Page 354 -

Empirical Exercises 353

for 172 U.S. cities in 1900.5 A detailed description is given in Lead_Mortality_
Description, also available on the website.

a. Compute the average infant mortality rate (Inf ) for cities with lead
pipes and for cities with non-lead pipes. Is there a statistically signifi-
cant difference in the averages?

b. The amount of lead leached from lead pipes depends on the chemis-
try of the water running through the pipes. The more acidic the water
(that is, the lower its pH), the more lead is leached. Run a regression
of Inf on Lead, pH, and the interaction term Lead * pH.

i. The regression includes four coefficients (the intercept and the
three coefficients multiplying the regressors). Explain what each
coefficient measures.

ii. Plot the estimated regression function relating Inf to pH for
Lead = 0 and for Lead = 1. Describe the differences in the
regression functions and relate these differences to the coefficients
you discussed in (i).

iii. Does Lead have a statistically significant effect on infant mortality?
Explain.

iv. Does the effect of Lead on infant mortality depend on pH? Is this
dependence statistically significant?

v. What is the average value of pH in the sample? At this pH level,
what is the estimated effect of Lead on infant mortality? What
is the standard deviation of pH? Suppose that the pH level is
one standard deviation lower than the average level of pH in the
sample; what is the estimated effect of Lead on infant mortality?
What if pH is one standard deviation higher than the average
value?

vi. Construct a 95% confidence interval for the effect of Lead on
infant mortality when pH = 6.5.

c. The analysis in (b) may suffer from omitted variable bias because it
neglects factors that affect infant mortality and that might potentially
be correlated with Lead and pH. Investigate this concern, using the
other variables in the data set.

5These data were provided by Professor Karen Clay of Carnegie Mellon University and were used in
her paper with Werner Troesken and Michael Haines, “Lead and Mortality,” The Review of Economics
and Statistics, 2014, 96(3).