Stata 1 Woolridge 3.C6 & Woolridge 9.C2 – Omitted variable bias, Proxy variables Use dataset WAGE2.dta again.

Consider the following model of wages:

log (wage) =  F0  + F1 educ + F2 IQ + u   (EQ1)

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 (EQ1) 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?

Now, consider the following model of wages:

log(wage) =  F0  + F1 educ + F2 exper + F3 tenure + F4married + F5 soutℎ

+ F6urban + F7 black + F8 ability + u                                         (EQ2)

f)    Estimate the model shown above – EQ2 – using the variable IQ as a proxy for ability. Confirm that your results are the same as those in Table 9.2, column (2).

g)   Now use the variable KWW (the “knowledge of the world of work” test score) as the proxy for ability. Compare your estimated returns to education when using the IQ test score and the      KWW test score as the proxy for ability.

h)   Now use both the variable KWW and the variable IQ together as proxy variables (i.e. put them both into the specification. What happens to your estimated return to education?

i)    In h), are IQ and KWW individually significant? Are they jointly significant?

Q1. 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?

Q2. 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 + 0.312 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?

Q3. 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. Eligibility for the federally funded school lunch program is very tightly linked to being economically disadvantaged. Why is this a sensible proxy variable for poverty?

The table that follows contains OLS estimates, with and without lnchprg as an explanatory variable.