  A linear and lagged relationship between inflation, unemployment and labor
force change rate, p(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+ A2, where A0, A1, and
A2 are empirical country-specific coefficients, was found for developed
economies. The relationship obtained for France is characterized by A0=-1,
A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a RMS
forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between
1971 and 2004. The relationship is tested for cointegration. All three
variables involved in the relationship are proved to be integrated of order
one. Two methods of cointegration testing are used. First is the Engle-Granger
approach based on the unit root test in the residuals of linear regression,
which also includes a number of specification tests. Second method is the
Johansen cointegration rank test based on a VAR representation, which is also
proved to be an adequate one via a set of appropriate tests. Both approaches
demonstrate that the variables are cointegrated and the long-run equilibrium
relation revealed in previous study holds together with statistical estimates
of goodness-of-fit and RMSFE. Relationships between inflation and labor force
and between unemployment and labor force are tested separately in appropriate
time intervals, where the Banque de France monetary policy introduced in 1995
does not disturb the long-term links. All the individual relationships are
cointegrated in corresponding intervals. The VAR and vector error correction
(VEC) models are estimated and provide just a marginal improvement in RMSFE at
the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on
the results obtained in the regression study.
