When does productivity go high?

Almost always during recessions. Almost no other time.

Output per Hour relative to Output

Productivity without "recession effects"

Productivity goes high after a recession -- after every recession:

Graph #1: Productivity (Percent Change from Year Ago)

That's pretty interesting until you notice how reliable it is. I mean, what does it tell us? It tells us "If you want productivity to go up, have a recession." Great. So when we come out of the recession, productivity goes high for a moment, and then drops way low again.

So, what happens if we finally "solve the economic problem" and never have another recession? Low productivity forever??

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Counting "recession effect" highs produces impressive but questionable productivity numbers. This graph from BLS says 2000-2007 had the best productivity growth since 1973:

Graph #2: Productivity as BLS sees it

But the 2001-2007 business cycle was -- by far -- the weakest of the postwar period. I think the BLS high number for 2000-2007 is a result of counting the recession-effect highs. Sometimes I wonder what productivity would look like if we could cut off those recession-effect highs and get a better feel for productivity in the good years.

But how would you decide which spikes to cut off? I mean, sometimes there is only one spike and sometimes there are two in quick succession. Should we count the two as one spike and cut them both off? What if it's more than two spikes? Should we cut them all off?

Obviously, we need a better plan.

//

If you want to measure productivity in the good years, you have to know what you mean by "good years". Here's a thought: Let's look at productivity in the context of debt service.

This next graph shows productivity as "percent change" (not like Graph #1) together with household debt service. As you know, I find a relation between the two: Low debt service implies low productivity; rising debt service implies rising productivity.

Graph #3: Productivity in the Context of Debt Service

I marked up the graph to show three "bottoms" of the debt service bowl, along with productivity at the bottom:

Graph #4: Productivity at the Bottom of the Debt Service Bowl

Consider one of the three; consider the economy since the crisis. These were not good years. During the recession? Not good. During the remarkable drop in debt service? Not good. How about all the while debt service has been at bottom? Not good. Nobody else puts it in terms of debt service, but this is what everyone has been saying.

My definition of NOT GOOD years is the time of recession, plus the years after it when debt service is falling or running low. The good years, then, begin when debt service is rising from the bottom. And the good years continue to the start of recession.

Having what looks like a workable definition, I downloaded the FRED data for Graph #3 and set to work.

//

Brought the data in to Excel. Went back to FRED for a recession indicator. Added columns for "Bowl Drop" (for times when debt service is falling) and "Bowl Bottom" (for times it is running low). I'll just put a "1" in those columns, on the rows where Debt Service is falling or running low.

I made a new column to total up the Recession, Drop, and Bottom columns. I figure I'll graph the Totals column. That way I can just put "1" in the cells for Bad Years and watch the graph change while I'm working.

Instead of showing "recession bars" on my graph I want to show "bad years" bars. That's what the Totals column is for. My bars will be wider than FRED's recession bars, because I'm including the Drop and Bottom years.

To make this all work I had to dig up the old recession_bars.pdf from the St. Louis Fed. But I needed to use the right axis to make the bar display work. So I had to move Debt Service off the right axis and onto the left with Productivity.

The axis values are different for Debt Service and Productivity. Conveniently though, if I add 11 to the Productivity values, I get the same vertical scale values that Debt Service uses. Couldn't get much simpler than that!

//

The "recession bars" thing worked great (but I need a version of the PDF written for Excel 2010). This one from econ.duke.edu helped.

//

This is the graph I came up with:

Graph #5:Productivity and Debt Service with Good Years on White Background

Basically, the recession bars are wider than before. Each one continues to the right until the red line starts to go up. At the 1990 recession the recession bar also inches leftward for six months (two quarters), as the bowl drop that time started before the NBER recession-start date.

I didn't fiddle with the white area between the 1980 and 1982 recessions. Obviously there is a "recession effect" productivity peak between those two recessions. But the Debt Service data only starts in 1980, and I don't want to guess about any "bowl drop" action. Besides, if I gray out the productivity peak after the 1980 recession, there's almost no white left before the 1982 recession. So I just left that one alone.

My next objective is to get average productivity growth rate values for the areas on white background. I have in mind to compare these values to the numbers on the BLS graph above.

