the table, with disposable personal income measured along the horizontal axis and consumption spending measured along the vertical axis. Notice that the points for 2012 and 2011 do not all fall exactlyon the line. To examine the relationship between two variables, economists often use the straight line that best fits the data.
Determining Cause and EffectWhen we graph the relationship between two variables, we usually want to draw conclusions about whether changes in one variable are causing changes in the other variable. Doing so can, however,lead to mistakes. Suppose you graph over the course of a year the number of homes in a neighborhood that have a fire burning in the fireplace and the number of leaves on trees in the neighborhood. You would get a relationship like that shown in the panel a of the two graphs below. The more fireplaces in use in the neighborhood, the fewer leaves the trees have. Can we draw the conclusion from this graph that using a fireplace causes trees to lose their leaves? Wwe know, of course, that such a conclusion would be incorrect. In spring and summer, there are relatively few fireplaces being used, and the trees are full of leaves. In the fall, as trees begin to lose their leaves, fireplaces are used more frequently. And in winter, many fireplaces are being used and many tress have lost all their leaves. The reason that the graph below is misleading about cause and effect is that there is obviously an omitted variable in the analysis- the season of the year. An omitted variable is one that affects other variables, and its omission can lead to false conclusions about cause and effect.Although in our example the omitted variable is obvious, there are many debates about cause and effect where the existence of an omitted variable has not been clear. For instance, it has been knownfor many years that people who smoke cigarettes suffer from higher rates of lung cancer then do nonsmokers. For some time, tobacco companies and some scientists argued that there was an omitted variable-perhaps a failure to exercise or a poor diet- that made some people more likely to smoke and more likely to develop lung cancer. If this omitted variable existed, then the finding that smokerswere more likely to develop lung cancer would not have been evidence concluded that the omitted variable did not exist and that in fact smoking does cause lun cancer.A related problem in determining cause and effect is known as reverse causality.The error of reverse causality occurs when we conclude that changes in variable X cause changes in variable Y when, in fact, it is actually changes in variable Y that cause changes in variable X. For example, panel b of the below graphs plot the number of lawn mowers being used in a neighborhood against the rate at which grass on lawns in the neighborhood is growing. We could conclude from this graph that using lawn mowers causes the grass to grow faster. We know, however, that in reality, the causality is in the other
direction. Rapidly growing grass during the spring and summer causes the increased use of lawn