A Debt Smoothie

You've seen debt like this before:

Graph #1: Household Debt relative to Disposable Personal Income

Debt relative to income. It went up until the mid-60s, ran flat to the early '80s, uphill till 2000, uphill fast, and then down.
 
But sometimes, maybe, you want a more detailed look. I do. Sometimes I want to look at the change in debt relative to the change in income.

But when you look at change relative to change, you lose all the stability provided by the accumulation of debt and by the achievement of income. It becomes like trying to drive an old Volkswagen beetle that needs a front-end alignment and a rear-end alignment: Try as you might, you can't keep that thing going straight down the road.

With neither the accumulation nor the achievement to provide mass, the changes are no longer small. Change is all there is. The data value may suddenly double, or fall to zero, or even go negative. It can happen. It can happen with every new piece of data.

You can figure the ratio, but ratios are not well suited to data like that. What you end up with is not very meaningful:

Graph #2: Change in Household Debt relative to Change in DPI

What can we say of this graph? Something happened in 1953-54. Something happened in 1987. And something happened in 2016. Other than that, we can't say much.

Oh, and nothing seems to have to happened during 2008-2010.

Change relative to change does not make a useful graph. That's unfortunate, because it is a useful concept.

What to do? You can look at the change in debt and the change in income as separate lines on a graph:

Graph #3: Change in Household Debt (blue) and Change in DPI (red)

But this is too messy to be of much use. I see that both lines tend to go up until 2008 or so. But I don't know how much of that is real change and how much is just inflation. Using a ratio like Graph #2, the inflation cancels itself out of the picture. Not so with Graph #3.

On this graph, too, it is hard to see if income is gaining on debt or losing out to it -- except for a few years before 2009 when debt (the blue line) runs high, and a few years after 2009 when debt runs low. But that was obvious even on the first graph today.

Is there no better way to look at the change in debt relative to the change in income? Of course there is! I'm sure I'm not the first person ever to do it, but I did figure it out for myself. So, I get to write about it.

There may be better ways, but here's what I do. I take the change in debt and the change in income and give each one its own graph. Then I add a trend line to each, to smooth out the jiggies. For this trend line I use a Hodrick-Prescott and a low value for the smoothing constant.

Graph #4: Change in Household Debt (blue) and Hodrick Prescott with a Smoothing Constant of 15

Using the low value for the smoothing constant allows the HP to follow the data closely, jiggies aside. I use the same approach for debt (above) and income (below).

Graph #5: Change in DPI (blue) and Hodrick Prescott with a Smoothing Constant of 15

Next, I take the two smoothed lines and put them together on a new graph. (Doing this all on one worksheet simplifies the work in Excel.)

Graph #6: Smoothed Debt from Graph #4 (blue) and Smoothed Income from Graph #5 (red)

Graph #6 is the smoothed version of Graph #3 above. #6 is a little easier to read. Before about 1965, the lines are too close together to see anything. From 1965 to the mid-80s the red runs above the blue: Disposable Income rises faster than Household Debt. But not much faster. We called Graph #1 "flat" in those years.

After 1985, income (red) runs mostly below debt, and by 1998 income runs entirely below debt... until the crisis, when debt growth heads downhill fast.

Using these smoothed values, I can take another look at the "change in debt" to "change in income" ratio. The next graph shows the blue line from Graph #6 divided by the red line from the same graph.

Graph #7: Change in Household Debt relative to Change in Disposable Personal Income

This is the "smoothed data" version of Graph #2 above. This time we have something to see. The ratio runs very high between 2001 and 2007, then collapses down to values not shown, and finally rises back into the "normal" range.

But that's not what interests me most on this graph. I like to look at the time before things went bad. I like to look back to when things were going bad, before it was obvious, to see what was happening then.

In 1952 the ratio runs close to 1.00 on the vertical scale. That's a one dollar increase in debt for every dollar increase in Disposable Income. By 1970 the ratio is down near 0.50, a fifty-cent increase in debt for every dollar increase in income. During those years, especially after 1963, debt growth was slower than income growth.

A lot of that slow debt growth was no doubt due to the rising inflation of the time. But the first three peaks on Graph #7 (1954, 1960, and 1962) also show a trend of decrease, and that all happened before the time of the inflation.

Look now from the low of 1970 to just before the sharp increase of 2001. There is a mostly gentle increase for three decades. Between 1970 and 2000, the ratio climbed from 50 cents more debt, to almost $1.50 more debt, for every dollar of increased income.

On Graph #1, by the year 2000 the ratio had not yet reached one dollar. On Graph #7, it is near a dollar and a half. Why the difference? Because #7 shows only the new addition to debt. If debt is increasingly rapidly in the moment, #7 shows it.

Graph #1 adds the new debt to the old. But the old debt was accumulated when debt was growing at a slower pace. Adding new and old debt together drags the number down.

Graph #1 shows the accumulation, and shows it correctly. Graph #7 ignores the accumulation, and instead shows how fast the debt is growing at any particular point. Graph #7 shows that debt was growing faster in the year 2000 than we might have thought by looking at Graph #1.

Change relative to change is a useful concept.


I took Graph #7 and put some trend lines on it, just straight trend lines.

Graph #8: Change in Household Debt relative to Change in DPI, with Trend Lines

The early trend, shown in red, emerges from the data from 1952 Q1 thru 1970 Q1. The mid-years trend, green, is based on the data for 1970 Q2 thru 2000 Q4. I did not show a late-years trend, as the data is nothing but a jumble of craziness.

These trend lines emphasize the debt-to-income decline of the 1952-1970 period, and the debt-to-income increase since 1970. This is not what you would expect if you were only looking at Graph #1, which shows the whole accumulation of household debt relative to the whole achievement of disposable personal income.


Does it bother you? It bothers me. The red trend line points downward. But it is encouraged to point down by the inflation since the mid-60s. If we eliminate the inflationary years from the calculation, will the trend line still point downward?

A similar question arises for the green trend line. The first part of the mid-years data is held down by inflation. And the last part of the mid-years data is well known to be high. If we look at only the first part of the mid-years data, will the green trend line still point upward?

Good questions.

Working backwards from 1970 Q1, I eliminated data from the early trend until the red trend line changed from downward- to upward-pointing. Almost flat, actually. Then I added back the last data item I removed, to make the trend line point down again. The selected dataset runs from 1952 Q1 to 1964 Q1.

Working backwards from 2000 Q4, I removed data from the mid-years trend on the green data all the way back to 1982 Q4. The trend line still slopes upward.

Graph #9, with Trend Lines based on Smaller Subsets of the Data

The straight green trend line is based on the data shown in green. The straight red trend line is based on the data shown in red. The data shown in blue is not used in the trend line calculations.

The trend lines run pretty flat in Graph #9. But the red one still does slope down, and the green one still does slope upward. So I feel confident in saying that household debt tended to grow more slowly than disposable personal income in the 1952-1964 period, before the "Great Inflation" kicked in.

And I feed confident in saying that, the Great Inflation notwithstanding, household debt tended to grow faster than disposable personal income in the 1970-1982 period.

Graph #1 does show increase from 1970 to 1982. Not a lot of increase, but enough to agree with Graph #9. So I'm good with that. But I need one more look at the early years, because the red on #9 goes down, but the plot on #1 goes up.

Graph #10: Percent Change from Year Ago, CMDEBT & DPI, Annual Data

Debt growth declines; disposable income growth increases.

There ya go.