//

So that all worked out okay. I got my "recession, drop, & bottom" data all on gray background, and I figured average productivity rates for the "good years" on white background.

I was ready to compare my numbers to the BLS numbers and I suddenly realized mine are quarterly growth rates and theirs are annual. Their numbers are like four times the size of mine.

And then I realized I didn't know how to figure what FRED calls an "annual rate" for quarterly data. I don't think you just multiply by four. Maybe you do, I don't know. So I scrounged around the web and finally found Annualizing Data at the Dallas Fed.

So now I have my productivity numbers as annualized rates. Turns out that 1994-2001 is the period of highest "good years" productivity, not the 2000-2007 period that BLS shows.

As expected. But look how high the productivity number goes for the "bad" years from 2001 to 2004:

Graph #6: Productivity Growth in Good Years (white background) and Bad Years (gray background)

That is a result of the recession effect. Average the productivity spike numbers into the years before the crisis, and you make the pre-crisis years look like a strong growth period when it was not.

Recession effects are not the same as a healthy economy. Not by a long shot.


// the Excel file

Ergo vigor

"Debt Service" is interest payments plus repayment of principal. So you would expect to see some similarity between household debt service and household debt. That similarity might be reduced by changes in interest rates and changes in the repayment period. But the similarity is easy to find:

Graph #1: Showing Similarity between Debt and Debt Service

The two data sets share an underlying pattern. I marked up the graph to emphasize it.

My markups of the graph are nearly continuous except in two places: at the start, because Debt Service numbers before 1980 are unavailable; and in the years before the crisis.

The gap before the crisis is much bigger for the blue than for the red; this suggests that a lag developed (or lengthened) at that point. The gap in the red contains a downward trend in the data. The gap in the blue contains a comparable downward trend followed by a pretty severe uptrend in debt service. Crisis-related? No doubt.

//

I couldn't resist predicting similarity at the end, where the red line rises and I expect the blue to follow.

//

I went over the graph and wrote down turning-point dates for the red series and corresponding dates for the blue series. For each pair I subtracted the one date from the other, and came up with a "length of lag" number. I took the lag lengths and put them on a graph:

Graph #2: Length of Lags in the Debt Service Pattern

The last two are red because we have not got to the end of those lag periods yet. My estimate of lag length is on the high side, between four and five years. One year less is plausible; two years less is not.

I plan to take this lag information and apply it to my projection of vigor in GDP. Off the top of my head, I'll say household debt begins rising just where it crosses the debt service line, in 2012 Q1 on Graph #1.

If the lag is four or five years, we should see debt service start rising some time between early 2016 and early 2017.

That increase will be the right side of the bowl shape in debt service. And remember, when we are going up the right side of that bowl, that is when we expect labor productivity to increase.

Ergo vigor.


// the Excel file

What Keynes said

What Binyamin Appelbaum said:

Growth remains slow despite the Federal Reserve’s campaign to stimulate the economy. Predictions of faster growth, followed a few months later by disappointment, have become an annual ritual.

What Keynes said:

[We assume] the existing state of affairs will continue indefinitely, except in so far as we have specific reasons to expect a change.

What I said:

From yesterday's post: High GDP growth soon, using my lowest projection

I'm trying to come up with "specific reasons", so people can stop assuming that "the existing state of affairs will continue indefinitely".

Putting numbers on vigor (7: Developing GDP)

From Wednesday we have this:

Graph #1: GDP to Household Debt since 2005, and Five Projections

We're looking at the ratio of GDP to household debt, a ratio that goes down except in abnormal circumstances. I should toss out not only the polynomial projection that goes crazy high but also the two projections that run flat.

I won't toss anything yet.

//

The graph shows GDP divided by debt. If I take those numbers and multiply them by the debt (household debt) I get GDP. Five projections of GDP out to 2025. These are predictions of a general trend. They do not predict recessions, which are disturbances to the general trend.

I'll take household debt and projections from Tuesday's spreadsheet. For now I'll just use the baseline estimate, the red line between the green and gold. Multiply Wednesday's data by Tuesday's, and we get estimates of GDP.

Graph #2: GDP and Projections to 2025

Yeah, I'm getting rid of the "Poly" projection, the tall one.

