Sunday, August 14, 2016

Reverse Engineering the Household Debt Service Ratio

Looking at household debt service as a percent of disposable personal income. Wondering how income affects the data, how debt affects it, and how saving affects it.

At FRED, the debt service number is given as "percent of disposable personal income". I figured saving the same way, and put the two together on a graph:

Graph #1: Debt Service (blue) and Household Saving (red) relative to DPI
My first impression was that the two lines tend to move in opposite directions: away from each other before the 1982 recession, but toward each other after it... away from each other after the 1991 recession and then toward each other again... and then away from each other from the late 1990s to the crisis, and then toward and past each other.

So then I took and put a minus sign in front of the formula for the red line, to turn it upside down:

Graph #2: Debt Service (blue) and Saving with a Minus Sign (red)
With the red line other-side-up, the red and blue do show signs of matching. I got low and then high from 1985 to 1990... low and then high again... then higher from 2000 to the crisis, and then low. The lines don't match well, but do show signs of matching. Makes me wonder what I can do to make them match better.

I thought about adding consumer debt (relative to disposable personal income) to the calculation of the red line. And then I remembered seeing those formulas that add two terms together after assigning a weight to each. And I said Yeah I can do that.

Ended up using "change in household debt" relative to DPI. And I just guessed some weights until I got something that looked somewhat like the debt service line. And I added a constant to push the red line up closer to the blue. Here is the result:

Graph #3: Using Savings and Household Debt to Reverse Engineer the Debt Service Ratio
Oh, was I pleased with myself!

The red line is very jiggy compared to the blue. But I expect I can smooth it out by using a Hodrick-Prescott calculation on it. Now I'm picturing a red line that looks even more like the blue, except everything happens about two years early. So I can lag the red line about two years to  make the lines more similar.

What that means is I'll get a peek into the future. My most recent data, from Q1 2016, will show up as a prediction of debt service for 2018! Now it's getting interesting.

I have to bring the data from FRED to Excel to do the lagging and the Hodrick-Prescott. I got all the data, which will let me calculate a number back to 1952 instead of 1980. I love this stuff.

Long story short, I figured the Hodrick-Prescott, tweaked the "weight" values a bit (by eye), and lagged my calculated numbers 8 quarters. Here's the result, back to 1980:

Graph #4: Not Perfect, but Not Bad!
The two-year lag is just about perfect for the high area (from 2000 to 2009). For the early years the red line should be lagged a little less.

But look at that big drop after 2008 Q1. At the peak the red line is a perfect match to the blue. At the bottom, by 2012, the lines have crossed. The economy slowed down during the big drop. I would need a longer lag there at the bottom, to push the red line more to the right.

But the most interesting thing on this graph, I think, is that it makes a prediction about the path the debt service ratio will take. It's going to go up. The blue line, like the red, is going to go up.

// The Excel file


Oilfield Trash said...


Two Questions

1. Why did you not use A072RC1Q156SBEA (Personal saving as a percentage of disposable personal income)

2. Why is your HP Constant set at 25 and not 1600 for QTR data.

When I make these tweaks I find a different story in the graphs.

The Arthurian said...

Hi O... I did start with 1600 for the H-P constant but it smoothed the line too much. What I was trying to achieve was a smoothed version of the jiggy line -- I want the smoothed version to follow the same path as the jiggy line, but not be jiggy.

Nobody ever told me it's okay to do that, but it seems right to me.

As for the saving data, I put three series on a graph and picked one. Let me look at yours and try to figure out what I did, and I'll get back to you on that.

The Arthurian said...

Okay, I went to the FRED link for graph #1 and added a new line for the A072RC1Q156SBEA series. It came out exactly on top of my red line.

I made my red line wider & changed yours to gold & you can see that yours rund right down the middle of mine.

The two are the same. It's just that I didn't have the foresight to use the one that was already divided by Disposable Personal Income!!!

Where yours differs from mine, my guess is it's because of the Hodrick-Prescott constant.

Or they could be different if you have a different way to calculate the H-P. That would be interesting. I got VBA code for Excel from the internets to do the H-P calc. Been using it for a while and have no trouble with it, but I don't have a way to compare the output with H-P as calculated by other programs.

Oilfield Trash said...


Paper below is a short one and I think you should give it a look over.

I have seen debates on what constant to use for monthly and yearly data, but no one seem to be in disagreement on QTR data.

If you are using the HP filter and QTR data 1600 is your constant.

The Arthurian said...

Oilfield, my thoughts on this topic are here.

Looking at what I did in the 14 August post, my objective was to take the red line from Graph #3 and smooth it until it was most similar to to the blue line. It seems to me that "standard" smoothing constants would have no bearing whatsoever on that task.

I think I might try the 6.25 number, though, the next time I need HP for annual data.

Oilfield Trash said...


I had some time last night and went through your spread sheet. I notice you did not calculate the trend on household debt serve with the HP algo.

So you are comparing filtered lagged data in your calculation, to raw data.

Is there a particular reason you did this?

When I filter household debt service with HP and lag 9 qtrs. with 1600 constant I can get a graph (which is now similar to yours) that represents the story Household Debt Service has broken from the trend. (your exercise in putting the calculate data together looks reasonable)

Which would support the argument interest rates are two low relative to savings.

Remember this graph and the separation of the Red and Green lines, you suggested the same opinion that interest rates look too low relative to savings.

The Arthurian said...

OT: " I notice you did not calculate the trend on household debt serve with the HP algo.
So you are comparing filtered lagged data in your calculation, to raw data.
Is there a particular reason you did this?"

Trying to simulate the debt service number. The sim was jiggy so I had to smooth it. But the debt service number was my target. I didn't want to change that; I wanted to duplicate it. So, no HP for the debt service.

That was my thinking, anyway. A lot of this is intuitive or from the back of my mind or just seems right. But I don't know that it *is* right, so I'm glad you evaluate these things. Somebody needs to check my work!

"... I can get a graph (which is now similar to yours) ..."

If we can calculate a version of 'debt service' ... that's spectacular! And if it shows anomalies, so much the better.

"Remember ... you suggested the same opinion that interest rates look too low relative to savings."

I remember.

This came up before: "If the simulation is good, maybe it shows that interest rates should have been higher in those years, higher than they actually were."

What it all means, I don't quite get yet.