Practice Q1 (i) There are omitted variba;es that are correlated with
education, for example, ability. Thus, the ZCM assumption does not hold;
(|) ≠ 0. (ii) Cov(,) = 0 Validity (cannot be tested) Cov(, ) is
‘large’ Relevance (can be tested) (iii) First stage: Regress the
endogenous variable on all the exogenous variables including our IV: = 0 + 1 + 22 + 3 + 4 + 5 + 6 + (*) Form the prediction of :
= 0 + 1 + 22 + + 6 Substitute for in the structural model
(8.1): log() = 0 + 1IV + + Our 1IV is our IV estimate. The
limitation of the procedure is that the standard errors from doing 2SLS
in two steps are incorrect. (iv) . . = 1IV ± × 1IV = 0.2791 ±
1.96 × (0.1255) Where we use = 1.96 as = 947, so ≈ ∞. Hence . . =
(0.0331, 0.5251) and the OLS estimate is within this . . (v) Run the
reduced form regression (*) in (iii) above. The exogenous variables,
call them 1, … , are all uncorrelated with in (8.1). Thus, any part of
that is correlated with in (8.1) will be left in . Then the idea of
the test for endogeneity is to take and use it to check for
endogeneity by adding it to the structural model. We are looking to see
if is correlated with . We run the regression: log() = 0 + 1 + 2 + + 6 + 0 + 2 by
OLS and test if 0 is statistically different from zero or not. If it
is, we have evidence to suggest is endogenous. (vi) Your choice
should hinge on whether the IV is valid and relevant. Given vary in the
Australian case by degree, maybe Cov(,) = 0 is not necessarily going to
hold if degree choice is a function of ability. Then, will be related
to ability. If IV is invalid then OLS would be a better choice.
Practice Q2 Practice Q3 (i) 0:1 = 2 = 3 = 4 = 5 = 0 1:0 is false -stat = (0.056/5) / ((1-0.056)/(20050-5-1)) = 237.81. 5,20044
= 3.02 with 1% significance level. Since -stat > critical value, we
reject 0. Conclude that the model for birth weight in (4.1) has
overall significance. 3 (ii) Var(|) = 2 If we have
heteroskedasticity, our estimates are unaffected. But our inference is
invalid because our standard errors are invalid. (iii) Either the BP,
White, or modified White tests would be appropriate. Refer to Lecture 8
for the steps that must be followed for each test. You would need to
describe / list the steps to get full marks.
