The trendline shows the shifting of the Phillips curve

My eyes popped right out my head when I saw George Lesica's graph of the Phillips curve. Here, take another look:

Source: https://lesica.com/exploring-the-phillips-curve.html
Copyright by George Lesica - Licensed CC BY-SA
Size reduced to fit my blog -- Click for larger image

The Phillips curve is no longer a meaningless cluster of dots. Lesica's graph shows "trade-off" curves in red and yellow and cyan and green and blue, all of them showing that inflation tends to be higher when unemployment is lower, and lower when unemployment is higher. That's what you're supposed to see in all those dots. Now, at last, I see it.


In the old PDF from 1958, where Bill Phillips introduced his curve to the world, he opened his remarks with these simple thoughts on supply and demand:

When the demand for a commodity or service is high relatively to the supply of it we expect the price to rise... Conversely when the demand is low relatively to the supply we expect the price to fall...

The supply and demand for labor works the same way, he said.


On the Phillips Curve graph, low unemployment is toward the left and high unemployment is toward the right. Low inflation is toward the bottom and high inflation is toward the top.

On the graph, "High inflation and low unemployment" is toward the upper-left. "Low inflation and high unemployment" is toward the lower-right. On the graph, a change from the the one state to the other produces a cluster of dots that is high on the left and low on the right. George Lesica's graph shows several of these clusters.


Time and time again I've seen people show a scatterplot with the dots all the same color. They put a straight-line trend on it, and point out that the trendline goes from low-on-the-left to high-on-the-right. That's not a Phillips curve, they say.

"As for inflation-unemployment “tradeoffs,” we should all be clear about what the data look like in practice..."
Source: Hussmann Funds

"If anything, [the trend line] suggests that higher unemployment and higher inflation in that very noisy data set go hand in hand."
Source: Illusion of Prosperity

"While playing with the data, a statistically significant relationship between inflation and employment growth emerges. 95 confidence interval on the slope returns (0.04, 0.22)."
Source: Synthenomics

"In English: there is no firm relationship here and the extremely weak relationship we do find runs in the opposite direction to what the Phillips Curve would predict."
Source: Fixing the Economists

"Indeed, if we do a reverse regression with the variable on the horizontal axis in the chart serving as the dependent variable, we can fit a long-run Phillips curve to the data, and that's the regression line in the chart."
Source: Stephen Williamson

"The Phillips curve is one of those 'regularities' that is more likely to exist in an economist mind than in reality."
Source: Naked Keynesianism

The trend line goes up-to-the-right, these people say, not down-to-the-right like the Phillips curve would. There is no Phillips curve, they say.

But the straight, upsloping trend line that these graphs show is not the Phillips curve. The trendline shows the shifting of the Phillips curve, not the shape of it.


Milton Friedman didn't say there's no Phillips curve. Friedman knew about supply and demand. He knew there is a tradeoff between inflation and unemployment.

What Friedman said was that the curve could shift to a different location, and we could end up with high inflation and high unemployment. High and high instead of high and low, he said.

He was right about that. When it happens, the scatterplot dots get more scattered on the graph. But if you have all the dots the same color, it doesn't look like different curves in different locations. It looks like there is no Phillips curve. But you can't really tell, because all the dots are the same color.


I wanted to duplicate George Lesica's graph. Duplicate it, because I never did manage to make a graph that shows the Phillips curve. Duplicate it, to learn how to make such a graph, and to make sure nobody's pulling my leg.

But there were things I didn't know. Was Lesica's data quarterly or monthly? I counted his blue dots and came up with way more than I should for quarterly data, so I went with monthly. Ended up with more than 800 rows of data in the spreadsheet. Would you guess there's 800 dots in the scatter above? I wouldn't.

And then, I didn't know how to handle the inflation rate, calculated (Lesica says) for the "subsequent 12 month period". It sounds simple. But when you have to work it out in a spreadsheet, there are many ways to do it. I was trying to duplicate one particular way without knowing which one. Here's what I did: From the first row of data I took the January 1948 unemployment rate, and paired it up with a calculation for inflation: the Jan 1949 CPI over the Jan 1948 CPI, minus 1, formatted as a percent. (The CPI numbers come as index values, so I had to calculate the inflation rate myself anyway.) Then I copied the calculation down the 800 rows.

Then I took my VBA code and modified it to generate the data subsets and make all the dots round and color them to match what George Lesica had done. Working out the colors was the hardest part. Here's how my graph came out:

Graph #2

I'm happy.

"Series1"  in the legend is Excel's original plot of the whole dataset. (I just left it there. Those dots are all hidden by the subset dots in various colors.)

My data (from FRED) runs from 1948 to March 2016. My scatterplot stops at March 2015 so that I can calculate the subsequent twelve months' inflation. George Lesica's graph stops in 2012. I have extra years. I made them brown, my dots after 2012. Coulda made them yellow, they fit right in with the yellow curve.

You'll want to compare the two graphs. "Note, for instance," George Lesica says, "the dark blue cluster in the upper right, they appear to form a curve that is convex to the origin, just as the theory says they should." I got the same dark blue cluster, forming the same curve.

If you go dot by dot, the two graphs still match up. Take the highest group, looks like five of those dark blue dots. The pattern of those five dots is almost identical on the two graphs. Below that group, a single dot (on both graphs) and to the right of it another group -- again with very similar arrangement on the two graphs. The slight variations could be due to data revisions or to different data sources (Did Lesica use the Consumer Price Index, or something else? I'm not sure) or to my choice of the calculation for the inflation rate.

But the slight variations don't concern me. I got curves, Phillips trade-off curves, identifiable by color. These curves correspond to those on the graph from George Lesica. Now I'm confident in his work and happy with mine, and I've finally managed to plot a Phillips curve that actually looks like a Phillips curve.

All in all, a good day.


// The Excel file.