Productivity and Debt Service

This graph shows productivity. I have circled the low productivity of the past few years, and also the low productivity of the 1990s in the years before "Goldilocks".

Graph #1: Productivity

When I take that graph and add household debt service to it, you can see that the circled years of low productivity are quite obviously related to the lows in debt service:

Graph #2: Productivity and Debt Service

Need I say more?

Low Debt Service plus Growing Debt equals Productivity

The red line is productivity, shown as percent change from year ago.

Graph #1: Household Debt & Debt Service (blue) and Productivity (red)

The blue line combines the household debt service ratio and the growth of household debt.

The two lines don't always match, mostly because of the big spike in productivity that we typically get after recessions. But set those spikes aside, and the lines do at least hint at similarity.

The red oval mid-graph highlights productivity and debt conditions during the "Goldilocks years".

The red oval on the right shows debt conditions even lower now than during 1993-1995, so there is plenty of room for things to go up.

Productivity has been low since 2011, as the graph shows. But productivity was also low after debt conditions bottomed out in the early 1990s, just before the Goldilocks years.

Productivity is going to pick up soon.

Illicit use of the Hodrick-Prescott?

The Hodrick and Prescott (1980, 1997) filter (hereafter, the HP filter) has become a standard method for removing trend movements in the business cycle literature.

I'm reading Notes on Adjusting the Hodrick-Prescott Filter for the Frequency of Observations, a short PDF by Morten O. Ravn and Harald Uhlig. The paper is © 2002 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology, so they're probably right.

Most applications of this filter have been to quarterly data, but data is often available only at the annual frequency, whereas in other cases monthly data might be published. This raises the question of how one can adjust the HP filter to the frequency of the observations so that the main properties of the results are conserved across alternative sampling frequencies.

Their topic is tweaking the HP calculation to allow for different data frequencies.

I use Kurt Annen's VBA code in Excel to do the HP calculation. The code creates a function named HP( ) that does all the work. All you have to give it is the range of source data and a constant.

The constant is how you allow for different data frequencies. Changing the constant changes the amount of "smoothing" you get when you graph the results. The trick is to use the right value for the constant.

I've always used the values 100 for annual data, 1600 for quarterly data, and 14400 for monthly data. Something I picked up from the EViews User Forum a while back. I have some old notes on it.

I shouldn't say I always use those values. I always start with those values. Sometimes I change them. For examples of how changing the value of the smoothing constant affects the results, see this old post.

In this recent post I show why, for one graph of monthly data, I abandoned my usual monthly constant of 14400 in favor of my default annual value 100. The larger value smoothed all the information out of the result -- like Kruger smoothing the head off a statue on Seinfeld.


For quarterly data, Ravn and Uhlig say, the value 1600 is commonly used. (It seems 1600 is the value Mr. Hodrick and Mr. Prescott used in the article that introduced the HP filter.) But for annual data Ravn and Uhlig note four different values: 100, 400, 10, and their own personal favorite, 6.25:

We then show that our recommendations work extremely well on U.S. GDP data: using a value of the smoothing parameter of 6.25 for annual data and 1600 for quarterly data produces almost exactly the same trend. This leads us to reconsider the business cycle “facts” reported in earlier studies. As an example, we cast doubt on a finding by Backus and Kehoe (1992) ...

Using a constant of 6.25 rather than 100 for annual data, the authors produce "almost exactly the same trend" that they get for quarterly data with a constant of 1600. Sounds good. But let me ask: Do you really want to get the same HP trend for the two series on this graph?

Graph #1: Quarterly (blue) and Annual (red) RGDP

I don't think so. The quarterly trend should show more detail.

Maybe if I'm looking at 50 years of data I'd want to think of "the" trend for the data, and it should be the same for both annual and quarterly. But if I'm focused on only a few years of data, it's probably because I'm looking for more subtle differences and I'd want to see more wiggle in the trend for the more wiggly line. I'm not looking at the 50-year trend. I'm looking at what's happened since the crisis.

Sometimes there's good reason to want the same trend from data with different frequencies. But sometimes there's good reason to want different trends.

