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\title{Basic Econometrics}
\author{Riccardo (Jack) Lucchetti}
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\section*{Foreword}
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This is a very basic course in econometrics, in that it only covers
basic techniques, although I tried to avoid the scourge of
over-simplification, so some may find it not so basic in style. What
makes it perhaps a little different from others you find on the Net is
that I made a few not-so-common choices.
\begin{enumerate}
\item Separating clearly the properties OLS has by construction from
those it has when interpreted as an estimator.
\item Using matrix algebra whenever possible.
\item Using asymptotic inference only.
\end{enumerate}
Point number one is modelled after the ideas in the two great
masterpieces, \cite{DMK-EIE} and \cite{DMK-ETM}. I have several
reasons for this choice, but it is mainly a pedagogical one. The
students I am writing for are people who often don't feel at ease with
the tools of statistical inference: they have learned the properties
of estimators by heart, they are not sure they can read a test, find
the concept of the distribution of a statistic a little unclear (never
mind asymptotic distributions), get confused between the variance of
an estimator and an estimator of the variance. In the best
cases. Never mind; no big deal.
There's an awful lot you can say on the base tool in econometrics
(OLS) even without all this, and that's good to know. Once a student
has learned how to handle OLS properly as a mere computational tool,
the issues of its usage and interpretation as an estimator and of how
to read the associated test statistics can be grasped more
correctly. If you mix the two aspects too early, a beginner is prone
to mistake properties of least squares that are true by construction
for properties that depend on some probabilistic assumptions.
Point number two is motivated by laziness. In my teaching career, I
have found that once students get comfortable with matrices, my
workload halves. Of course, it takes some initial sunk cost to convey
properly ideas such as projections and properties of quadratic forms,
but the payoff is very handsome. This book contains no systematic
account of matrix algebra; we're using just the basics, so anything
you find on the Net by googling ``matrix algebra lecture notes'' is
probably good enough. However, let me recommend appendix A in
\cite{HansenOnline}.
As for probability and statistics, I will only assume some familiarity
with the very basics: simple descriptive statistics and basic
properties of probability, random variables and expectations. Chapter
\ref{sec:inference} contains a cursory treatment of the concepts I
will use later, but I wouldn't recommend it as a general reference on
the subject. Its purpose is mainly to make the notation explicit and
clarify a few points. For example, I will avoid any kind of reference
to maximum likelihood methods. For a more substantial read, it's hard
not to recommend, again, the online material by Bruce Hansen: his
``Probability and Statistics'', is available online at
\url{https://www.ssc.wisc.edu/~bhansen/probability/}.
I don't think I have to justify point number three. I am writing this
in \the\year, when typical data sets have hundreds, if not thousands
observations and nobody would ever dream of running any kind of
inferential procedure with less than 50 data points. Apart from OLS,
there is no econometric technique in actual use that does not depend
vitally on asymptotics, so I guess that readers should get familiar
with the associated concepts if there is a remote chance that this
will not be put them off econometrics completely. The $t$ test, the $F$
tests and, in general, all kinds of degrees-of-freedom corrections are
ad-hockeries of the past; unbiasedness is overrated. Get over it.
I promise I'll try to be respectful of the readers and don't treat
them like idiots. I assume that if you're reading this, you want to
know more than you do about econometrics, but this doesn't give me the
right to assume that you need to be taken by the hand and treated like
an 11-year-old.
Finally, a word of gratitude. A book like this is akin to a software project,
and there's always one more bug to fix. So, I'd like to thank first all my
students who helped me eradicate quite a few. Then, my colleagues Allin
Cottrell, Stefano Fachin, Francesca Mariani, Giulio Palomba, Luca Pedini, Matteo
Picchio, Claudia Pigini and Alessandro Pionati for making many valuable
suggestions. Needless to say, the remaining shortcomings are all mine. Claudia
also allowed me to grab a few things from her slides on IV estimation, so thanks
for that too. If you want to join the list, please send me bug reports and
feature requests. Also, I'm not an English native speaker (I suppose it
shows). So, Anglophones of the world, please correct me whenever needed.
The structure of this book is as follows: chapter
\ref{chap:descriptive} explores the properties of OLS as a descriptive
statistic. Inference comes into play at chapter \ref{sec:inference}
with some general concepts, while their application to OLS is the
object of chapter \ref{chap:regression}. Chapters \ref{chap:hetero}
and \ref{chap:dynamic} contain extensions of the basic model for
cross-sectional and time-series datasets, respectively. Finally,
chapter \ref{chap:IV} deals with instrumental variable
estimation. Each chapter has an appendix, named ``Assorted results'',
where I discuss some of the material I use during the chapter in a
little more detail.
\begin{cornicetta}
In some cases, I will use a special format for short pieces of
texts, like this. They contain extra stuff that I consider
interesting, but not indispensable for the overall comprehension of
the main topic.
\end{cornicetta}
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\chapter{OLS: algebraic and geometric properties}
\label{chap:descriptive}
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\chapter{Some statistical inference}
\label{sec:inference}
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\chapter{Using OLS as an inferential tool}
\label{chap:regression}
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\chapter{Diagnostic testing in cross-sections}
\label{chap:hetero}
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\chapter{Dynamic Models}
\label{chap:dynamic}
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\chapter{Instrumental Variables}
\label{chap:IV}
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\chapter{Panel data}
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\addcontentsline{toc}{chapter}{Bibliography}
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\end{document}
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