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 x for the independent variables. We use f to represent the actual mathematical relationship (usually a linear polynomial).

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).]


          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 Southeast Asia collapsed. This is a an inverse correlation. Is there any relationship of event A to event B? Probably not! Consider these arguments, however.

          In 1948, England established their National Health Service, which pays all the medical expenses of their citizens. A writer noted that in 1948, the life expectancy in England was 67 years, but after half a century of socialized medicine, the life expectancy had risen to 74 years. This is a direct correlation, but is there a causal linkage?

          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 U.S. economy endured a severe recession, and tax cuts are one way to fight a recession. Economists still debate the effects of the Reagan tax cuts.

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