- The following equation explains weekly hours of television viewing
by a child in terms of the child’s age, mother’s education, father’s
education, and number of siblings: thours* = B0 + B1age + B2age^2 +
B3motheduc + B4fatheduc + B5sibs + u. We are worried that tvhours” is
measured with error in our survey. Let tvhours denote the reported hours
of television viewing per week.
- What do the classical errors-in-variables (CEV) assumptions require
in this application? ANSWER: Classical Errors-in-Variables (CEV) Assumes
the following:
- The true relationship between the observed outcome variable (thours)
and the true values of the explanatory variables (age, motheduc,
fatheduc, sibs) is linear.
- The true explanatory variables (age, motheduc, fatheduc, sibs) are
uncorrelated with the measurement error in “tvhours.”
- The dependent variable “thours” is measured without error.
- The measurement error in “tvhours” is uncorrelated with the true
values of “thours.” and the variance of the measurement error in
“tvhours” is constant across all levels of the true values.
- There is no perfect linear relationship between the true values of
explanatory variables, ensuring that all variables have variation.
- Do you think the CEV assumptions are likely to hold? Explain. The
CEV assumptions are unlikely to hold. Children who do not watch TV at
all, tvhours* = 0, and it is very likely that reported TV hours is zero.
So if tvhours* = 0 then e0 = 0 with high probability.
```{r} #C2 Use the data set WAGE2 for this exercise. library(wooldridge)
data(“wage2”) wage2 #(i)Use the variable KWW (the “knowledge of the
world of work” test score) as a proxy for ability in place of 10 in
Example 9.3. What is the estimated return to education in this case?
(i)The coefficient of educ is 0.06. #(ii) Now, use IQ and KWW together
as proxy variables. What happens to the estimated return to
education?
- The coefficient on educ becomes about 0.05. Comparing to the
estimate KWW is used as a proxy, the return to education is smaller.
#(iii) In part (ii), are IQ and KWW individually significant? Are they
jointly significant?
- The t statistic of IQ is 3.08. The t statistic of KWW is 2.07, both
of them are significant at 5% level against a two-sided alternative.
They are jointly very significant also with F 2,925≈ 8.59 and p-value ≈
0.0002. ```