Relationship between inflation, unemployment and labor force change rate in France: cointegration test

TL;DR

This study investigates the long-term relationships between inflation, unemployment, and labor force change rate in France, demonstrating cointegration and providing a model with accurate four-year horizon forecasts.

Contribution

It introduces a country-specific linear model linking inflation, unemployment, and labor force change, validated through cointegration tests for France and developed economies.

Findings

Variables are cointegrated and follow a long-term equilibrium relationship.

The model forecasts GDP deflator with 1.0% RMS error at four years.

Long-term links remain stable despite monetary policy changes.

Abstract

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.