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Many economic variables tend to change exponentially rather than arithmetically over time.
That is, the variable increases and sometime decreases as a percent of its value.
Thus if GDP is 100 it might increase by 2, and if GDP is 1,000 the increase is likely to be 20. Both situations involve a two-percent increase in GDP. Consider a time series (for example, an annual time series, X) that has experienced significant growth. On a normal (arithmetic) graph, which plots X against time (year), earlier values would be close to the horizontal (time, year) axis and later values far above the horizontal axis. On a logarithmic graph, which plots log X against time, the same percentage change in X will look that same, regardless of the size of the observations. This means that the slope of the graph (year-to-year change in log X) is the year-to-year growth rate of X itself. Thus the log graph makes it easy to see how a series growth rate changes over time. |