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14.30 Introduction to Statistical Methods in Economics
Spring 200
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14.30 Introduction to Statistical Methods in Economics
Lecture Notes 1
Konrad Menzel
February 3, 2009
1
Introduction and Overview
This class will give you an introduction to Probability Theory and the main tools of Statistics. Probability
is a mathematical formalism to describe and analyze situations in which we do not have perfect knowledge
of all relevant factors. In modern life, we are all routine consumers of statistical studies in fields ranging
from medicine to sociology, and probabilistic reasoning is crucial to follow most of the recent debates in
economics and finance.
In the first half of this class, we’ll talk about probabilities as a way of describing genuine risk  or our
subjective lack of information  over events.
Example 1
In subprime lending, banks offered mortgages to borrowers who were much less likely to repay
than their usual clientele. In order to manage the risks involved in lending to prospective homeowners
who do not own much that could serve as collateral, thousands of these loans were bundled and resold as
”mortgage backed securities,” i.e. the bank which made the original loans promised to pay the holder of
that paper whatever repayment it received on the loans. Eventually, there were more complicated financing
schemes under which the pool was divided into several ”tranches”, where a first tranche was served first,
i.e. if the tranche had a nominal value of, say, 10 million dollars, anyone holding a corresponding claim
got repaid whenever the total of repayments in the pool surpassed 10 million dollars. The lower tranches
were paid out according to whatever money was left after serving the highpriority claims.
How could it be that the first ”tranche” from a pool with many very risky loans was considered to be ”safe”
when each of the underlying mortgages was not? The lowpriority tranches were considered riskier  why?
And why did in the end even the ”safe” securities turn out to be much riskier in retrospect than what
everyone in the market anticipated? We’ll get back to this when we talk about the Law of Large Numbers,
and under which conditions it works, and when it doesn’t.
Usually in order to answer this type of question, you’ll have to know a lot about the distribution (i.e.
the relative likelihood) of outcomes, but in some cases you’ll actually get by with much less: in some
cases you are only concerned with ”typical” values of the outcome, like expectations or other moments
of a distribution.
In other cases you may only be interested in an average over many repetitions of a
random experiment, and in this situation the law of large numbers and the central limit theorem can
sometimes give you good approximations without having to know much about the likelihood of different
outcomes in each individual experiment.
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 Fall '09
 Economics, Set Theory, Probability theory, Naive set theory, Empty set, Intersection

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