322 The Basics of financial economeTrics
The field of descriptive statistics discerns different types of data. Very
generally, there are two types: nonquantitative (i.e., qualitative and ordinal)
and quantitative data.
If certain attributes of an item can only be assigned to categories, these
data are referred to as qualitative data. For example, stocks listed on the
New York Stock Exchange (NYSE) as items can be categorized as belong-
ing to a specific industry sector such as “banking,” “energy,” “media and
telecommunications,” and so on. That way, we assign each item (i.e., stock)
as its attribute sector one or possibly more values from the set containing
“banking,” “energy,” “media and telecommunications,” and so on.^1 Another
example would be the credit ratings assigned to debt obligations by credit
rating agencies such as Standard & Poor’s, Moody’s, and Fitch Ratings.
Except for retrieving the value of an attribute, nothing more can be done
with qualitative data. One may use a numerical code to indicate the differ-
ent sectors, for example 1 = “banking,” 2 = “energy,” and so on. However,
we cannot perform any computation with these figures since they are simply
names of the underlying attribute sector.
On the other hand, if an item is assigned a quantitative variable, the
value of this variable is numerical. Generally, all real numbers are eligible.
Depending on the case, however, one will use discrete values only, such as
integers. Stock prices or dividends, for example, are quantitative data draw-
ing from—up to some digits—positive real numbers. Quantitative data can
be used to perform transformations and computations. One can easily think
of the market capitalization of all companies comprising some index on a
certain day while it would make absolutely no sense to do the same with
qualitative data.^2
cross-Sectional data and time Series data
There is another way of classifying data. Imagine collecting data from
one and the same quantity of interest or variable. A variable is some
quantity that can assume values from a value set. For example, the vari-
able “stock price” can technically assume any nonnegative real number
of currency but only one value at a time. Each day, it assumes a certain
value that is the day’s stock price. As another example, a variable could
be the dividend payments from a specific company over some period of
time. In the case of dividends, the observations are made each quarter.
(^1) Most of the time, we will use the term “variable” instead of “attribute.”
(^2) Market capitalization is the total market value of the common stock of a company.
It is obtained by multiplying the number of shares outstanding by the market price
per share.