Download Introduction to Econometrics

UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
Introduction to Econometrics
Econometrics: The process of analyzing data to build economic models, understand economic
relationships, and produce economic forecasts/predictions.
Variable: Something in the world that (1) can be observed, (2) can be measured/described, and (3) has
the potential to vary.
Data are (1) observations of variables, (2) where the observations are described/measured, and (3) where
the observations are recorded (written down, or stored in some way).
Population: A collection of individuals of interest. (The individuals can be people, consumers, firms,
states, countries, etc.)
Typically, the individuals in a population have a number of characteristics that can be observed, that can
be measured/described, and that have the potential to vary. These characteristics are variables. For
example, a population of people have characteristics such as height, weight and gender; these
characteristics are variables. When we observe these variables, describe/measure them, and record our
observations, we are collecting data.
Statistics: The study of the collection, summary, analysis, interpretation, and presentation of data. A
“statistic” is a number that summarizes or interprets data. Statistics are typically calculated for the
variables that describe various characteristics of a population.
Sample: A subset of a population.
Random/Representative/Unbiased Sample: A sample selected from a population such that each
member of the population has the same chance/probability of being included in the sample.
Why Take Samples? (Why don’t we just measure everyone in the population?)
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Insufficient time or money to sample entire population (although technically possible).
Sometimes, it is technically impossible to sample the original population, and only a sample of
data remains (e.g., dinosaur bones provide sample of extinct dinosaur population, financial
statements from banks in 1929)
Sometimes, sampling is destructive; so, you don’t sample the whole population, because you
don’t want to destroy the whole population (e.g., testing lightbulb life)
Sometimes, it’s easier to maintain quality control of the sampling process if you limit the scope of
the sampling effort. (Less, higher-quality data can be better than more, lower-quality data.)
Statistical Implications of Sampling: When we have data on just a sample from a population, rather
than data on the full population, we don’t have full information on the population. As a result, we have to
adjust our statistical formulas, depending on whether we have just a sample of data, or data on the full
population. Therefore, there will often be two versions of any statistical formula, one that is appropriate
when working with data on a full population, and one that is appropriate when working with just a sample
of data from the population.
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UNC-Wilmington
Department of Economics and Finance
ECN 377
Dr. Chris Dumas
Some Math Terminology
For the purposes of this course, let’s define some terminology:
N = population size = number of individuals in the population
n = sample size = number of individuals in a sample
X = a variable that measures some characteristic of the individuals in a population or
sample
Index Variables
Often, an “index variable,” is used to label a list of variable values. For example,
if we have 9 values of variable X in our dataset, we could label the nine values
using “i” as an index variable as follows:
“X1, X2, X3, X4, X5, X6, X7, X8, X9”
or
Xi, where i = 1 to 9
If the number of values is uncertain (or is itself a variable), then we can use a
variable such as “n” to denote the (unknown) number of values in the list. We
can then write the list as:
“Xi, where i = 1 to n”
“Sigma Notation”
The Greek letter “Sigma,”
or “to add up.”

, is a mathematical operator meaning “to sum up,”
We can use the sigma operator together with index variables to denote the concept
of “adding up a bunch of things in a list.” For example, if we have nine X’s in a
list, indexed by index variable i, and we want to add them up, we can write:
9
X
i 1
i
which simply means “add up all nine X’s from X1 through X9,” in other
words:
9
X
i 1
i
≡ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9
If we have “n” things in the list, we can write:
n
X
i 1
i
≡ X1 + X2 + X3 + . . . + Xn
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