How sensitive are estimates of the marginal propensity to consume to measurement error in survey data in South Africa Reza C. Daniels UCT reza.daniels@uct.ac.za Vimal Ranchhod vimal.ranchhod@gmail.com

Outline Context Question Econometric problem Proposed solution Data Results Caveats Conclusion

Context Best micro level data in SA for incomes and expenditures comes from StatsSA income and expenditure surveys (ies 95, 00 and 05) From here, we can estimate the marginal propensity to consume (MPC), i.e. what proportion of every rand of disposable income do households spend. This can be broken up into various categories of expenditure. The marginal propensity to save (MPS) is defined as 1 – MPC, with corresponding definition.

Context (2) A common problem in survey data is measurement error in responses. i.e. The data captured might not truly reflect the financial reality being measured. In the `classical measurement error’ case, this leads to attenuation bias. Estimated relationships are weaker than the true relationships. For other types of measurement error, even being able to sign this bias may not be possible.

Question How sensitive are estimates of the MPC to measurement error (m.e.) in the IES data. We propose to estimate this sensitivity using an instrumental variables approach, with wage data from the same households, but from a different survey, namely the LFS 2000:2, as our candidate instrument.

Suppose the “true” relationship is: Econometric Problem Suppose the “true” relationship is: Yi = B0 + B1 Xi* + ui , where: Y is the outcome variable of interest, X* is the ‘true’ value of the dependent variable, And u is a mean zero error term. The subscript i refers to person i, where i=1, …, n It can be shown that, asymptotically, the OLS estimator of B1 obtained from a regression of Y on X* will be consistent if and only if: Cov(X* , u) = 0

OLS estimator with measurement error Suppose that we observe X instead of X*, Where X = X* + e, E[e]=0, cov(X* , e) = 0 and cov(u, e)=0 By regressing Y on X, we can show that the probability limit of our estimate of B1 from an OLS regression = B1 + cov(X, u-B1e)/Var(X) = B1 – B1 (Var(e)/[Var(X*) + Var(e)]) This is known as attenuation bias. In essence, regardless of the type of m.e. we are considering, the crucial question to ask is whether or not the covariance between the observed X and the composite error term is zero.

M.E: An IV solution Suppose we had another variable, Z, which is: Correlated with our observed X, and Uncorrelated with the composite error term, v=(u-B1e) Then Z would provide a valid instrument for the endogenous regressor X. In particular, another noisy measure of X* , eg. Z=X* + k would suffice, if k is uncorrelated with both u and e.

Asymptotically plimBhat1,IV = B1 + (corr(Z,v)/corr(Z,X1))*(var(v)/var(X1))0.5 (Recall that v=(u-B1e)) Now, var(v) ≠0, var(X1)≠0 and corr(Z,X1)≠0, therefore the IV works iff corr(Z,v)=0. i.e corr(X1* + k, u-B1e)=0, So the crucial requirement is that k and e are uncorrelated.

Implementing the solution We match data on individuals from the IES 2000 and LFS 2000:2. The data were obtained in October and September respectively. IES contains more detailed information on multiple sources of income and categories of expenditure, expenditure at HH level. LFS contains information on employment status and wage income.

Summarizing the Data Table 1: Summary statistics of sample Variable   # of individuals 103214 # of HHs 25964 Mean HH size 3.96 % of sample Mean HH Yd p.a. Mean HH Exp p.a. Ratio of exp/Yd African 79.4 21006 20933 0.997 Coloured 10.4 35837 35533 0.992 Indian 2.0 75232 69010 0.917 White 8.1 124999 129938 1.040 Total 32058 32244 1.006 Male 47.5 40198 40277 1.002 Female 52.5 19590 19937 1.018 Notes: 1. Means do not include sampling weights. 2. Means are obtained by race or gender of HH head.

Mean Expenditure by Category As % of Yd alcohol & cigs 634.0 2.0 beverages 533.3 1.7 clothes 1384.6 4.3 durable goods 1097.9 3.4 education 980.8 3.1 food 6706.1 20.9 health 2241.7 7.0 housing 4792.6 14.9 insurance 3578.6 11.2 other non durable 955.5 3.0 own production 679.3 2.1 recreation 47.9 0.1 hh services 1002.1 transport 2944.7 9.2 utilities 1025.8 3.2 TOTAL EXPENDITURE 32300.1 100.8 Total Disposable Income 32058 Notes: 1. Proportion in sub-category do not necessarily add to 100, due to omitted categories such as debt servicing.

OLS and IV coefficients yd s.e alcohol & cigs 0.00362*** -0.00014 0.00235*** -0.00072 beverages 0.00321*** -6.5E-05 0.00499*** -0.00035 clothes 0.00978*** -0.00017 0.00998*** -0.00091 durable goods 0.0142*** -0.00028 0.0184*** -0.0014 education 0.0153*** -0.00029 0.0208*** food 0.0355*** -0.00045 0.0461*** -0.003 health 0.0274*** 0.0378*** -0.0018 housing 0.0747*** -0.0016 0.0688*** -0.0077 insurance 0.217*** -0.0019 0.242*** -0.0094 other non durable 0.0828*** -0.0011 0.00574 -0.0057 own production 0.315*** -0.0033 0.325*** -0.016 recreation 0.00214*** -0.00011 0.00244*** -0.00054 hh services 0.0317*** -0.00037 0.0513*** transport 0.0639*** -0.00082 0.105*** -0.0042 utilities 0.0119*** -0.00018 0.0124*** -0.00092 TOTAL 0.981*** -0.0054 1.049*** -0.026

Caveats Sensitive to imputation method of wage data from categories. Conceptual difficulties on how to treat debt financing and dissaving or borrowing. IVs are fairly weak, many HH’s get income from grants. If m.e. correlated with income levels, eg. Rich HHs always understate, then its not clear that the solution is valid. Non-response also not accounted for.

Conclusion Promising avenue of investigation IV’s do have significant first stages Lots more to be done … Do by income quintile, And by age of HH head, or some form of HH composition.