1. How sensitive are estimates of the marginal propensity to consume to measurement error in survey data in South Africa
Reza C. Daniels
UCT
Vimal Ranchhod

2. Outline Context Question Econometric problem Proposed solution Data
Results
Caveats
Conclusion

3. 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.

4. 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.

5. 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.

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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
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.

13. OLS and IV coefficientsyd
s.e
alcohol & cigs
***
***
beverages
***
-6.5E-05
***
clothes
***
***
durable goods
0.0142***
0.0184***
education
0.0153***
0.0208***
food
0.0355***
0.0461***
-0.003
health
0.0274***
0.0378***
housing
0.0747***
0.0688***
insurance
0.217***
0.242***
other non durable
0.0828***
own production
0.315***
0.325***
-0.016
recreation
***
***
hh services
0.0317***
0.0513***
transport
0.0639***
0.105***
utilities
0.0119***
0.0124***
TOTAL
0.981***
1.049***
-0.026

14. 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.

15. 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.