Inflation as a function of labor force change rate: cointegration test for the USA

TL;DR

This paper establishes a cointegrated, predictive relationship between inflation and labor force change rate in the USA, demonstrating its effectiveness for inflation forecasting and emphasizing the importance of accurate labor force data.

Contribution

It provides the first cointegration validation of the inflation-labor force relationship for the USA and demonstrates its practical utility in inflation forecasting.

Findings

The relationship is cointegrated and long-run stable.

Labor force change is a weakly exogenous variable.

The model achieves a 0.8% RMS forecasting error at two years.

Abstract

A linear and lagged relationship between inflation and labor force change rate, p(t)= A1dLF(t-t1)/LF(t-t1)+A2 was found for developed economies. For the USA, A1=4.0, A2=-0.03075, and t1=2 years. It provides a RMS forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best among other inflation forecasting models). This relationship is tested for cointegration. Both variables are integrated of order one according to the presence of a unit root in the series and its absence in their first differences. Two methods of cointegration testing are applied: the Engle-Granger one based on the unit root test of the residuals including a variety of specification tests and the Johansen cointegration rank test based on the VAR representation. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds. According to the Granger causality test, the labor force change is proved to be a weakly exogenous variable - a natural result considering the time lead and the existence of a cointegrating relation. VAR and VECM representations do not provide any significant improvement in RMSFE. There are numerous applications of the equation: from purely theoretical - a robust fundamental relation between macroeconomic and population variables, to a practical one - an accurate out-of-sample inflation forecasting at a two-year horizon and a long-term prediction based on labor force projections. The predictive power of the relationship is inversely proportional to the uncertainty of labor force estimates. Therefore, future inflation research programs should start from a significant improvement in the accuracy of labor force estimations.