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 = β0 + β1 avgtrain + β2 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 β1 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) = β0 + β1 educ + β2IQ + 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).

 .

(b) Run the simple regression of log(wage) on educ and obtain the slope coefficient  β1 .

(c) Run  the   multiple  regression  of  log(wage)  on  educ   and  IQ   and  obtain  the  slope

coefficients β1 and β2 respectively.

(d) Verify that β1  = β1  + β2 δ1 .

(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:

voteA90 = 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

—

voteA90 = 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 = β0  +  β1 log(expend) +  β2 log(enroll) + β3poverty + 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.