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0.159062
agesq
8.059894
1.883162
0.059710
male
928.322677
0.809919
0.418008
e401k
399.304958
0.405301
0.685266
F statistic
=
59.9718
p value
=
0.0000 VER. 10/23/2012. © P. KOLM 83 (iii) Estimate the equation by LAD and report the results in the same form as for OLS. Interpret the LAD estimate of β6 .
Solution: The equation estimated by LAD is
nettfa = 12.5 − 0.262inc + 0.00709inc 2 − 0.723age
(1.38) (0.010) (0.00008) (0.067) +0.011age 2 + 1.02male + 3.74e401k
(0.0008) (0.205) (0.177) n = 9,275, Psuedo R2 = 0.109
Now, the coefficient on e401k means that, at given income, age, and gender, the
median difference in net financial assets between families with and without
401(k) eligibility is about $3,740. VER. 10/23/2012. © P. KOLM 84 LeastAbsolute Deviation Estimates
Dependent Variable =
net tfa
Rsquared
=
0.1320
Rbarsquared
=
0.1315
sigma^2
= 3553.5000
DurbinWatson =
1.8710
Nobs, Nvars
=
9275,
7
# iterations
=
501
convergence
=
7.6280557e008
***************************************************************
Variable
Coefficient
tstatistic
tprobability
intercept
12.491012
4.348519
0.000014
inc
0.261571
10.066903
0.000000
incsq
0.007086
32.109169
0.000000
age
0.722663
5.880983
0.000000
agesq
0.011073
7.655559
0.000000
male
1.018349
3.795858
0.000148
e401k
3.737259
10.871461
0.000000 VER. 10/23/2012. © P. KOLM 85 (iv) Reconcile your findings from parts (ii) and (iii). Solution: The findings from parts (i) and (iii) are not in conflict. We are finding that
401(k) eligibility has a larger effect on mean wealth than on median wealth.
Finding different mean and median effects for a variable such as nettfa, which
has a highly skewed distribution, is not surprising. Apparently, 401(k) eligibility
has some large effects at the upper end of the wealth distribution, and these are
reflected in the mean. The median is much less sensitive to effects at the upper
end of the distribution. VER. 10/23/2012. © P. KOLM 86 References
Hayashi, F. (2000). Econometrics. Princeton, New Jersey, Princeton University Press.
Wooldridge, J. M. (2009). Introductory Econometrics: A Modern Approach, SouthWestern Pub. Footnotes 1 (a) This assumption is weaker than the former in the sense that the former (the zero conditional mean assumption) implies this one. In fact, one way to characterize the zero conditional mean assumption, E(u  x1, x2,..., xk ) = 0 , is that any
function of explanatory variables is uncorrelated with the error term u. (b) While OLS is always consistent under this
weaker condition, it can be biased. This would be the case if E(u  x1, x2,..., xk ) depends on any of the x j .
2 It can be shown that Avar ˆ
( n (β − β )) = σ
j j 2 a j2 is the asymptotic variance of ˆ
n (β j − β j ) (for the slope coefficients), ˆ
ˆ
and a j2 = plim (n −1 ∑ rij2 ) where rij are the residuals from regressing x j on the other independent variables. We say that
ˆ
β j is asymptotically normally distributed. The asymptotic theory of OLS is best derived using matrix notation, see, for example, Chapter 2 in Hayashi (2000).
3 In fact, in the asymptotic case instead of using the Ftest we use the Waldstatistic. The Waldstatistic is calculated as qF, where F is the Fstatistic and q are the number of restrictions. As you may recall from statistics, there is a
2
relationship between the F and chisquare distributions : If X ∼ Fv ,v then lim v1X ∼ χv . Therefore, for the Ftest in OLS
1 2 v2 →∞ 1 we have that F ∼ Fq ,n −k −1 then lim qF ∼ χq2 .
n →∞ 4 Mathematically, we would say that “we assume the x’s to be linearly independent.” 5 Note that MLR. 3, i.e. E(ui∗  xi1,..., xik ) = 0 , is valid because hi is only a function of ( xi1,..., xik ). VER. 10/23/2012. © P. KOLM 87...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.
 Fall '14

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