All Terrain Thinking

A Compendium of things I think are Important

Economics: It's not just whats' in your wallet

Time-Series Graphs

A time-series graphs is a line graph where time is measured on the horizontal axis and the variable being observed is measured on the vertical axis. You can see the importance of these graphs by browsing your textbook and seeing how often they appear. As you study these graphs, ask yourself whether you have a systematic approach to analyzing them? You should, if you are to extract from the graph the information that is embedded in it.

To extract the information embedded in any time-series graph, you should begin by conceptually decomposing the movement of the variable being graphed into its separate components: long term trends, short term cyclical movements, seasonal patterns, and unexplained fluctuations called noise. For example, if we were looking to forecast retail sales in Rhode Island, we could expect the change in sales in any month would be larger if the State were in the midst of a period of sustained growth rather than decline, if the State economy was in the midst of a recovery rather than in the throes of a recession, if we were talking about December rather than January.

When decomposing the movement in sales of widgets, economists' favorite hypothetical good, it is easiest if you begin with the trend. This would usually be reflected in the 'average slope' which can be determined by the unsophisticated eyeball approach or the sophisticated regression approach. Does the curve slope up, does it slope down, is there a definite change in the direction or the magnitude of the slope over time? These are the questions that you must attempt to answer at the outset of your analysis. Comments such as wages have grown on average approximately 4 percent per year for the past two decades or that labor productivity rose at a rate of approximately 2 percent per year during the post W.W.II period refer to these trends. In the graph below, the underlying trend appears to be positive throughout the entire time under review.

It is clear from this graph, however, that there are also significant variations about this trend, variations which are referred to as cycles, business cycles to be more precise. These business cycles are a pervasive feature of capitalist economies. The reoccurring pattern of recessions (R) followed by expansions (E) characterizes nearly all measures of economic performance in nearly all economies. If you have any doubts, just look at the graphs of inflation, unemployment, interest rates, budget deficits, trade deficits, and exchange rates which you will find in your macroeconomics texts. You will see that the peaks and troughs of the various time-series graphs often tend to coincide with each other.

Two examples of 'real' world time-series graphs appear below. In the first we can see the history of inflation in the United States over the past 120 years. What is it that you see in this graph? My suggestion is that you look for cycle and trends - the short-term and long-term patterns. You should make a list of what you 'see' in the graph, and then read on. What do I see? I see two peaks, one associated with WWI (1916-1920) and one following WWII (1946-1948). [One of the limitations is that I cannot identify exactly which year it is peaking, but if that is what mattered, it may be best to use a table. Some other features of the graph are: (1) there are no negative numbers (deflation) after 1948, (2) there is an upward trend beginning approximately 1960 that ends approximately 1980, (3) there is a downward trend that extends from 1980 through the early 1990s.

In the second time series graph we have both the interest rate and the inflation rate. You would construct this graph if you were looking to find relationships between relationships. For example, the inflation line describes the relationship between inflation and time, while the second line describes the relationship between interest rates and time. What we see is that they tend to have similar patterns - interest rates tend to rise when inflation rates tend to rise (1970s) and tend to fall when inflation rates fall (1980s).

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