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 KwaZulu- Natal province. Income Convergence in South Africa: Fact or Measurement Error?

Theory and Literature Review Define income mobility as ∆Y i,t ≡ Y 2 – Y 1 To determine how initial income influences income change studies have run regression of the form: ∆Y i,t = α + β 1 Y i,t-1 + β 2 Z i, + β 3 X i,t-1 + β 4 X i,t + ε i,t In case β 1 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 Y it is available and biased by ε it it states: Y it = Y* it + ε it 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 Y i,t-1 using Y i,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 + β 1 X it + β2Ψ it + β 3 *ln(Income per Capita) i,t-2 + ε it If lagged initial income variable is a good instrument, this regression will give a consistent coefficient β 3. To test the robustness of the results we use a second instrument: ∆Ln (Income per Capita) i,t = α + β 1 X it + β 2 Ψ it + β 3 *ln(Asset index) i,t-1 + ε it 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 self- reported satisfaction of the household head. Income Convergence in South Africa: Fact or Measurement Error?

OLS IV 1 st stage2 nd stage Outcome Change in log (Income per Capita) between 1998 and 2004 Ln(Income per Capita, 1998) Change in log (Income per Capita) between 1998 and 2004 Ln (Income per Capita in 1998)-0.848***-0.557*** Education of household head Education of household head *** *** Female household head-0.278*** *** Black-0.438***-0.354** Employed0.865***0.183**0.795*** HH size-0.084***-0.019**-0.075*** Ln(Income per Capita in *** Constant5.001***3.440***3.391*** Observations714 R-squared Under-identification test (LM Statistic)49.38 Weak identification test (Wald F Statistic)63.25 Weak-instrument-robust inference (P-val) Table 1: Income Convergence in KwaZulu-Natal Province (KIDS )

Results Income Convergence in South Africa: Fact or Measurement Error? Table 2: Effect of measurement error on initial income KIDS Lagged Income IV: Second lag Income IV: Lag Asset Index IV: Set (combining the two instruments) Coefficient *** (0.037) *** (0.124) *** (0.124) *** (0.097) Drop in %34%44%39%

OLS IV 1 st stage2 nd stage Outcome Change in log (Income per Capita) between 2008 and 2010 Ln(Income per Capita, 2008) Change in log (Income per Capita) between 2008 and 2010 Ln (Income per Capita in in 2008)-0.623***-0.238*** Education ** Education Squared0.005***0.006***0.003** Coloured0.308*** *** Indian0.451***0.582***0.081 White0.506***0.834***0.041 Employed0.546***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 ***0.178** IV: Household Wealth, *** Constant3.935***5.812***2.013*** Observations5,673 R-squared Under-identification test (Lm statistic) Weak identification test (Wald rk F statistic) Weak-instrument-robust inference (P-value) Table 3: National Income Convergence (NIDS )

Results Income Convergence in South Africa: Fact or Measurement Error? Table 3: Effect of measurement error on initial income NIDS Lagged Income IV: Lag Asset Index IV: Lag Satisfaction IV: Set (combining the two instruments Coefficient *** (0.025) *** (0.079) *** (0.121) *** (0.075) Drop in %62%39%58%

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 NOYES Household was poor in 2008 NO 2497 (77.34%) 755 (32.32%) YES 853 (25.46%) 1581 (67.68%) Predicted values (for 2010) Household was poor in 2010 NOYES Household was poor in 2008 NO 2,591 (77.9%) 661 (28.01%) YES 735 (22.10%) 1699 (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 sample BlackIndianUrbanRural Lagged Income (OLS) ***-0.855***-0.775***-0.824***-0.863*** IV set ***-0.577*** ***-0.509*** Change of OLS results when using IV in % 39.3%32.5%79.7%32.4%41.0% Observation NIDS Full sample Black/ Coloured White/ Indian UrbanRural Lagged Income (OLS) ***-0.661*** ***-0.717*** IV set ***-0.323*** ***-0.592*** Change of OLS results when using IV in % 57.8%51.2%88.8%73.1%17.4% Observation

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?