Graph #3: GDP and Projections (Red Poly omitted)

I should keep only the lower of the two remaining projections shown. Actually four remain, but there is some overlap, so only two are visible. I should keep the lowest one. In this series of posts, my argument is that GDP is going to go high. (My evidence is what's happening to Debt Service, which we talked about some days back.) I should keep the lowest one so that, when debt goes high, it isn't because I picked a high projection. We'll get to that.

In the legend, the projections are all called red. "Red" is a reference to the color of the baseline estimate on Tuesday's graph #1. The middle projection, based on the 2010-2016 numbers for household debt.

Right now I want to look at "percent change from year ago" numbers for GDP:

Graph #4: GDP and Projections (Percent Change from Year Ago)

Yeah, I'll just keep the one projection, the lowest one. Linear, called "Red Lin", actually the green line.

Once again, the projections are smooth while the blue line is jiggy. I'm thinking, to make them comparable I should show the Hodrick-Prescott for the whole thing. So: Keep the low projection, add a Hodrick-Prescott, and make the historical data faint.

Graph #5: GDP with the Lowest Projection, and the H-P Trend

Now we're getting there. The jiggies run higher than the trend, which made the low projection unimpressive on Graph #4. But as #5 shows, the uptrend will be quite impressive.

To refresh your memory, this estimate of future GDP is based on present trends in household debt service, household debt, and the ratio of GDP to household debt.


// the Excel file

Putting numbers on vigor (6: Projecting GDP)

We now have a projection for household debt ten years into the future. Nine years, whatever. My idea is to look at the "household debt to GDP" ratio and see if I can predict that graph ten years out also, and then divide the debt out of it and end up with a prediction for GDP.

My first thought was to make a prediction based on a particular part of the debt-to-GDP ratio. Omit the early years when debt was particularly low. Omit the "Great Inflation" years when GDP was particularly high. And omit the "housing bubble" years when debt was particularly high. I'm left with the the years from 1986 to 2000, where the ratio runs straight and somewhat uphill.

Graph #1: Household Debt as a Percent of GDP

It's easy to imagine the future if it follows a straight line. And it seems right, because the line runs uphill.

Then I looked at the "GDP to household debt" ratio and it seemed a better choice. The general trend of the line is down rather than up. So the changes in recent years are smaller, rather than bigger. I felt I could make a better prediction because the recent changes are smaller. It's the same numbers, just B divided by A instead of A divided by B -- I know that, but I went with it anyway. The first (rightmost) four worksheets in today's Excel file develop this idea.

What I imagine looks something like this:

Graph #2: GDP as a Multiple of Household Debt

It's easier to see on this graph than the previous one: In the years before 1960 the blue line was high (but coming down) because debt was so low (but growing quickly)... From the mid-1960s to the mid-1980s the blue line was high because inflation pushed the GDP numbers up... and after 2000 the blue line went low because there was so much "housing bubble" debt.

//

I was not comfortable with the idea of using 15- to 30-year old data to predict future data values. But I went through the motions in a spreadsheet. It turned out that both the exponential and linear trend lines (based on the 1986-2000 period) ran quite near the most recent data.

I could explain that to myself (no Great Inflation, etc.) but I had no great confidence in the explanation. So I decided to set this work aside and take another crack, using a different approach.

I decided to see how the trends look if I use only the most recent data.

I looked at the numbers. The last three show decrease. Before that, the numbers were pretty reliably increasing since 2009. If I wanted to avoid using numbers from the housing boom correction, I was left with only the last three values. So I went with that.

I was even more unhappy about using only three values than I was about using only the 1986-2000 data. So I was extra cautious. I figured I'd apply all of Excel's different trend line types to those three data points, and see what turned up.

The next five graphs show the three most recent values in red (at the right end of the blue line) and the older data in blue. The trend line based on the three red values is shown as a black line. The five graphs are the same except for the black line and its identifier in the legend.

Unbelievably, four of the five trend lines turned out good. That is, four of them are surprisingly similar to the red line on Graph #2, which was my previous best guess. I show all five.