Here are the two graphs from my "recent" post linked above, and my thoughts at the time:

Today I want to look at the monthly GDP data from Macroeconomic Advisers. I have their data thru May now:

Graph #2: Monthly RGDP since Jan 2009 with an Unresponsive H-P Constant

The blue line shows RGDP growth from 12 months prior. The red line is the Hodrick-Prescott using the constant I'd normally use for monthly data. I think this constant makes the red line a little too unresponsive, there being only about seven years of data.

Here is the same graph with a more responsive Hodrick-Prescott:

Graph #3: Monthly RGDP since Jan 2009 using a More Responsive H-P Constant

Now the red line follows the blue more closely. It helps us see the up-and-down pattern in the jiggy blue data. We are at a low spot now, and evidently RGDP growth has been trending down since the end of 2014.

Graph #2 shows a trend that is essentially flat. Graph #3 shows that RGDP growth has been trending down for a year and a half. Graph #3 is much more informative, and its trend line clearly does a better job of showing the path of RGDP than does Graph #2. But the thing of it is, Graph #3 uses the "wrong" smoothing constant. It uses my default annual value on monthly data!

I chose the annual value on purpose, because I wanted about as much smoothing on the monthly data as I normally get on annual data. It worked.

PS: I went out of my way to find monthly data for Graphs #2 and #3. Monthly, because it shows more variation. It would make no sense to smooth the monthly trend down till it showed as little variation as the annual!

The Relation Between Debt Service and RGDP Growth

Showing Hodrick-Prescott curves for Household Debt Service and Real GDP Growth:

1980-83: A low level of debt service (blue) allows rapid increase in RGDP growth.
1984-86: Rising debt service hinders growth. The red line peaks and turns downward.
1986-89: Reduced growth and reduced borrowing allow debt service to fall.
1990-93: Falling debt service encourages growth. The red line bottoms and turns upward.
1994-97: Rising growth leads to increasing debt service.
1997-99: Rising debt service hinders growth. The red line peaks and turns downward.
2000-06: Reduced growth and increased borrowing keep debt service rising.
2006-08: Reduced growth and reduced borrowing allow debt service to fall.
2008-10: Falling debt service encourages growth. The red line bottoms and turns upward.
2010-13: Falling debt service encourages growth. The red line rises.
2013-16: The fall in debt service slows. The increase in growth also slows.

Easier to follow if you print out the page and mark it up.

// The Excel file (contains VBA code)

Debt service and economic growth

Some generalizations:

Debt service is a financial cost imposed on the non-financial sector -- on production and consumption. To the extent that debt service moves money from the non-financial to the financial sector, it hinders production and undermines consumption.

The data on debt service is for households. So I will confine my remarks to household expenditure, to consumption.

When debt service is low, consumers have more money left over for other things. When debt service is high, consumers have less money left over for other things.

When debt service is rising, it is an indication that consumer debt is high or that consumer borrowing is on the rise. If borrowing is on the rise, GDP is probably on the rise. If debt is high, maybe not.

When debt service is falling, it is an indication that debt has been falling or has been rising more slowly than usual. If the latter, GDP may be on the rise. If the former, maybe not.

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

What I said eleven months back

Here it is. I finally found my old post from September 2015. Almost a year ago.

I'm gonna chop off the introductory stuff, revise what's left to eliminate references to the introductory stuff, and present it again:

2½ Times Longer and 2½ Times Deeper

Suppose we take the "Household debt service" graph and stretch the X axis a few years into the future. (FRED lets me do that, but when I capture and display the link, it reverts back to 2015.) Anyway, here's a screen shot:

Image #1

Next I change the blue line to dashed red, turn off the recession bars, stretch the graph out to the year 2030 again, and take another screen shot. Then I load it into Paint.NET, use the "magic wand" (at 20% tolerance) to erase the white background, and save the file as a GIF:

Image #2

Then I crop it so it shows just the 1990s, and put a black border on it. Actual size:

Image #3

Then I open up Image #1 so I have two files to work with in Paint.NET. I create a new layer in Image #1.

