor income of individual iYLEi sum of earnings YLFi fringe benefitsYLXi other labor incomeYLSi share of entrepreneurial income

Entrepreneurial Income

i iYLS SEγ=

If entrepreneurial income is available for individual i, its share to individual`s labor is calculated as:

where return to labor for individual is γ (estimated to be 2/3)

SEi self-employment income

YLSi return to labor income

Entrepreneurial Income – Household Level

If return to self-employment reported on ahousehold, return to labor of individual i in thehousehold j has to be estimated

Regress household entrepreneurial income on the total number of self-employed individual in the household (Wj)

Estimation of Entrepreneurial Income

fjj j f

j

WSE W

Wα β= + ∑

Wfj number of self-employed individuals in the household jin age group f ( starting from 10)

and ;

j fjf

W W= ∑

Estimation of Entrepreneurial Income (cont ..)

fi fijij j

f fjf

WSE SE

Wβ

β=

∑

Individual coefficients are summed by household; Share of this household sum is calculated for each individual

fijW Dummy variable, working = 1, zero otherwise

Production - Indonesia 1996

0

50,000

100,000

150,000

200,000

250,000

300,000

1 9 17 25 33 41 49 57 65 73 81 89 97

Mon

htly

(Rp) Earnings

Self-Employment

Labor Income

Labor Income Taiwan 1978 - 2002

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

1 5 9

13

17

21

25

29

33

37

41

45

49

53

57

61

65

69

73

77

81

85

Mon

thly

(TW

)

Source: Comfort Sumida

Adjust to National Level

f f fYL YL Nζ=

NIPA

f ff

YYL Nζ = ∑

1. Estimate the age profile2. Multiply by the population

3. Adjust to National IncomeAnd Product Account (NIPA) total

Adjusted Labor Income

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

88

Rela

tive

to M

ax

Taiwan

Indonesia

Intra-household Transfers

List of NTA Table

T1. Flow AccountT1.1 Lifecycle DeficitT1.2 Asset ReallocationT1.3 Public TransfersT1.4 Private Transfers

T2. Wealth Account

Total Domestic by Age Foreign

0-4 … 90+

Inter-vivos Transfers

Inflows

Outflows

Health

Inflows

Outflows

Other Consumption

Inflows

Outflows

Outflows

Intra-household Transfers

Education

Inter-household transfers

Inflows

Table 1.4 Private Transfers

Transfers Outflow

AssumptionsDeficit of household members are financed by taxing members` surplus including the household headConsumption of housing and durable assets are financed by intra-household transfers from head to household members

Define Disposable Income

( ) ( ) ( ) ( ), , , ,g fd l cash xY i j Y i j i j i jτ τ= + +

( ) ( ),d di

Y j Y i j= ∑

Individual i disposable income

Household j disposable income

( ),lY i j

( ),gcash i jτ

( ),fx i jτ

Labor income

Public transfers

Inter-household transfers

Define Surplus

Surplus if

( ) ( ), ,fd currentY i j c i j>

( ) ( ) ( ) ( ) ( ), ,, [ , , ] f

d current

fd current Y i j c i j

i j Y i j c i j D+>

Δ = −

( ) ( ), ,fd currentY i j c i j

D>

= 1 if the condition in the subscriptis met and zero otherwise

Define Deficit

Deficit if

( ) ( ), ,fd currentY i j c i j<

( ) ( ) ( ) ( ) ( ), ,, [ , , ] f

d current

fcurrent d Y i j c i j

i j c i j Y i j D−<

Δ = −

Calculate the Inflow

( ) ( ) 1, , ( , )frasset ii j i j c i j Dτ + −

≠= Δ +

( ) ( ),fr fr

ij i jτ τ+ += ∑

Intra-household transfers inflow to individual i is to current deficit plus the value of asset consumption for non-heads

for household j

Calculate the Tax

( ) ( )( )min 1,

fr jtax j jτ +

+⎛ ⎞

= ⎜ ⎟Δ⎝ ⎠

Tax rate assessed on each individual`s surplus

Calculate Intra-household Transfers Outflow

( ) ( ) ( ) 1, ,frii j tax j i j Dτ − +≠= − Δ

( )( ) ( )

( ) ( )( ) ( ) ( )

,~

1

, ,

, ( )1,

asset hfri

i j i j

tax j i j c jj D

j j Dτ

− +

+

−=− +

Δ >Δ

⎡ ⎤Δ +⎢ ⎥= −+ Δ − Δ⎢ ⎥⎣ ⎦

Non-head

Head

Calculate Intra-household Sector Inflow

( ) ( )( , , ), , ,( , )

fr current

current

c i j xi j x i jc i j

τ + −= Δ

( ) 1, , ( , , )frii j x c i j x Dτ +≠=

Current consumption

Asset consumption

Calculate Intra-household Sector Outflow

( ) ( )( ) ( ),

, , ,fr

currentfr frcurrentfr

current

j xi j x i j

jτ

τ ττ

+− −

+=

( ) ( ) 1, , ( , ) (1, , )frii j x c j x c j x Dτ −== −

Current consumption

Asset consumption

Intra-Household Transfers Outflow

-80,000

-70,000

-60,000

-50,000

-40,000

-30,000

-20,000

-10,000

0

0 5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

Month

ly

Education

Health

Other Consumption

Asset Consumption

Intra-Household Transfers Inflow

0

10,000

20,000

30,000

40,000

50,000

60,000

1 6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

Month

ly

education

health

other consumption

Assets

Intra-Household Transfers Inflow and Outflow Excluding OtherConsumption

-10,000

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

8,000

10,000

0 5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95Month

ly

Education Inflow Healtｈ Inflow

Assets Inflow Education Outflow

Health Ouflow Assets Outflow

LOWESS

Smoothing: Lowess

Lowess: locally weighted scatter plot smoothEach smoothed value is determined by neighboring data points defined within the spanCommand in STATA

Lowess yvar xvar, bwidth(#) gen(newvary) nograph

Lowess Procedure (cont ..)

Define spanA window of neighboring points to include in the smoothing calculation for each data pointThis window moves across the data set as the smoothed response value is calculated for each predictor valueA large span increases the smoothness but increases the resolution of the smoothed data set

Lowess Procedure (cont ..)

Compute the regression weights for each point in the span

33

1( )

ii

x xwd x

⎛ ⎞−⎜ ⎟= −⎜ ⎟⎝ ⎠

x predictor value associated with the response value to be smoothedxi the nearest neighbors of x as defined by the spand(x) distance along the abscissa from x to the most distant predictor

value within the span

The data point to be smoothed has the largest weight and the most influence on the fit

Data point outside the span have zero weight and no influence on the fit

Lowess Procedure (cont .. )

A weighted linear least squares regression is performedLowess uses a first degree polynomialThe smoothed value is given by the weighted regression at the predictor value of interest

1. Span does not change2. Regression weight function might not be symmetric about the data point to be smoothed3. Regression weight is depending on the nearest neighbors

a/b using asymmetric functionc/d using symmetric function

LOWESS

0

10

20

30

40

50

60

70

80

90

100

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

百

際

bwidth = 1

bwidth = 0.08

Non-smoothed

bwidth = 0.3

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

data

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

data

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

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