Graph #3a: Exponential Trend

Graph #3b: Linear Trend

Graph #3c: Log Trend

Graph #3d: Power Trend

Graph #3e: Polynomial Trend

The polynomial trend shows its penchant for making "bowl" shapes. It is far from the blue line for most years on the graph. As for the others, I was astounded. All four black lines run close to the blue line. The first three follow the general downsloping path since around 1960; the fourth follows it from the start.

In every case except the polynomial, the black trend line runs particularly close to the blue line in the 1986-2000 period that I first considered.

The linear trend line, my personal favorite, not only touches the last three values and clings tightly to the blue line for 1986-2000, but also meets the blue line in 1964. This line, in other words, is very much like my red line on Graph #2, only better.

With these results, I was no longer concerned that using only three data points was a problem. Instead, it appears that with these last three points the GDP-to-household-debt ratio has pretty well returned to its general trend. It looks like we are done recovering from the housing bubble.

//

To get data for my ten-year projection, I modified each of the five graphs #3 above as follows:

1. Remove the dates and date formatting from the x axis.
2. Reselect the data so that the first data used to figure the trend is the first data shown on the graph; for accuracy, increase the number of digits displayed in the trendline label.
3. Copy the equation from the trendline label, use it calculate data for the projection, and show the resulting data as a new line on the graph to verify that it matches Excel's trend line.

After modification, the linear trend graph looks like this:

Graph #4: Showing the Trend Calculation Developed and Tested

The others are on sheet "FRED Graph (4)" of the Excel file.

//

After I developed and tested the calculations for all five trend lines, I gathered 'em up and put all five projections together on one graph:

Graph #5: GDP to Household Debt (blue) and Five Projections

The blue line on graph #5 shows all the way back to the start of the FRED data. Now that you've seen the projections in context, I'll trim off the blue before 2005:

Graph #6: GDP to Household Debt since 2005, and Five Projections

The five data projections look like three. It is hard to distinguish one from another without looking at the Excel file. The projection that sweeps up and to the right is the polynomial calculation (making another bowl). The projection that runs downward is really two lines: Linear and Exponential. The gray projection that runs flat is also two lines: Log, and Power.

//

Almost done.


// the Excel file

Putting numbers on vigor (5: A look at the Debt Projections)

I'm going back to the three projections we started with yesterday, the ones I decided to keep. I'll even keep the red, green and gold colors for the projections, as we won't be adding any more lines to the graph.

Graph #1: Household Debt and Three Projections to 2025

Here's a look at the growth of those numbers:

Graph #2: Percent Change from Year Ago, Household Debt & Projections

Oh. These don't seem to be realistic projections of debt growth. Not that they are too smooth, but that they level off so quietly. They gradually top out rather than rising to a vigorous peak. It doesn't seem right. It doesn't seem to be the way debt normally behaves. What can I do to check this?

I'll compare these projections to the bowl of the 1990s.

After 20 years of economic sluggishness, what did household debt look like when we were coming out of the bowl, transitioning to the "new economy" of the latter 1990s? It looked like this:

Graph #3: Percent Change from Year Ago, Household Debt 1988-1996

A gradual transition. No vigorous peak. It quietly levels off. And it levels off at about 7.5%, just like the red line on Graph #2. Talk about coincidence!

Okay, I changed my mind. I like those Graph #2 projections.


// the Excel file

Putting numbers on vigor (4: Projecting household debt)

Well, I left myself a mess. In part 3 of this series we came up with several possible futures for household debt. What to do with them, what to do.


This is the debt we're looking at, household debt:

Graph #1: Household Debt

The image is current as of 10 September 2016. The last data value shown is for the first three months of 2016. That point on the graph represents just over 14 thousand billion dollars of household debt. That's just about the same as it was at the start of the so-called Great Recession.

This next graph shows that same data, in Excel, along with three estimates of household debt out to the end of 2025.

Graph #2: Household Debt and Three Projections

The most interesting thing about this graph is that it makes 14 thousand billion dollars look like nothing.

The red and green lines we saw before, in black. They are Excel's trend lines in the first graph of 10 September.

The red line here extends the trend based on data from 2010 Q1 to 2016 Q1. The green line extends the trend based on data from 2013 Q1 to 2016 Q1. We see slower growth of debt in the green line than the red. These lines show nothing more than a continuation of changes that occurred in the last few years. The difference originates in the choice of years the trends are based on.