I switch back to the cropped GIF file, make it twice as big, no, 2½ times as big, and copy it.

Then I switch back to Image #1, paste the enlarged cropped GIF into place, "flatten" and save the file, and show you what I got:

Image #4

See how the first few years of the dotted red overlay follow very much the same path as the blue line after the 2007 peak? This doesn't guarantee that anything will happen tomorrow, of course. But the striking similarity of the two downtrends makes me think that the uptrends might also turn out to be similar.

So we may soon get a few years when the economy seems pretty good again, while debt races upward even faster than it did before the crisis -- if we have the stomach for that. When those good years come, you know whatever political party is in power will claim all the credit.

Right now, though, nobody expects a few good years.

Funny thing. I had to cut off the last sentence. This was the original ending:

Right now, though, nobody expects a few good years.

I don't either.

I didn't expect the good years back in September of 2015, but I do now. So that last sentence had to go.

Bill McBride: "I don't expect a downturn for employment any time soon"

Bill McBride:

This graph [at Calculated Risk] shows the job losses from the start of the employment recession, in percentage terms, compared to previous post WWII recessions. Since exceeding the pre-recession peak in May 2014, employment is now 4.3% above the previous peak.

Note: I ended the lines for most previous recessions when employment reached a new peak, although I continued the 2001 recession too on this graph. The downturn at the end of the 2001 recession is the beginning of the 2007 recession. I don't expect a downturn for employment any time soon (unlike in 2007 when I was forecasting a recession).

Bill McBride's graph says no downturn. Sounds good.

The secret

Base money, 1918-2016, on a log scale:

Graph #1: Base Money (AMBSL) on a Log Scale

I marked it up by eye so you can see what I'm looking at:

Graph #2: General Trends in Base Money Growth

There's a flat in the 1920s and a flat in the 1950s and a flat again now. Lots of people like the flats, because no inflation. But that is over-simplified. There is something more to be said.

When base money runs flat for a while, as it did in the 1920s, conditions arise which require massive increase, as in the 1930s and '40s. After that increase, base money can run flat again for a while, as in the 1950s.

Another example: Money took a turn around 1960 and started to increase. It increased for a good long time. Then around the year 2000 somebody took it into their head to gradually flatten out base money again. They created a nice, gradual curve to achieve the flattening. Then, all of a sudden, conditions arose which required massive increase. Just like in the 1930s.

(For the record: Yes, it was the flattening that created the crisis.)

After you get massive increase, base money can run flat for a while. That's what happened after World War Two. It is happening again now. We know it worked after World War Two. We don't know if it will work now. I think it will work, and predict vigor. Everyone else seems to think otherwise.

That's fine. I don't know what will happen. I'm reading my graphs and saying as loudly as I can what I think the graphs are telling me. But I could be wrong. Maybe the massive increase since 2008 wasn't massive enough. Maybe going flat now is bringing the economy down again. Today's graphs offer no hint. Yesterday's graphs tell me the massive increase was adequate.

After you get an adequate massive increase, base money can run flat for a while. But after a while, the lack of increase in base money seems to create big problems that require another massive increase in the money. This is important. This is something we need to look at.


After you get the massive increase, you don't have "too little" base money any more. You get economic vigor -- that word, again -- and economic growth. And then, after a while if you flatten the money (or just leave it flat) you get the big problems and you need the massive increase again.

What's missing from this picture is private debt. The growth of base money and the growth of private debt must match. If this does not happen, if private debt grows faster than base, eventually times get hard. And after that you have a crisis. The solution, which is massive increase in base money, solves the problem by reducing the private-debt-to-base-money ratio.

The solution appears to work reliably. But some people don't like it. They don't want the quantity of money inflated.

Hey, if you want base to run flat, then you have to make private debt run flat. If you want private debt to increase, you have to make base money increase. The secret is that the two must stay in proportion.

The two must stay in proportion. Knowing this, you would want to seek the debt-to-base ratio that gives the best economic growth. And you would then want to change base and debt together, so they grow at a rate that keeps prices stable. That way, you cover all your bases: growth, and price stability.