Monday, May 2, 2016

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:

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.


Oilfield Trash said...


"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 do not get it. It either is a curve or not. Curve shifting??

Just to put all my cards on the table, I do not agree with Solow and Samuelson interpretation of this alleged relationship between the level of unemployment and the rate of inflation.

In particular, Phillips extended his model to consider the impact of expectations upon prices.

Given how much his work has been falsely denigrated by neoclassical economists for ignoring the role of expectations in economics, this aspect of his model deserves attention prior to considering the Phillips Curve itself.

Below is Keens Take on the Phillips Curve.

Phillips didn’t merely talk about expectations: he extended his model to incorporate them. As part of this project, Phillips also hypothesized that there was a nonlinear relationship between ‘the level of production and the rate of change of factor prices [labor and capital]. The role of this relationship in his dynamic model was to limit the rate at which prices would fall when unemployment was high, in line with ‘the greater rigidity of factor prices in the downward than in the upward direction’. In a dynamic model itself, this does not lead to a stable trade-off between inflation and unemployment – which is the way his empirically derived curve was subsequently interpreted – but rather limits the volatility of the cycles that occur compared to what a linear relationship would yield.

(Maybe this is what your are seeing in the colors)

BurkeyAcademy said...

Here is a YouTube video I made some time ago using quarterly data and an animated graph in R, so you can see the evolution of various patterns. I provide a link so that you can download the code and data in the Description section of the video.

Oilfield Trash said...

Burkey Academy and Art

Seems that you are trying to explain the various patterns of feedback effects and disequilibrium dynamics (expectations) with a traditional linear Phillips Curve.

Instead it may be much easier to say the model economy is inherently cyclical, and there is no equilibrium ‘trade-off’ between inflation and unemployment. A nonlinear ‘Phillips Curve’ perspective.

That is what I see in the patterns and colors. No need to talk about curve shifting.

The Arthurian said...

Oilfield, seems to me YOU are the one trying to "explain" the "Feedback effects" and all the rest. Me and Burkey are just looking at the graph and trying to distinguish one bunch of dots from another.

You seem to want to explain the graph while at the same time ignoring rather than seeing what it shows.

Don't let "curve shifting" make you nervous.

They do not seem to have realised that, unless the supply of labour is a function of real wages alone, their supply curve for labour will shift bodily with every movement of prices.

The Arthurian said...

Good stuff, BurkeyAcademy! Too many people think the Phillips scatter is an ink blot. By looking at chronological development of the scatter, you're seeing how things changed over time. By making chronological groupings, George Lesica did the same. So much more interesting than an ink blot!

Hey, nice site you've got there.