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.

a pdf of this post is here.

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.

Phillips

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).

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