.

**VARIABLES
AND RELATIONSHIPS**

Reality
is very complex, and economists, like other scientists, use models to analyze
reality. A model is a simplified version of the real world and only includes
the elements that we believe are the most important. For example, we think that
prices are the most important factor in determining the demand for bread. We
also think that income and population are important. Other economic factors
will be left out of the model.

Each
of these elements of a model is a *variable*. Our model for the demand for
bread has four variables: (1) the quantity of bread demanded,
(2) the price of bread, (3) the income of consumers, and (4) the number of
consumers. Each variable can be expressed by numbers.

The
*dependent variable* is the tail of the dog -- its number value depends on
the number values of the other variables. In our model, the dependent variable
is the quantity of bread demanded (#1). The other three variables are the *independent
variables* and their number values, taken together, will determine the
quantity of bread that consumers want to buy.

Models
can be expressed using mathematical notation. We often use ** y** for
the dependent variable and

*y
= f (x)*

In the demand for bread, we would use **Qd** for quantity demanded, **P** for price, **Y** for income, and **N** for population. The **+**
and **-** signs show direct and inverse relationships.

*Qd** = f (-P,+Y,+N)*

Among
the independent variables, the price of bread (#2) is the most important, so we
match the quantity (#1) and price (#2) variables together in tables and graphs.
The table containing these numbers is called a *schedule*, and the graph
of these numbers is called a *curve*. Since we are not including income
and population, we have to assume that these variables don't vary! We call this
condition "ceteris paribus" which means that income and population
are held constant. If income changes, for example, we will need a new set of
quantity numbers for our schedule, and the location of our curve will change.

The
relationship of the dependent variable and each of the independent variables
can be direct or inverse. In a *direct relationship*, a higher value of
the independent variable is related to a higher value of the dependent variable
(or vice-versa). Mathematically, a direct relationship is also a *positive** relationship*.

In
an *inverse relationship*, a higher value of the independent variable is
related to a lower value of the dependent variable (or vice-versa). Mathematically,
an inverse relationship is also a *negative relationship*. [The word
"indirect" does not mean inverse!]

In
our example, the quantity of bread demanded (#1) is inversely related to the
price of bread (#2). These two variables are used for the demand schedule and
the demand curve. In the schedule, higher values of price are linked to lower
values of quantity demanded. In the demand curve, the curve will slope downward
to the right (a "negative" slope). When there is a change in price,
we say there has been a "change in the quantity demanded".

The
demand for bread is directly related to income (#3). If income takes higher
values, then the demand for bread will also take higher values. In the demand
schedule, the quantity demanded at each price will be higher. In the demand
curve, the quantity demanded will be further to the right at each price level.
We say that there is an "increase in demand" and "the curve
shifts to the right". If income takes lower values, the process is reversed.
We say that there is a "decrease in demand" and "the curve
shifts to the left". We call these shifts in the demand curve a
"change in demand". [The demand for bread is also directly related to
changes in population (#4).]

**TWO
CAUSATION FALLACIES**

Statistics
lets economists use real world data to identify these types of relationships
for our models. But sometimes, data can be misleading. For example, consumption
spending by households and gross domestic product move up and down together.
This is a *positive (direct) correlation*. Variables that are directly
related will also show a positive correlation. There are two questions: (1) are
these variables related, and (2) which are the independent and dependent
variables? Economists believe consumption spending and GDP are related, and
that consumption is the dependent variable. In fact, this relationship of
consumption to output is the "consumption function" developed by John
Maynard Keynes to help explain the causes of the Great Depression of the 1930s.

Natural
gas use and ice cream sales show a *negative (inverse) correlation* --
when gas sales are high, ice cream sales are low, and vice-versa. Are these two
variables inversely related? Economists argue that these two variables are not
related to each other at all. If anything, we are observing the impact of
seasonal changes in the weather.

** Related
variables will be correlated variables; correlated variables may not be related
variables.**

Another
type of data problem arises from the timing of events. This is sometimes called
the *post hoc, ergo propter hoc* fallacy. It
assumes that a later event is always due to an earlier event.

If
event A is followed by event B, are we observing related events or just a
coincidence? For example, we observe (A) an increase the in the money supply,
followed by (B) an increase in the price level. Can we conclude that the price
level is a dependent variable which is directly related to the money supply
which is an independent variable? Economists assert that this relationship does
exist, and it is the important "equation of exchange" which we use to
explain the power of monetary policy.

In
early 1997, (A) Madonna had a baby. In late 1997, (B) the economies of

In
1948,

In
1981, the Reagan Administration cut personal income taxes by 25 percent. By the
mid-1980s, the federal government deficit was over $200 billion per year. Did
the Reagan tax cuts create the later deficit? In 1981 and 1982, the

** A
dependent event will be a later event; not all later events are dependent
events.**