Income Convergence in South Africa:
Fact or Measurement Error?
Tobias Lechtenfeld
&
Asmus Zoch
Data
• KwaZulu-Natal Income Dynamics Study (KIDS)
• Provincial study
• 3 waves:1993, 1998 and 2004
• National Income Dynamics Survey (NIDS)
• Reprehensive National
• 2 waves: 2008 and 2010
• Outcome variable: Income change
• Instruments:
• Second lagged income
• Household wealth
• Reported satisfaction
Income Convergence in South Africa: Fact or Measurement Error?
Outline
• Theory and Literature Review
• Empirical Strategy
• Results
• Income Convergence in KwaZulu-Natal
• Income Convergence at National Level
• Source of Measurement Error
• Conclusion
Income Convergence in South Africa: Fact or Measurement Error?
Theory and Literature Review
• Recent papers for micro income dynamics in developing
countries have found :
• „a strong tendency of a regression towards the mean“
• E.g. Fields et al. (2003), Woolard and Klasen (2005).
• However, to make a valid statement about income mobility
one has to take into account measurement error.
• For South Africa:
•
Agüero et al. (2007) note that measurement error could account
for up to 60% of mobility between 1993 and 1998 in the KwaZuluNatal province.
Income Convergence in South Africa: Fact or Measurement Error?
Theory and Literature Review
• Define income mobility as ∆Yi,t ≡ Y2 – Y1
• To determine how initial income influences income change
studies have run regression of the form:
∆Yi,t = α + β1Yi,t-1 + β2Zi, + β3Xi,t-1 + β4Xi,t + εi,t
• In case β1<0 there is conditional convergence if β1>0 there is
conditional divergence
• Yet, if Y is measured with error, such error is present on
both sides of the regression => attenuation bias
Income Convergence in South Africa: Fact or Measurement Error?
Empirical Strategy
• If true income Y*it is not observable and only self-reported
income Yit is available and biased by εit it states:
• Yit = Y*it+ εit
• For income dynamics this means that the initial income
coefficient is also measured with error and can cause an
overestimation of the true effect.
• To solve the problem we follow the suggestion by Antman
and McKenzie (2007) and instrument Yi,t-1using Yi,t-2.
Income Convergence in South Africa: Fact or Measurement Error?
Empirical Strategy
• Run IV regression using KIDS:
∆Ln (Income per Capita)i,t = α + β1Xit + β2Ψit +
β3*ln(Income per Capita)i,t-2 + εit
• If lagged initial income variable is a good instrument, this
regression will give a consistent coefficient β3.
• To test the robustness of the results we use a second
instrument:
∆Ln (Income per Capita)i,t = α + β1Xit + β2Ψit +
β3*ln(Asset index)i,t-1 + εit
Income Convergence in South Africa: Fact or Measurement Error?
Empirical Strategy
• Finally, to test for over-identification we use the full set of
instruments.
• The Hansen J statistic implies that the over-identification
restrictions are valid and the set of instruments is appropriate.
• For the National Income Dynamics Survey (NIDS) there is no
second lag available.
• Therefore, we use again an asset index as well as selfreported satisfaction of the household head.
Income Convergence in South Africa: Fact or Measurement Error?
Table 1: Income Convergence in KwaZulu-Natal Province (KIDS 1998-2004)
OLS
IV
IV
1st stage
2nd stage
Ln(Income per
Capita, 1998)
Change in log (Income
per Capita) between
1998 and 2004
Outcome
Change in log (Income
per Capita) between
1998 and 2004
Ln (Income per Capita in 1998)
-0.848***
Education of household head
-0.022
0.036
-0.034
Education of household head2
0.005***
0.002
0.005***
Female household head
-0.278***
-0.108
-0.228***
Black
-0.438***
-0.354**
-0.272
Employed
0.865***
0.183**
0.795***
HH size
-0.084***
-0.019**
-0.075***
Ln(Income per Capita in 1993
-0.557***
0.360***
Constant
5.001***
3.440***
3.391***
Observations
714
714
714
R-squared
0.54
0.428
0.491
Under-identification test (LM Statistic)
49.38
Weak identification test (Wald F Statistic)
63.25
Weak-instrument-robust inference (P-val)
0.0008
Results
Table 2: Effect of measurement error on initial income
KIDS
Lagged
IV:
Second
Income
Income
lag IV:
Lag
Index
Asset IV: Set (combining
the two
instruments)
Coefficient -0.848***
(0.037)
Drop in %
-0.557***
-0.476***
-0.521***
(0.124)
(0.124)
(0.097)
34%
44%
39%
Income Convergence in South Africa: Fact or Measurement Error?
