Spencer at Angry Bear yesterday posted a couple of revealing charts of long-term health care costs. They provoked a good discussion of issues about how we represent economic data in graphic form. Adjusted for inflation? As a percentage of GDP? Per-capita? All three? (Somewhat wonkish.)

Here is another option. Use logarithmic values to make up and down moves directly comparable, and measure the time series against its own growth curve. Spencer’s chart of year-over-year percent change is probably just as effective, but it depends on what you’re looking to see.

On a vertical scale of nominal values, moves that rise or decline by the same percentage won’t always look the same. In fact, hardly ever. For example, a move up from 10 to 15 and another from 1,000 to 1,500. They are both 50% increases but, plotted together on the same chart, the second move from 1,000 to 1,500 will look 100 times bigger than the first (+500 vs. +5). The familiar logarithmic scale is drawn with equal segments of rising multiples of 10: from 1 to 10, 10 to 100, 100 to 1,000 and so on. It’s designed to make moves that are the same percentage look the same. However, I use logarithmic (log) values rather than a log scale because, in MS Excel, the scale doesn’t always fit the data very well. In log10 values the example just given looks like this (Table 1):

Notice that the increases are identical (0.176). On a chart +500 and +5 will *look* the same.

Figure 1 shows total health care expenditures (in inflation-adjusted, log10 values) with a growth curve plotted from 1960 to 1994, then projected to 2010. The 1960-94 period is arbitrary—any growth trend would do. But I like this one because it gives us a good metric for evaluating the latest 15 years of health care costs (1994-2009) and their slowing growth rate. Figure 2 does the same for per-capita costs. (Click on a chart to open it full-size in a separate window.)

Figure 3 plots the percent that each data series moves above/below its growth curve. (The two growth curves appear together here as the 0% line.) This gives us a strong visual measure of the trend, in particular the comparison of slowing growth in total costs to the greater slowing in per-capita costs. You can see the difference just by comparing Figures 1 and 2, but it’s more effective to compare the two series together on the same chart.

We have to be careful with a chart like this. Slowing growth is not the same as a decline: inflation-adjusted expenditures rose 4.3% compounded annually in the 15 years from 1994 to 2009. Of course, as one commenter at Angry Bear points out, the slowing growth may just be the result of health care costs rising above people’s ability to pay for it, a condition aggravated by the fact that 50 million men, women, and children in the U.S. are uninsured today. If they can’t pay, then many don’t seek medical care even when they need it.

In the end, it depends on what you think is important to show in a chart. The rise in nominal costs? Inflation-adjusted costs? The relation of costs to their long-term trend? Whichever it is, there is a way to chart it that’s more effective than the alternatives. Finally, what all this is about is the *rhetoric* of visual presentation. What do you want to say with a chart? Or, better, what does a chart enable you to see that you don’t see otherwise?

Jim:

You may enjoy this: http://www.angrybearblog.com/2011/08/medicare-sky-is-falling.html