# A bit More on the Phillips Curve

I have been playing with the Livingston survey economic forecasts and, in particular, with the median forecast of CPI inflation over the following 6 and 12 months. The survey was conducted each June and December since June 1946. For some reason, the data are available in two files one with forecasts made December 2003 and earlier and the other with forecasts made June 2004 through December 2013. To avoid the risk of data snooping (and from laziness) I downloaded and analysed only the pre-2004 data. Yesterday, I downloaded the 2004-2013 forecasts (of the CPI December 2004 through December 2014).

Here I look at Livingston Survey median inflation forecasts and nominal wage growth, following up on these posts (which describe the other data I used).

Here I add the newly downloaded inflation forecasts and show that since 1990 nominal wage growth has not been associated with Livingston forecast inflation (at least once unemployment is taken into account).

A graph and some regressions after the jump

ldfinf12 is the forecast of inflation over the next 12 months, ldwinf is the growth of Business Sector: Compensation Per Hour over the next 12 months.unem is the unemployment rate.

Over the full sample

. reg ldwinf unem ldfinf12

Number of obs = 130
R-squared = 0.3616
Root MSE = 2.0467

ldwinf | Coef. Std. Err. t
————-+————————————————–
unem | -.5611155 .1144068 -4.90
ldfinf12 | .5609176 .0684526 8.19
_cons | 6.557312 .6501197 10.09

(Note these are overlapping 12 month periods sampled every 6 months so the disturbances can’t be independent).

Now using forecasts made June 1990 and later

. reg ldwinf unem ldfinf12 if dat>1989.9

Number of obs = 46
R-squared = 0.2856
Root MSE = 1.4973

ldwinf | Coef. Std. Err. t
————-+————————————————–
unem | -.534131 .1400077 -3.82
ldfinf12 | .163519 .2904923 0.56
_cons | 6.264191 1.373529 4.56

The coefficient on the inflation forecast becomes much smaller.

Here is a possibly valid test of the null that it is zero (that is standard errors are calculated assming ma1 disturbances)

. newey ldwinf unem ldfinf12 if dat>1989.9,lag(1)

Regression with Newey-West standard errors Number of obs = 46
maximum lag: 1
| Newey-West
ldwinf | Coef. Std. Err. t
————-+————————————————–
unem | -.534131 .1572818 -3.40
ldfinf12 | .163519 .3714307 0.44
_cons | 6.264191 1.766739 3.55

When only 21st century data are used, the coefficient is even smaller

. newey ldwinf unem ldfinf12 if dat>1999.9,lag(1)

Regression with Newey-West standard errors
Number of obs = 26
maximum lag: 1
| Newey-West
ldwinf | Coef. Std. Err. t
————-+————————————–
unem | -.382222 .1617927 -2.36
ldfinf12 | .0168252 .6484933 0.03
_cons | 5.476139 2.419621 2.26

now wage growth (ldwinf6) and forecast inflation (ldfinf6) over the next 6 months

. reg ldwinf6 unem ldfinf6 if dat>1989.9

Number of obs = 47
R-squared = 0.2120

ldwinf6 | Coef. Std. Err. t Conf. Interval]
————-+————————————————–
unem | -.2657846 .0875081 -3.04
ldfinf6 | .0925689 .1406687 0.66
_cons | 3.057346 .8000887 3.82

and

. reg ldwinf6 unem ldfinf6 if dat>1999.9

Number of obs = 27
R-squared = 0.2054
Root MSE = .90156

ldwinf6 | Coef. Std. Err. t
————-+———————————-
unem | -.2099769 .1086516 -1.93
ldfinf6 | .0786299 .2443446 0.32
_cons | 2.678293 1.174396 2.28

The regressions do not suggest that price inflation does not cause future wage inflation because inflation expectations are anchored. As measured by the Livingston survey, Livingston inflation forecasts are not anchored. The regressions suggest that expected inflation hasn’t affected nominal wages in recent decades.

Of course, the Livingston survey participants are not major negotiators of wages (they deal with their own salaries and I guess a few research assistants).