ECMT2150 INTERMEDIATE ECONOMETRICS Week 6 Tutorial
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ECMT2150 INTERMEDIATE ECONOMETRICS
Week 6 Tutorial – Specification Issues I: OVB, Proxy Variables
1. Woolridge Question 3.8
Suppose that average worker productivity at manufacturing firms (aveprod) depends on two factors, average hours of training (avgtrain) and average worker ability (aveabil):
avgprod = F0 + F1 avgtrain + F2 avgabil + u
Assume this equation satisfies the Gauss-Markov assumptions. If training grants have been given to firms whose workers have less than average ability, so that avgtrain and avgabil are negatively correlated, what is the likely bias in obtained from the simple regression of avgprod on avgtrain?
2. Computer Exercise (Woolridge 3.C6) Use Data Set WAGE2. Consider the following model of wages:
log (wage) = F0 + F1 educ + F2 IQ + u
Suppose we are interested in the effect of education (educ) on wages (wage). In particular, we would like to understand how our estimates may be biased if we do not account for ability (IQ).
(a) Run the simple regression of IQ on educ and get the slope coefficient, say 1 . (b) Run the simple regression of log(wage) on educ and obtain the slope coefficient .
(c) Run the multiple regression of log(wage) on educ and IQ and obtain the slope coefficients and respectively.
(d) Verify that = + 1 .
(e) What does this tell you about the bias in the estimated relationship between education and wages if we do not account for ability?
3. Wooldridge Chp 9 Q2
We have a model of voting outcomes in 1990 for incumbents who were elected in 1988. Candidate A was elected in 1988 and was seeking reelection in 1990; voteA90 is Candidate A’s
share of the two-party vote in 1990. The 1988 voting share of Candidate A is used as a proxy variable for quality of the candidate. All other variables are for the 1990 election. The following equations were estimated, using the data in VOTE2.dta:
vo—teA90 = 75.71 + 3. 12 prtystrA + 4.93democA
(9.25) (0.046) (1.01)
−0.929 log(expendA) − 1.950 log(expendB) (0.684) (0.281)
n = 186, R2 = 0.495
and
vo—teA90 = 70.81 + 0.282 prtystrA + 4.52democA
(10.01) (0.052) (1.06)
−0.839 log(expendA) − 1.846 log(expendB) + 0.067vote88A
(0.687) (0.292) (0.053)
n = 186, R2 = 0.499
a) Interpret the coefficient on voteA88 and discuss its statistical significance.
b) Does adding voteA88 have much effect on the other coefficients?
4. Wooldridge Chp 9 Q3
Let math10 denote the percentage of students at a Michigan high school receiving a passing score on a standardized math test (see also Example 4.2). We are interested in estimating the effect of per student spending on math performance. A simple model is:
math10 = F0 + F1 log(expend) + F2 log(enroll) + F3poverty + u where poverty is the percentage of students living in poverty.
a) The variable lnchprg is the percentage of students eligible for the federally funded school lunch program. Why is this a sensible proxy variable for poverty?
b) The table that follows contains OLS estimates, with and without lnchprg as an explanatory variable.
Explain why the effect of expenditures on math10 is lower in column (2) than in column (1). Is the effect in column (2) still statistically greater than zero?
c) Does it appear that pass rates are lower at larger schools, other factors being equal? Explain.
d) Interpret the coefficient on lnchprg in column (2).
e) What do you make of the substantial increase in R-squared from column (1) to column
(2)?
2022-09-26
Specification Issues I: OVB, Proxy Variables