Transcript NBER Digest, and Car Discounts

http://www.nber.org/digest/
Does Poverty Cause Domestic Terrorism?
Who knows? (Regression alone can’t establish causality.) There does appear
to be some level of positive association.
But the level of political freedom within a nation also plays a role.
The article states: “… the relationship between the level of political rights
and terrorism is not a simple one. Countries with an intermediate range of
political rights experience a greater risk of terrorism than countries either
with a very high degree of political rights or severely authoritarian countries
with very low levels of political rights.”
This clearly signals a nonlinear relationship (a downward-bending “U”), and
suggests adding the square of the “political rights” variable to a model which
predicts a nation’s level of domestic terrorism. And indeed, this is what the
author did.
The second appendix to the full article reports the following regression (the
“no rights” variable takes values between 1 (great political freedom) and
7 (an oppressive authoritarian regime)):
Regression: log(Global Terrorism Index)
constant log(GDP/cap) no rights (no rights)2
coefficient
something -0.0948
0.2966
-0.0300
std error of coef
something 0.0434
0.1073
0.0127
significance
something 3.0491%
0.6422% 1.9451%
adjusted coef of det
24%
• there’s strong evidence that the squared variable
belongs in the relationship (from the significance
level of the squared term)
• the no-rights variable relates to domestic terrorism
in the form of a downward-bending “U” (the
coefficient of the squared term is negative)
• the “U” peaks at a no-rights level of
‐0.2966/(2(-0.0300)) = 4.94 (using the –b/(2c)
formula), i.e., between the extremes, as seen in this
chart from the article.
CEO Overconfidence, Corporate Investment,
and the Market’s Reaction
The next article examines the link between the personal characteristics of a
CEO, and his/her propensity to invest corporate resources unwisely.
It reports (in the middle of the second column): ”… overconfidence among
acquiring CEOs is one important explanation of merger activity. Using a
dataset of large U.S. companies from 1980 to 1994 and the CEOs’ personal
portfolio decisions as measures of overconfidence, they find that
overconfident CEOs conduct more mergers and, in particular, more valuedestroying mergers. These effects are most pronounced in firms with
abundant cash or untapped debt capacity.”
In other words, the effect of CEO overconfidence on overinvestment in valuedestroying merger activity depends on the availability of ready financial
resources (waiting to be misspent).
What we have here is an interaction, captured in the regression model by the
introduction of the product of the “overconfidence” and “ready financial
resources” variables.
Smoking, Drinking, and Drug Use Respond
to Price Changes
Finally, the last article, suggests “that legalization and taxation (of currentlyillegal drugs) — the approach that characterizes the regulation of cigarettes
and alcohol — may be better than the current approach.”
It notes (starting at the bottom of the first column on the last page of the
Digest): “Alcohol use and abuse cannot be correlated indisputably with
reductions in the real prices of alcoholic drinks without factoring in other
elements. These include changes in the minimum legal drinking age and the
redefining of blood-alcohol levels in regard to drunk driving.
However, when these factors are taken into account, the 7 percent increase in
the real price of beer between 1990 and 1992 attributable to the Federal
excise tax hike on that beverage in 1991 explains almost 90 percent of the 4percentage-point reduction in binge drinking in that period.”
Clearly, a direct regression of “binge drinking” onto “real price of alcoholic
drinks” suffers from specification bias, and fails to accurately capture the true
effect of price on alcohol abuse. But, when the confounding variables – “legal
drinking age” and “illegal blood-alcohol level” – are taken into account, the
price effect is clearly revealed in the resulting “more complete” model.
General Qualitative Data,
and “Dummy Variables”
• How might we have represented “make-of-car” in the motorpool case,
had there been more than just two makes?
– Assume that Make takes four categorical values (Ford, Honda, BMW, and
Sterling).
•
•
•
•
Choose one value as the “foundation” case.
Create three 0/1 (“yes”/”no”, so-called “dummy”) variables for the other three cases.
These three variables jointly represent the four-valued qualitative Make variable.
Here are the details.
• We’ll use this representational trick in order to include “day of game”
(either Friday, Saturday, or Sunday) in a model which predicts attendance
at a professional indoor soccer team’s home games. Here is the example.
– Using this trick requires that we extend the “significance level” (with respect
to whether a variable “belongs” in the model) to groups of variables. This is
done via “analysis of variance” (ANOVA).
Discounts on Car Purchases: Does
Salesperson Identity Matter?
• Assume there are five salesfolks:
• Andy, Bob, Chuck, Dave and Ed
• Take one (e.g., Andy) as the foundation case, and add
four new “dummy” variables
•
•
•
•
DB = 1 only if Bob, 0 otherwise
DC = 1 only if Chuck, 0 otherwise
DD = 1 only if Dave, 0 otherwise
DE = 1 only if Ed, 0 otherwise
• The coefficient of each (in the most-complete model)
will differentiate the average discount that each
salesperson gives a customer from the average
discount Andy would give the same customer
Does Salesperson Identity Matter?
Imagine that , after adding the new variables (four new columns
of data) to your model, the regression yields:
Discountpred = 980 + 9.5  Age – 0.035  Income + 446  Sex
+ 240  DB + (–300)  DC + (–50)  DD + 370  DE
• With similar customers, you’d expect Bob to give a discount
$240 higher than would Andy
• With similar customers, you’d expect Chuck to give a discount
$300 lower than would Andy, $540 lower than would Bob,
and also lower than would Dave (by $250) and Ed (by $670)
Does “Salesperson” Interact with “Sex”?
• Are some of the salesfolk better at selling to a particular Sex of customer?
– Add DB, DC, DD, DE, and DBSex, DCSex, DDSex, DESex to the model
– Imagine that your regression yields:
Discountpred = 980 + 9.5  Age - 0.035  Income + 446  Sex
+ 240  DB – 350  DC + 75  DD + 10  DE
– 375  (DBSex) – 150  (DCSex) – 50  (DDSex) + 450  (DESex)
– Interpret this back in the “conceptual” model:
Discountpred = 980 + 9.5  Age – 0.035  Income + 446  Sex
+ (240 – 375Sex)  DB + (–350 – 150Sex)  DC
+ (75 – 50Sex)  DD + (10 + 450Sex)  DE
Discountpred = 980 + 9.5  Age – 0.035  Income + 446  Sex
+ (240 – 375Sex)  DB + (–350 – 150Sex)  DC
+ (75 – 50Sex)  DD + (10 + 450Sex)  DE
– Given a male (Sex=0) customer, you’d expect Bob (DB=1) to give
a greater discount (by $240-$3750 = $240) than Andy
– Given a female (Sex=1) customer, you’d expect Bob to give a
smaller discount (by $240-$3751 = -$135) than Andy
– Chuck has been giving smaller discounts to both men and
women than has Andy, and Dave and Ed have been giving larger
discounts than Andy to both sexes
– And we could take the same approach to investigate whether
“Salesperson” interacts with Age, including also DBAge,
DCAge, DDAge, DEAge in our model
Outliers
An outlier is a sample observation which fails to
“fit” with the rest of the sample data. Such
observations may distort the results of an entire
study.
– Types of outliers (three)
– Identification of outliers (via “model analysis”)
– Dealing with outliers (perhaps yielding a better
model)
• These issues are dealt with here.
Additional Session 4 Materials
• Optional readings on logarithmic
transformations, and on testing for differences
(benchmarking)
• Two more thorough sample exams.
– One based on a firm converting from Microsoft office
software to open-source Linux software, choosing
between training programs, with a 90-minute
prerecorded Webex tutorial
– One based on a real-estate developer studying the
impact on home values of having a clubhouse in a
development