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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 Least-Absolute Deviation Estimates
Dependent Variable =
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, South-Western 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
and a j2 = plim (n −1 ∑ rij2 ) where rij are the residuals from regressing x j on the other independent variables. We say that
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 F-test we use the Wald-statistic. The Wald-statistic is calculated as qF, where F is the F-statistic and q are the number of restrictions. As you may recall from statistics, there is a
relationship between the F and chi-square distributions : If X ∼ Fv ,v then lim v1X ∼ χv . Therefore, for the F-test 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