Table 3: National Income Convergence (NIDS 2008-2010)
OLS
IV
1st stage
2nd stage
Outcome
Change in log (Income
per Capita) between
2008 and 2010
Ln (Income per Capita in in 2008)
-0.623***
Education
-0.019
-0.035**
-0.011
Education Squared
0.005***
0.006***
0.003**
Coloured
0.308***
0.088
0.175***
Indian
0.451***
0.582***
0.081
White
0.506***
0.834***
0.041
Employed
0.546***
0.351***
0.401***
Number of children in HH
-0.191***
-0.157***
-0.131***
Number of adults in HH
-0.069***
-0.102***
-0.047***
HH moved place
0.1
-0.243***
0.178**
IV: Household Wealth, 2008
Change in log (Income
Ln(Income per
per Capita) between 2008
Capita, 2008)
and 2010
-0.238***
0.435***
Constant
3.935***
5.812***
2.013***
Observations
5,673
5,673
5,673
R-squared
0.409
0.548
0.28
Under-identification test (Lm statistic)
109.734
Weak identification test (Wald rk F statistic)
666.324
Weak-instrument-robust inference (P-value)
0.0097
Results
Table 3: Effect of measurement error on initial income
NIDS
Lagged
IV: Lag Asset
IV: Lag
IV: Set
Income
Index
Satisfaction
(combining the
two instruments
Coefficient -0.623***
(0.025)
Drop in %
-0.238***
-0.378***
-0.263***
(0.079)
(0.121)
(0.075)
62%
39%
58%
Income Convergence in South Africa: Fact or Measurement Error?
Source of Measurement Error
• The aggregate measurement error can have several sources:
• the rich understate household income
• the poor overstate income, or
• both effects are driving the bias in the income
convergence estimates
Income Convergence in South Africa: Fact or Measurement Error?
Source of Measurement Error
Figure 1: Income change by income level in 2008, NIDS
Transition matrix
Measured values
Household was poor in 2010
Household was
poor in 2008
NO
YES
NO
YES
2497
755
(77.34%)
(32.32%)
853
1581
(25.46%)
(67.68%)
Predicted values (for 2010)
Household was poor in 2010
Household was
poor in 2008
NO
YES
NO
YES
2,591
661
(77.9%)
(28.01%)
735
1699
(22.10%)
(71.99%)
Sources of Measurement Error
• Income convergence for different groups?
• Urban vs. rural
• Black, Coloured vs. Indian, White
• Higher convergence for black population?
• To test these hypothesis, finally IV regression were also run for
various sub-groups.
Income Convergence in South Africa: Fact or Measurement Error?
Table 5: Measurement Error by Race and Location, KIDS and NIDS
KIDS
Full
Black
Indian
Urban
Rural
-0.855***
-0.775***
-0.824***
-0.863***
-0.577***
-0.157
-0.557***
-0.509***
32.5%
79.7%
32.4%
41.0%
sample
Lagged Income -0.848***
(OLS)
IV set
-0.515***
Change of OLS 39.3%
results
when
using IV in %
Observation
714
609
105
252
462
NIDS
Full
Black/
White/
Urban
Rural
sample
Coloured
Indian
-0.661***
-0.365
-0.590***
-0.717***
-0.323***
-0.041
-0.159***
-0.592***
51.2%
88.8%
73.1%
17.4%
5341
332
2808
2876
Lagged Income -0.623***
(OLS)
IV set
-0.263***
Change of OLS 57.8%
results
when
using IV in %
Observation
5673
Conclusion
• Using KIDS and NIDS, substantial measurement error in
reported income data is found
• Employing an instrumental approach it is possible to mitigate
the effect of measurement error
• Our results suggest that previously estimated income
dynamics have been largely overestimated by about 40-60%
• In a breakdown of the source of the measurement error it
appears that the poor substantially overstate their incomes
Income Convergence in South Africa: Fact or Measurement Error?
Questions
1. Story Line clear and precise?
2. Analysis well motivated?
3. IV strategy convincingly presented?
4. Mixed analysis of NIDS and KIDS useful?
5. Analysis of source of bias helpful?