## Sunday, September 16, 2012

### Crossings

When you show real and nominal output on the same graph, the inflation-adjusted line always crosses the nominal line at the base year. And if, as a rule, there is always inflation, then before the base year, the inflation-adjusted line is always higher. And after the base year, it is always lower. The year we pick for the base determines where the lines cross, where the adjusted numbers are higher, and where the adjusted numbers are lower.

For example, Graph #1 compares US GDP and inflation-adjusted GDP. You can see that the two lines cross between 2000 and 2010. And you know that they cross in 2005, because the base year for figuring inflation-adjusted GDP is 2005, by standard practice. If you don't know the standard practice, you can look at the label on the left-hand border of the graph. It gives the units as Billions of Chained 2005 Dollars (for the blue line) and Billions of Dollars (for the red). In 2005, the two were equal.

 Graph #1: GDP and Inflation-Adjusted GDP cross in 2005

Graph #2 shows the same numbers, all "indexed" to 1980. That's a quick-and-dirty way of showing the inflation-adjusted numbers with 1980 as the base year. Note that the left-hand label now says "Index" and the numbers on the vertical scale do not represent dollars, but relative sizes:

 Graph #2: Both series indexed to 1980

Similar to Graph #1, Graph #3 below compares GDP to inflation-adjusted GDP, but the inflation-adjustment is calculated on the fly. Compare the equations given in the top border: On Graph #1, a pre-calculated series is used; Graph #3 shows the calculation.

 Graph #3: GDP and Inflation-Adjusted GDP (calculated for 2005 base)

That calculation takes unadjusted GDP, divides by GDPDEF to remove the price changes, and multiplies by 99.993 to convert all the values to 2005 dollars. (Why 99.993 and not 100 exactly? Can't say. Rounding, maybe. The 99.993 number is from FRED's annual GDPDEF values.)

Now that we have the graph set up to calculate the inflation-adjustment, it is easy to show it for different base years. In Graph #4 I took out the 2005 price number (99.993) and in its place used the 1980 price number (47.793). That moved the blue line, making Graph #4 comparable to Graph #2:

 Graph #4: GDP and Inflation-Adjusted GDP (calculated for 1980 base)

Graph #5 is the same graph again, but with 1964 as the base year:

 Graph #5: GDP and Inflation-Adjusted GDP (calculated for 1964 base)

Why 1964? Because that's just before the Great Inflation.