Based on my notes of 8 September, I'd say the green line here is probably a low-ball estimate of debt growth. The red line represents a more likely path for future debt growth; that would be my guess. But I think there is some chance that debt will grow at a faster rate than indicated.

I took the difference between red and green, and added that difference to the red line to get an even higher estimate of household debt in the years ahead: the gold line. Based on the three projections shown, by the end of 2025 household debt will be something over $20 trillion, something over $25 trillion, or something over $30 trillion.


I want to use the red line on Graph #2 as a base line. Household debt may accumulate at a slower rate (green) or a faster rate (gold) but I expect it to be somewhere in the neighborhood of the red.

To this graph I want to add the estimates of future debt based on Graphs #4 and #5 of 9 September. For these I have to work out values based on the trend lines, and then take "debt service" out of those values to get predictions of future household debt.


Trying to think of a way to present this mess of lines. Colors, you know. I'll keep the historical data blue. But I'll change the red, green and gold from Graph #2, making all three red for the next graph. The middle of these three lines is my "baseline estimate" for household debt over the next decade. The other two red lines are low-ball and high-ball estimates. The three red lines together show the central path and a plausible range for that debt.

This leaves any color other than red or blue which can be used for the "polyline" estimate (see Graph #4 of 9 September) and the "power" estimate (Graph #5 of the 9th) and also a "linear" estimate (see the Excel file linked below).

I'll show the historical data back only to the year 2005, and make the graph taller to spread the lines out a bit.

Graph #3: Household Debt and Six Projections

Okay. Look at the three lowest projections -- dark gray, light gray, and dashed red. These are pretty well clustered together. The dark gray line is based on Excel's "power" trendline using historical data from 2010 to 2016. The other two use historical data from 2013 to 2016, the period of slower increase.

The green line is based on a linear trend line and on the "slower" 2013-2016 data.

All the lines end a little above 20 trillion, a little above 25 trillion, or a little above 30 trillion, as before.

So what does it mean that the three new lines run fairly close to the three red lines? It certainly does not mean that my predictions are right. I think it means that I maintained the same assumptions all through the process of calculation and that I didn't make any really big mistakes.

But it might mean that I failed to maintain my assumptions and made one or more lucky mistakes that nicely offset the changes in my assumptions.

Hey, this is prediction. I'm only trying to get an idea what might happen. It doesn't "mean" anything. But it is useful, because if I get an idea what might happen to household debt, maybe I can get an idea what will happen to economic growth.

Talk about assumptions!

Anyway, having looked at all these lines, I think I will just keep the red lines and forget about the rest. That will give me a range of possible paths to the future.

And somehow, we end up back where this post started, with just the three lines.


// see also 2020 vision

// the Excel file

Putting numbers on vigor (3.75: A look at the last time)

A little worried now about vigor. I've been shouting "vigor" since March. This is September. I didn't expect vigor by now, no. But I got worried when I looked at the two trend lines on yesterday's graph. It looks like things are getting slower. Less vigorous.

Yeah, maybe I was expecting vigor by now, yesterday. What was I thinking??

So I thought I'd take a look at what happened in the 1990s when there was a similar "bowl shape" in the household debt service data.

This is Household Debt Service (TDSP at FRED) from 1990 thru 1996:

Graph #1: The Bowl-Shape in Household Debt Service, 1991-1995

I colored in one side of the bowl red and the other side green. So you can see the bowl, and so you can see the parts of it I'm looking at.

Now I'll take the red part and the green part and put trend lines on them. I'm making the trendline for the red line dashed-red and the one for the green line dashed-green. Both are second order polynomial trend lines, which make a nice bowl shape.

Graph #2: Trend Lines Added

Right away, I relaxed a little bit. There is a delay of several months between the dashed red and green lines on the right side. More than on the left side. If I was doing this in late 1993, I'd be saying But the line is supposed to be going up now, looks like it isn't going up! And I'd have been all worried for nothing.

So I'm not gonna worry about our bowl. We should start seeing it pretty soon, the right side curving up. If it doesn't come today I don't have to lose any sleep over it.

// the Excel file