Inflation, Unemployment, and Labor Force: ThePhillips Curve and Long-term Projections for Japan

Ivan. O. Kitov1 and Oleg I. Kitov2

1Russian Academy of Sciences2Department of Economics and Institute for New Economic Thinking, University of Oxford

Introduction

Objective: Estimate several empirical relationships between inflation, π(t),unemployment rate, u(t), and the change rate of labor force level, l(t) = dlnLF (t)/dtfor Japan within the Phillips curve framework.

Contribution 1: The rate of labor force change has never been tested in any econometricsetting as a predictor of inflation and/or unemployment.

Contribution 2: No autoregressive term in the Phillips curve - causal relationship betweeninflation, unemployment rate and labor force rate of change.

Approach: The original Phillips curve (PC) formulation (1958) as well as the reversedirection of causation introduced by Fisher (1973) considers the link between inflationand unemployment as a causal one - the autoregressive term is absent.

Empirical Relationships: Estimate two individual relationships between the change rate oflabor force and inflation, and the change rate of labor force and unemployment as well asa generalized relationship between all three variables:

π(t) = α1 + β1u (t − t1) + ε1 (t) (1)

π(t) = α2 + β2l (t − t2) + ε2 (t) (2)

u(t) = α3 + β3l (t − t3) + ε3(t) (3)

π(t) = α + βl (t − t2) + γu (t − t1) + ε (t) (4)

where:I π(t): inflation rate

I u(t): unemployment rate

I l(t): rate of change of labor force

Methodology:

I Boundary Elements Methods on the cumulative curves

I Johansen cointegration tests

Data on Inflation and Unemployment Rate

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

1970 1980 1990 2000 2010 2020

Rat

e, 1

/y

DGDP, OECD

CPI, SB

0.00

0.01

0.02

0.03

0.04

0.05

0.06

1960 1970 1980 1990 2000 2010 2020

Rat

e

u, OECD

u, SB

Forecasting: Construct long-term forecasts of inflation and unemployment rate usingvarious labor force projections for Japan.

Inflation Through Labor Force

GDP Deflator: There is no time lag between inflation and unemployment in Japan.Coefficient α1, defining the level of inflation in the absence of labor force change, ispractically indistinguishable from zero.

π(t) = 0.0007(0.002)

+ 1.31(0.19)

l (t − t1) (5)

Consumer Price Index: The estimated relationship has a different slope but a similarintercept term close to zero. This means that the watershed between inflation anddeflation in Japan is a zero growth rate of labor force.

π(t) = −0.0084 + 1.90l (t − t1) (6)

DGDP and CPI Predicted vs Actual: The annual curves are smoothed with MA(3) todemonstrate that the model error is likely a realization of random noise - the predictedand observed curves practically coincide in amplitude and turning points.

-0.04

0

0.04

0.08

1980 1985 1990 1995 2000 2005 2010 2015

Rat

e,1

/ y

CPI(t)

Predicted

After 2003

0

0.1

0.2

0.3

1980 1985 1990 1995 2000 2005 2010 2015

Cu

mu

lati

ve v

alu

e

CPI(t)

Predicted

After 2003

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1980 1985 1990 1995 2000 2005 2010 2015

Rat

e,1

/ y

DGDP

Predicted

After 2003

DGDP, measured MA(3)

Predicted, MA(3)

-0.05

0.00

0.05

0.10

0.15

0.20

1980 1985 1990 1995 2000 2005 2010 2015

Cu

mu

lati

ve v

alu

e

DGDP

Predicted

After 2003

Unemployment Rate and Generalized Phillips Curve

Measurement Issues:

I If the link between labor force and inflation is a causal one, all short-term oscillationsand uncorrelated noise in the data should be related to inaccurate measurements.

I Measuring precision of the change in labor force level should increase with the timebaseline.

I Use cumulative curves: the net change during the 30 years should be measured withlower relative uncertainty than during one year.

Unemployment Rate: Find a structural break in the beta coefficient in 1976. The drivingforce of unemployment is the change in labor force, which is defined by the working agepopulation and the rate of participation in labor force.

u(t) = −0.179l(t) + 0.0432, for t < 1977 (7)

u(t) = −1.556l(t) + 0.0432, for t ≥ 1977 (8)

Generalized Phillips Curve: The three involved variables are linked by a long termcointegrating relation. The Johansen test shows one cointegartion relation for thesethree variables. Univariate unit root tests applied to the residual time series (modelerror) also reject the null of a unit root for the residual series.

π(t) = −10.0l(t) + 0.9u(t) + 0.161, for t < 1982 (9)

π(t) = 2.80l(t) + 0.9u(t) − 0.0392, for t ≥ 1982 (10)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1960 1970 1980 1990 2000 2010

Rat

e

u

Predicted

After 2003

0

0.5

1

1.5

2

1960 1970 1980 1990 2000 2010 2020

Cu

mu

lati

ve v

alu

e

u

Predicted

-0.05

0.00

0.05

0.10

0.15

0.20

1960 1970 1980 1990 2000 2010 2020

Rat

e,1

/ y

CPI

Predicted

0.0

0.5

1.0

1.5

1960 1970 1980 1990 2000 2010 2020C

um

ula

tive

val

ue

CPI

Predicted

Long-term Projections

Labor Force Projections: The National Institute of Population and Social SecurityResearch projections of total population. We use the 2005 population projection andconsider a constant rate of labor force participation fixed to 0.521, as measured in 2000.Labor force in Japan projected to decrease from 67,000,000 in 2010 to 57,000,000 in2050.

Labor Force Measurements and Long-term Projection:

-0.02

-0.01

0.00

0.01

0.02

0.03

1960 1970 1980 1990 2000 2010 2020

Rat

e, 1

/y

l, OECD

l, SB

l, BLS

45,000

50,000

55,000

60,000

65,000

70,000

1960 1980 2000 2020 2040 2060

#, ×

10

00 Labor force

Projection

Inflation and Unemployment Long-term Projections:

I DGDP will be negative (between -1% and -2% per year) during the next 40 years

I Unemployment will increase from 4.0% in 2010 to 5.0% in 2050.

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1980 1990 2000 2010 2020 2030 2040 2050 2060

Rat

e,1

/ y

DGDP

Predicted

Projection

0

0.01

0.02

0.03

0.04

0.05

0.06

1960 1980 2000 2020 2040 2060

Rat

e

u

Predicted

Projection

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

1980 1990 2000 2010 2020 2030 2040 2050 2060

Rat

e,1

/ y

DGDP

Predicted

Projection

0

0.01

0.02

0.03

0.04

0.05

0.06

1960 1980 2000 2020 2040 2060

Rat

e

u

Predicted

Projection

Conclusions:

I Inflation and unemployment rate are related through the rate of change of labor force.

I The relationship is cointegrating, no autoregressive terms, no lags and one break.

I In-sample predictions are quite accurate and improved by smoothing.

I Based on cumulative curves, errors are likely to be due to measurement inconsistencies.

I Long-term projection: falling inflation and rising unemployment.