# What’s happening with the Phillips curve ?

Paul Krugman notes that it is standard practice to estimate an accelerationist Phillips curve in which the change in inflation is related to unemployment. He also notes that recent data seem to form the original Phillips curve, that is the scatter of inflation on unemployment forms a curve. He asked if someone might have rolling estimates of the Phillips curve using data from a window of fixed length (say 10 years) for different start dates. His bleg is my command.

To get to the punch line and cut to the chase, this little note concludes that Krugman is right. I admit that’s a dog bites man result, but that’s life.

update: if you are interested in the topic, you really should read the comments by Mark A. Sadowski and Nick Rowe — too much to pull back, but worth reading.

As always, I will provide a fresh look by poking around FRED and doing what seems sensible to me (that is I don’t remember the standard choices of variables and specifications).

The variables I downloaded are

CPIAUCSL “Consumer Price Index for All Urban Consumers: All Items, Index 1982-84=100, Quarterly, Seasonally Adjusted”

PCECTPI “Personal Consumption Expenditures: Chain-type Price Index, Index 2009=100, Quarterly, Seasonally Adjusted”

JCXFE “Personal Consumption Expenditures: Chain-type Price Index Less Food and Energy, Index 2009=100, Quarterly, Seasonally Adjusted”

CPILFESL “Consumer Price Index for All Urban Consumers: All Items Less Food & Energy, Index 1982-84=100, Quarterly, Seasonally Adjusted”

OILPRICE “Spot Oil Price: West Texas Intermediate (DISCONTINUED SERIES), Dollars per Barrel, Quarterly, Not Seasonally Adjusted”

LNU03025703 “Of Total Unemployed, Percent Unemployed 27 Weeks and over, Percent, Quarterly, Not Seasonally Adjusted”

UNRATE “Civilian Unemployment Rate, Percent, Quarterly, Seasonally Adjusted”

HCOMPBS “Business Sector: Compensation Per Hour, Index 2009=100, Quarterly, Seasonally Adjusted”

The dependent variable is a rate of growth of compensation per hour in the “Business Sector”. Uusally I will look at the annual rate of growth based on quarterly data so growth from the first quarter of 2000 to the first quarter of 2001 or from the second quarter of 2000 to the second quarter of 2001. Sometimes I will look at the quarterly growth rate (multiplied by four to roughly annualize it).

One explanatory variable will be the civilian unemployment rate in the quarter preceding the year of wage growth (first quarter of 2001 in my first example). The other explanatory variable is a lagged annual inflation rate in the year ending with that quarter. The coefficient which interests Krugman is the coefficient on lagged inflation. He suspects that it has declined and is close to zero for the recent past. For inflation I use CPI inflation and personal consumption expenditure deflator inflation excluding food and energy (the core inflation measure favored by the FOMC). To eek out every bit of precision I will almost always estimate using overlapping four quarter intervals, so I report Newey West standard errors allowing moving average correlation with three lags. This is the absolutely minimal concession to time series econometrics.

Quarterly data on unemployment, the CPI and hourly compensation are available from 1948q1 on (so annual inflation rates are available from 1949q1 on). However, the personal consumption deflator excluding food and energy is available only from 1959q1 on.

The most basic full sample regression is

Regression with Newey-West standard errors Number of obs = 256

| Newey-West

ldwinf | Coef. Std. Err. t

————-+————————————-

infcpi 0.505 (0.0764) 6.62

unem -0.392 (0.0960) -4.08

_cons 0.057 (0.0064) 8.87

The coefficient on lagged CPI inflation is considerably too low to be accelerationist and this is not allowed. So how about per capital deflator excluding food and energy inflation (infpcec)

Regression with Newey-West standard errors Number of obs = 212

maximum lag: 3

| Newey-West

ldwinf | Coef. Std. Err. t

————-+————————————–

infpcec | 0.889 (0.083) 10.73

unem | -0.654 (0.105) -6.24

_cons | 0.061 (0.007) 8.91

OK that’s better (and shows why the FOMC favors infpcec over infcpi). Note that there are fewer observations. According to this regression the world began in 1960, which makes perfect sense to me (born 1960q4) but might seem odd to Krugman who is older than I am (it’s very hard to find people on the web about whom I can type that).

Estimating with cpi inflation but only for 1960q1 on shows that the difference is partly due to dropping the anchored inflation expectations 50s and partly due to well the point of using core inflation

newey ldwinf infcpi unem if infpcec!=., lag(3)

Regression with Newey-West standard errors Number of obs = 212

maximum lag: 3

| Newey-West

ldwinf | Coef. Std. Err. t

————-+———————————

infcpi 0.635 (0.054) 11.82

unem -0.420 (0.104) -4.03

_cons 0.052 (0.007) 7.16

In any case from now on I will use core inflation infpcec, because the point is to focus on the recent past.

