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512 Chapter 12 Instrumental Variables Regression

meanwhile, attendance falls by 2 million for moderately violent
movies and by 1 million for nonviolent movies. What is the pre-
dicted effect on assaults? Construct a 95% confidence interval for
the change in assaults. [Hint: Review Section 7.3 and material sur-
rounding Equations (8.7) and (8.8).)]

c. It is difficult to control for all the variables that affect assaults and
that might be correlated with movie attendance. For example, the
effect of the weather on assaults and movie attendance is only
crudely approximated by the weather variables in the data set. How-
ever, the data set does include a set of instruments, pr_attend_v,
pr_attend_m, and pr_attend_n, that are correlated with attendance
but are (arguably) uncorrelated with weekend-specific factors (such
as the weather) that affect both assaults and movie attendance. These
instruments use historical attendance patterns, not information on a
particular weekend, to predict a film’s attendance in a given weekend.
For example, if a film’s attendance is high in the second week of its
release, then this can be used to predict that its attendance was also
high in the first week of its release. (The details of the construction
of these instruments are available in the Dahl and DellaVigna paper
referenced in footnote 5.) Run the regression from part (b) (includ-
ing year, month, holiday, and weather controls) but now using pr_
attend_v, pr_attend_m, and pr_attend_n as instruments for attend_v,
attend_m, and attend_n. Use this regression to answer (b)(i)–(b)(iii).

d. The intuition underlying the instruments in (c) is that attendance in a
given week is correlated with attendance in surrounding weeks. For
each move category, the data set includes attendance in surround-
ing weeks. Run the regression using the instruments attend_v_f,
attend_m_f, attend_n_f, attend_v_b, attend_m_b, and attend_n_b
instead of the instruments used in part (c). Use this regression to
answer (b)(i)–(b)(iii).

e. There are nine instruments listed in (c) and (d), but only three are
needed for identification. Carry out the test for overidentification
summarized in Key Concept 12.6. What do you conclude about the
validity of the instruments?

f. Based on your analysis, what do you conclude about the effect of vio-
lent movies on (short-run) violent behavior?

E12.3 (This requires Appendix 12.5) On the textbook website, www.pearson-
globaleditions.com/Stock_Watson, you will find the data set WeakInstrument,