Coupla versions of a graph, coupla different worlds

Suppose, in a different world, we take a job that pays a dollar an hour. After each year, we get a ten-cent raise. After the first year, that 10-cent raise is a ten-percent increase. That's decent.

After 10 years, we're making $2 per hour. Now the ten-cent raise is a five-percent increase. Not so decent.

In our 31st year we're making $4 per hour, and now a ten-cent raise is only a 2.5 percent increase. It's still ten cents, but it is not enough.

And in our 41st year we're making $5 per hour, and a ten-cent raise is a 2 percent increase.

In a different different world, we take a job that pays a dollar an hour, but we get a 10 percent raise after each year. Now, no matter how many years we work, every raise is 10 percent. After 8 years we're making more than $2 an hour; after 15 years we're making more than $4 an hour; and after 18 years we're making more than $5 an hour. There's no comparison to that other world.

There's no comparison between ten-cent changes and ten-percent changes.

 

Okay, forget those jobs. I want to look at GDP. Make it Real GDP, where prices never go up. And make it Real GDP per person -- per Capita -- because if Real GDP only doubles when population doubles, we're not gaining anything. (BTW, this still doesn't consider changes to income inequality.)

Real GDP per Capita is not like wages. Someone decides what our wage will be, or maybe we come to an agreement on a number. That doesn't happen with GDP. With GDP we have to wait and see how it turns out: Sometimes the economy grows. Sometimes it doesn't. And if we guess ahead of time what the number will be, it is only a guess. It's not like that with wages.

We wait and see what GDP turns out to be, and what it is after they take inflation out of it, and what it is after they divide by population. And after all that, we can do what I do -- grab the data from FRED or somewhere, and look at how much it changes from one year to the next. 

We can look at the change as an amount (like a ten-cent raise) or as a percent (like a ten-percent raise). I want to look at it both ways, and compare the two.

But changes and growth rates of GDP are jiggy. The numbers change from year to year, and it is hard to get a feel for how things are going. Staying about the same? Improving? Getting worse? So I like to look at periods longer than a year. Longer periods help to smooth out the jiggies by blending them together.

I'm using data that starts in 1948. My first 10-year period takes 1948 as a base year and compares the 1958 value to it, so I have 10 yearly changes (even though I'm using 11 years to do it). (And actually, it is 4 times as many changes because I'm using quarterly data.)

The 1948-to-1958 change is plotted at 1958; next I plot the 1949-to-1959 change at 1959, and so forth up to the most recent data. (Actually, first the 1948Q1-to-1958Q1 change, plotted at 1958Q1, and then the1948Q2-to-1958Q2 change, plotted at 1958Q2. Annual data is SO MUCH easier to work with!)

The data I'm plotting is the average of the changes for each 10-year period. I made one graph showing the 10-year averages of "Change from Year Ago" values of the Real GDP per Capita data, and another showing the 10-year averages of "Percent Change from Year Ago" values. 

And it's probably taking longer to read this than it took me to make the graphs, but that's how it goes sometimes.

Here is the "Change from Year Ago" graph, showing the change in terms of amounts:

This graph shows a general upward trend, with large declines in the early 1960s, the mid 1970s, the early 1980s, the early 1990s, and around 2008. Remember, though, that any year we look at on this graph shows the average for the 10-year period ending at that year. Every point on the graph is the result of a decade of economic data.

Next is the "Percent Change from Year Ago" graph. It shows the same general pattern and the same low-point dates, but the general trend this time is downward:

The relatively large drops are for the most part explained as caused by multiple recessions within the 10-year periods. The low at 1961 shows the effects of the 1953-54 recession, the 1957-58 recession, and the 1960-61 recession. The mid-1970s drop shows the effect of the 1969-70 and 1973-75 recessions. The drop of the early 1980s shows effects from the 1973-75, the 1980, and the 1981-82 recessions. The drop of the early 1990s shows effects from the 1990-91 recession and the Savings and Loan Crisis. And the fall from 2006 to 2011 shows effects from the 2001 recession, the Global Financial Crisis, and the Great Recession of 2007-09. These brief explanations apply equally to both of the graphs.

Setting those large declines and their consequences aside, it is fairly easy to see a general upward trend from the late 1960s to the last data point (2024Q3) on the "Change from Year Ago" graph, and a general downward trend from the mid-1960s to the last data point on the "Percent Change from Year Ago" graph. And now at last, we get to what I wanted to get to.

The Change in Real GDP per Capita shows a trend of increase, and the Percent Change in Real GDP per Capita shows a trend of decrease.

If you look at the raw data for Real gross domestic product per capita (which I used for both graphs) you might notice that the plotted line shows a slight upward curve. If you narrow your browser, the graph narrows with it; this may make it easier to see the curvature. 

I use the edge of a sheet of paper as a straight-edge. I put the straight-edge paper on the low side of the line, hiding most of the lower half of the graph. If you put it on the high side of the line (hiding the upper part of the graph) the things I say below won't make any sense.

The first thing I noticed was that using the paper straight-edge made the drop of 2008-09 look like the most significant event on the graph. The second was that the upward curve of the plotted line continues even after the 2008-09 event.

So the raw data shows an upward curve. This corresponds to the general upward trend of the first graph.

Now, if you want, you can change the vertical scale to a log scale:

• If you narrowed your browser, above, change it back.
• Click the "edit graph" button just above the right end of the graph.
• In the Edit window that opens, click the "Format" tab
• Find "Log Scale" and "Left" partway down the page and click the checkbox to make the vertical scale a Log Scale.

The plotted line on the graph changes from upward-curving to downward curving.

With the Log Scale checkbox checked, I lined-up my paper straight-edge on the middle years (1965 to 1990 or 2000) and the paper I was using covered up the years before 1965 and the years after 1990 (or 2000). With the checkbox checked, the line is down-curving.

And of course, the final step is to uncheck the checkbox and do the straight-edge thing again. With the straight-edge lined up with the data on the 1961 low and the 1990 high, I see most of the data before 1961, and I see the plotted line trying to get out from under the paper by around 1995, and again trying to get out from under the paper a few years after the Great Recession of 2008-09. With the checkbox not checked, the line is upward-curving. Tilt your head so that the part you put the straight-edge on looks "horizontal" and you will see both ends of the plotted line curving "up" and away from the straight-edge.

What the two graphs show is that Real GDP per Capita continues to increase, but the increase has been slowing for decades. The straight-edge technique shows the same.

The general uptrend of the "Change from Year Ago" graph shows the continuing increase. The general downtrend of the "Percent Change from Year Ago" graph shows the increase slowing.

Long-term slowing of economic growth is indistinguishable from the decline of civilization.