Now how about the estimate for 1970 on ?

Regression with Newey-West standard errors Number of obs = 172

maximum lag: 3

—————————————————

| Newey-West

ldwinf | Coef. Std. Err. t

————-+————————————-

infpcec | 0.936 (0.094) 9.96

unem | -0.635 (0.141) -4.50

_cons | 0.057 (0.010) 5.96

—————————————————–

Even more accelerationist.

OK from 1980 on

Regression with Newey-West standard errors Number of obs = 132

maximum lag: 3

Newey-West

ldwinf | Coef. Std. Err. t

————-+——————————–

infpcec | 0.699 (0.090) 7.83

unem | -0.449 (0.115) -3.92

_cons | 0.049 (0.009) 5.58

For what it’s worth (not much) STATA thinks that it can reject the null of an accelerationist Phillips curve against the alternative of a 1960s vintage Phillips curve with less than one for one feed through of lagged price inflation to wage inflation.

Now from 1990 on

Regression with Newey-West standard errors Number of obs = 92

maximum lag: 3

Newey-West

ldwinf | Coef. Std. Err. t

————-+————————————–

Infpcec | 0.031 (0.470) 0.07

unem | -0.510 (0.139) -3.67

_cons | 0.065 (0.016) 4.05

WHAT ! There is basically no evidence that lagged price inflation has any partial correlation with wage inflation therefore no sign that it has any causal effect. In this super crude regression, there is no hint of evidence that variation of expected inflation has any effect on wage bargaining.

As usual I point out that the estimated equation is not absolutely not a Paleo Keynesian Phillips curve as estimated in the 1960s before Friedman and long before the rational expectations revolution. The Paleo Keynesian view was that expected inflation mattered and that it could be modeled with a coefficients on lagged inflation which were not constrained to add up to one. The increase in those estimated coefficients as new data from the 70s became available was the empirical support for the rational expectations revolution (the rational expectations revolutionaries also invented the claim that Paleo Keynesians didn’t deal with expected inflation at all in a cheep almost slanderous rhetorical trick – basically they were claiming that Paleo Keynesias believed in an equation like the empirical estimate using data from 1990 on).

Now it is very strange that the increase in estimated coefficients caused the widespread to universal conviction that there was something fundamentally wrong with then existing macroeconomics, but an even more dramatic decrease has generally been ignored (strange to people who don’t know how contemporary macroeconomics works anyway).

OK 1995 on

Regression with Newey-West standard errors Number of obs = 72

maximum lag: 3

—————————————————-

| Newey-West

ldwinf | Coef. Std. Err. t

————-+————————————–

infpcec | -1.47 (0.708) -2.08

unem | -0.619 (0.140) -4.43

_cons | 0.099 (0.020) 5.04

Good grief the coefficient on lagged inflation is negative. I am quite sure this is spurious. The sample is now very small (only 18 years so only 18 non overlapping periods). I think what happened is that the late 90s happened to be a period of low price inflation and high wage growth – there is a productivity miracle – dot.com bubble omitted variable (or persistent disturbance of whatever) which took over the regression. I admit this little regression casts doubt on the whole exercize and feel virtuous for reporting it.

OK this century data from 2000q1 on

Regression with Newey-West standard errors Number of obs = 52

maximum lag: 3

–

Newey-West

ldwinf Coef. Std. Err. t

————-+———————————————–

infpcec | -0.718 (0.950) -0.76

unem | -0.405 (0.165) -2.46

_cons | 0.069 (0.026) 2.61

This is what Krugman saw. There is no sign of an effect of lagged price inflation on wage inflation – no wage price spiral.

In this scatter the dates next to the dots are the beginnings of the one year period of wage growth. There is basically a downward slope. The two outliers are 2008q1 – 2009q1 when average hourly compensation actually declined (what a shock). This probably explains the statistically insignificantly negative coefficient on lagged inflation as a period of relatively high core inflation (food and energy prices working through the input-output table) happened to precede the crash. I don’t know what happened starting in 2011.75 (that is the fourth quarter of 2011). It might have had something to do with an election result in November 2012, but I had and have no guess as to the cause.

I have to admit that this note adds little to Krugman’s post. I haven’t systematically estimated rolling regressions. As usual, the data are so dramatically different from what they are supposed to be according to currently standard macro theory that I don’t see any point in doing anything fancy (also I am lazy).

“I have to admit that this note adds little to Krugman’s post. I haven’t systematically estimated rolling regressions. As usual, the data are so dramatically different from what they are supposed to be according to currently standard macro theory that I don’t see any point in doing anything fancy (also I am lazy).”

