Mathematical Tools for Econometrics Review Exam
What have we assumed? What is our Data Generating Process
(DGP)?
E(ei) = 0
Var(ei) = 2
Cov(ei , ek) = 0
ik
X1 , X2 , , Xn are fixed across samples
GAUSSMARKOV ASSUMPTIONS
bg4 dominates other three estimators
Algebra of Variances Notes
Population variances are also expectations.
One value of independent observations is that
Cov(Yi ,Yj ) = 0, killing all the cross-terms in the variance of
the sum.
Checking Understanding
Consider the Data Generating Process (DGP
Algebra of Covariances Notes
Population Covariances are also expectations.
Data Generating Processes
In this class, we are trying to draw inferences from a sample
(our data) back to an underlying process.
We begin by making very
concrete assumptions about
Algebra of Summations Exam Review
The S symbol is a shorthand notation for discussing sums of
numbers.
It works just like the + sign you learned about in elementary
school.
Summations: A Useful Trick
Double Summations
The Secret to Double Summations:
keep
Algebra of Expectations Notes
Expectations are means over all possible samples (think
super Monte Carlo).
Means are sums.
Therefore, expectations follow the same algebraic rules as
sums.
See the Statistics Appendix for a formal definition of
Expectations.
Data Generating Process Notes
The Data Generating Process is our model of how the world
really works.
The DGP includes some parameter (usually called
something like b ) that we would like to know.
We dont usually want to describe the data, we want to make
Populations and Samples Notes
Two uses for statistics:
Describe a set of numbers
Draw inferences from a set of numbers we observe to a
larger population
The population is the underlying structure which we wish to
study. Surveyors might want to relate 6000
Linear Estimators Notes
bg1 is unbiased. Can we generalize?
We will focus on linear estimators
Linear estimator: a weighted sum of the Y s
Note: we will use hats to denote estimated quantities
Linear estimator:
Example: g1 is a linear estimator.
Checking
Sample Statistics Exam Review
In a sample, we know exactly the mean, variance,
covariance, etc. We can calculate the sample statistics
directly.
We must infer the statistics for the underlying population.
Means in populations are also
called expectations.
Descriptive Statistics Notes
Mode: the most frequently occurring value.
Variance: the mean squared deviation of a number from
its own mean. The variance is a measure of the
spread of the data.
Standard deviation: the square root of
the variance. The stand
A Strategy for Inference Notes
The DGP tells us the assumed relationships between the
data we observe and the underlying process of interest.
Using the assumptions of the DGP and the algebra of
expectations, variances, and covariances, we can derive key
p