Labor Income Estimation Smoothing Method - … Income.pdf · Labor Income Definition All...
Transcript of Labor Income Estimation Smoothing Method - … Income.pdf · Labor Income Definition All...
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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