That’s OK. John Williams already did the rolling regressions, and largely confirms your observations. Page 2:

“In order to see whether the intrinsic persistence in

inflation has changed over the past few decades, I

estimated this Phillips curve model over and over

for different data samples. In each case, the sample

ending point is held fixed at the most recent observation

of the second quarter of 2006.The sample

start date ranges from the first quarter of 1980 to

the fourth quarter of 1999. Because many of these

data samples are quite short, I estimate this model

using Rudebusch’s (1992) median-unbiased estimator

that corrects for the bias in standard least squares

estimation that can occur with small samples. I look

at two popular measures of “core” inflation based on:

(1) the price index of personal consumption expenditures

(PCE), and (2) the Consumer Price Index

(CPI). In both cases, the “core” price index excludes

prices of food and energy components. For the CPI,

I use the Bureau of Labor Statistics’ methodologically

consistent series that corrects for changes in

methodology over the past few decades.

The estimated sum of coefficients on lagged inflation

falls well below one for samples that begin in

the early 1990s or later, indicating that inflation has

become much less persistent in the past 15 years.

Figure 2 shows the resulting estimated sum of the

coefficients on lagged inflation, where the date on

the horizontal axis indicates the starting date of the

sample used for estimation.The decline in the estimated

degree of inflation persistence is evident in

both measures of core inflation.”

http://www.frbsf.org/economic-research/publications/economic-letter/2006/october/inflation-persistence-in-an-era-of-well-anchored-inflation-expectations/el2006-27.pdf

John Williams later used this result to argue that accelerating deflation was unlikely. Page 3:

“This forecast is based on the “average” behavior of

inflation over the past five decades, which includes

both periods when inflation expectations were reasonably

well anchored, such as the past two decades,

as well as periods when they clearly were not, such

as the late 1960s and the 1970s (see Orphanides and

Williams 2005). As discussed byWilliams (2006),

the behavior of inflation over the past 15 years differs

markedly from that in the preceding quarter century.

A Phillips curve model estimate using data since

1993 is consistent with well-anchored inflation expectations

and precludes the emergence of a deflationary

spiral. Indeed, over the past 16 years, the U.S.

inflation rate is negatively related to the change in

the unemployment rate, rather than its level, similar

to the pattern seen in the data from the 1920s and

1930s (see Gorodnichenko and Shapiro (2007) for

related evidence).”

http://www.frbsf.org/economic-research/publications/economic-letter/2009/march/risk-deflation/el2009-12.pdf

The “pattern to which John Williams refers is described in greater detail on the previous page:

“Analysis of the relationship between prices and unemployment

during the 1920s and the Depression

indicates that the inflation rate was closely linked to

the change in the unemployment rate, rather than the

level of the unemployment rate. That is,when unemployment

was rising, prices fell, and when unemployment

was falling, prices rose. This finding indicates

that inflation did not fall into a deflationary spiral as

would be expected if inflation expectations were not

well anchored. Instead, deflation lasted only while the

economy was getting worse and turned to positive

inflation once the unemployment rate stabilized.”

This is what Robert Gordon once termed the “rate of change effect”.

Interestingly, the “rate of change effect” was observed by A.W. Phillips in his original paper on the Phillips Curve. Page 290:

“There is also a clear tendency for the rate of change of money wage rates at any given level of unemployment to be above the average for that level of unemployment is decreasing during the upswing of a trade cycle and to be below the average for that level of unemployment when unemployment is increasing during the downswing of a trade cycle.”

http://www.policonomics.com/wp-content/uploads/The-Relation-Between-Unemployment-and-the-Rate-of-Change-of-Money-Wage-Rates….pdf

Here’s a working link:

http://public.econ.duke.edu/~kdh9/Courses/Graduate%20Macro%20History/Readings-1/Phillips.pdf

This sort of result is exactly what you should expect. if the central bank is targeting inflation. The whole point of inflation targeting is to ensure that expected inflation does not vary over time, so you should not be able to estimate any effect of expected inflation on actual inflation.

Mark Thanks for the information and the link. I think I will update the post to advise readers to read comments rather than pull them all back.

Nick yes. The results are consistent with what central bankers call “anchored inflation expectations” and would occur if inflation were successfully targeted. There are two problems. First inflation is not equal to the target — this could be because the true target is 0 to 2% not 2 % (or 2-4% as a goal not a target in the 80s). Second TIPS breakevens *are* still correlated with lagged inflation. There are two facts (both reported at this blog) one is that lagged inflation has a negative correlation with wage inflation, the other is that the R squared od TIPS breakevens on lagged inflation is about 50%.

You can explain the one I just reported, but not the one I reported February 25 2013 http://angrybearblog.strategydemo.com/2013/02/more-on-adaptive-inflation-expectations.html

Also there are survey’s of price level forecasts made by people chosen as experts. I haven’t reported much on this, but I have been looking at median CPI forecasts from the Livingston survey