# test if economic indicators have no explanatory power
linearHypothesis
(fatalities_mod4,
test =
"F"
,
c
(
"log(income)"
,
"unemp"
),
vcov. =
vcovHC,
type =
"HC1"
)
#> Linear hypothesis test

10.6.
DRUNK DRIVING LAWS AND TRAFFIC DEATHS
301
#>
#> Hypothesis:
#> log(income) = 0
#> unemp = 0
#>
#> Model 1: restricted model
#> Model 2: fatal_rate ~ beertax + state + year + drinkagec + punish + miles +
#>
unemp + log(income)
#>
#> Note: Coefficient covariance matrix supplied.
#>
#>
Res.Df Df
F
Pr(>F)
#> 1
275
#> 2
273
2 31.577 4.609e-13 ***
#> ---
#> Signif. codes:
0
***
0.001
**
0.01
*
0.05
.
0.1
1
Model (5) omits the economic factors.
The result supports the notion that
economic indicators should remain in the model as the coefficient on beer tax
is sensitive to the inclusion of the latter.
Results for model (6) demonstrate that the legal drinking age has little explana-
tory power and that the coefficient of interest is not sensitive to changes in the
functional form of the relation between drinking age and traffic fatalities.
Specification (7) reveals that reducing the amount of available information (we
only use 95 observations for the period 1982 to 1988 here) inflates standard
errors but does not lead to drastic changes in coefficient estimates.
Summary
We have not found evidence that severe punishments and increasing the min-
imum drinking age reduce traffic fatalities due to drunk driving. Nonetheless,
there seems to be a negative effect of alcohol taxes on traffic fatalities which,
however, is estimated imprecisely and cannot be interpreted as the causal effect
of interest as there still may be a bias. The issue is that there may be omitted
variables that differ across states
and
change over time and this bias remains
even though we use a panel approach that controls for entity specific and time
invariant unobservables.
A powerful method that can be used if common panel regression approaches fail
is instrumental variables regression. We will return to this concept in Chapter
12.

302
CHAPTER 10.
REGRESSION WITH PANEL DATA
10.7
Exercises
This interactive part of the book is only available in the HTML version.

Chapter 11
Regression with a Binary
Dependent Variable
This chapter, we discusses a special class of regression models that aim to ex-
plain a limited dependent variable. In particular, we consider models where the
dependent variable is binary.
We will see that in such models, the regression
function can be interpreted as a conditional probability function of the binary
dependent variable.
We review the following concepts:
•
the linear probability model
•
the Probit model
•
the Logit model
•
maximum likelihood estimation of nonlinear regression models
Of course, we will also see how to estimate above models using
R
and discuss an
application where we examine the question whether there is racial discrimination
in the U.S. mortgage market.
The following packages and their dependencies are needed for reproduction of
the code chunks presented throughout this chapter on your computer:
•
AER
(Kleiber and Zeileis, 2020)
•
stargazer
(Hlavac, 2018)
Check whether the following code chunk runs without any errors.