ACADEMIA SUMMARIES
STUDENT SOLUTIONS MANUAL
The original paper contains 28 sections, with 10 passages identified by our machine learning
algorithms as central to this paper.
Paper Summary
SUMMARY PASSAGE 1
C3.5
(iii) No. We are interested in the coefficient on log(employ), which has a t statistic of .2, which is very
small. Therefore, we conclude that the size of the firm, as measured by employees, does not matter,
once we control for training and sales per employee (in a logarithmic functional form).
SUMMARY PASSAGE 2
Solutions To Computer Exercises
≈ (iv) The coefficient on [log(dist)] 2 , when it is added to the model estimated in part (iii), is about .0365, but its t statistic is only about -.33. Therefore, it is not necessary to add this complication.
SUMMARY PASSAGE 3
(I)
Because the estimate depends on two coefficients, we cannot construct a t statistic from the
information given. The easiest approach is to define dummy variables for three of the four
race/gender categories and choose nonblack females as the base group. We can then obtain the t
statistic we want as the coefficient on the black female dummy variable.
SUMMARY PASSAGE 4
C7.5 The Estimated Equation Is
It shows that the effect of 401(k) eligibility on financial wealth increases with age. Another way to
think about it is that age has a stronger positive effect on nettfa for those with 401(k) eligibility. The
coefficient on e401k⋅(age − 41) 2 is −.0038 (t statistic = −.33), so we could drop this term.
SUMMARY PASSAGE 5
Solutions To Computer Exercises
(ii) The simple regression estimates using the 1988 data are ≈ grant β < 0 at the 5% level.
SUMMARY PASSAGE 6
(I) There Is Substantial Serial Correlation In The Errors Of The
Equation, And The Ols Standard Errors Almost Certainly
Underestimate The True Standard Deviation In ˆE
(vi) The coefficient on is only .042, and its t statistic is barely above one (t = 1.09). Therefore, an
ARCH(2) model does not seem warranted. The adjusted R-squared is about .113, so the ARCH(2)
fits worse than the model estimated in part (ii).
SUMMARY PASSAGE 7
(I) From Equation
(ii) From equation (15.20) with σ u = σ x , plim 1 β = β 1 + Corr(x,u), where 1 β is the OLS estimator.
So we would have to have Corr(x,u) > .5 before the asymptotic bias in OLS exceeds that of IV. This is
a simple illustration of how a seemingly small correlation (.1 in this case) between the IV (z) and error
(u) can still result in IV being more biased than OLS if the correlation between z and x is weak (.2).
SUMMARY PASSAGE 8
C16.5
We need π 10 ≠0 for Δlog(taxpc it ) to be a reasonable IV candidate for Δlog(polpc it ). When we
estimate this equation by pooled OLS (N = 90, T = 6 for n = 540), we obtain 10 π = .0052 with a t
statistic of only .080. Therefore, Δlog(taxpc it ) is not a good IV for Δlog(polpc it ).
SUMMARY PASSAGE 9
Solutions To Computer Exercises
where Φ(⋅) denotes the standard normal cdf, if β 0 = 0 then P(favwin = 1|spread) = Φ(β 1 spread)
and, in particular, P(favwin = 1|spread = 0) = Φ(0) = .5. This is the analog of testing whether the
intercept is .5 in the LPM. From the table, the t statistic for testing H 0 : β 0 = 0 is only about -.102, so
we do not reject H 0 .
SUMMARY PASSAGE 10
C17.5 (I) The
Then 1 θ = −.16. To obtain the t statistic, I write β 2 = θ 1 − β 1 , plug in, and rearrange. This
results in doing Tobit of ecolbs on (ecoprc − regprc), regprc, faminc, and hhsize.