Nonlinear relationship of real GDP per capita and labor force participation rate proposed in 2008 fits the data between 1966 and 2021

In 2008, we published a working paper titled “The driving force of labor force participation in developed countries” in the ECINEQ (Society for the Study of Economic Inequality) Working Paper Series also available at  Research Papers in Economics (RePEc/IDEAS). In this paper we proposed a simple model of the change in the labor force participation rate, dLFP/LFP, as a nonlinear function of the real GDP per capita, G: 

N(t₂) = N(t₁){ 2[dG(t₁-T)/G(t₁-T) - A₂/G(t₁-T)] + 1}                                                (1)

dLFP(t₁)/LFP(t₁) = N(t₁-T)/B + C                                                     (2)

where N(t) is the number of people with a specific age (just the operational variable for this equation), A2, B, and C are empirical coefficients dependent on the measuring units of the G, which is prone to multiple updates. The model also includes the possibility of a time delay, T,  between the G and LFP change.  Figure 6 from the paper demonstrates the overall fit between the measured LFP and that predicted by equation (1) since 1964. The predicted time series is obtained from (1) with the following constants and coefficients: N(1959)=4.5E+6, A₂=$350, B=-1.23E+8, C=0.04225. The goodness-of-fit between the predicted and observed LFP is extremely high: R²=0.99. More important is that the timing of main turns in the observed time series is well predicted at a two-year horizon – the predicted series is still two years ahead of the observed one: T=2 years. In Figure, 6 both curves are synchronized due to a two-year back-shift of the predicted curve. There are three major deviations between the curves – all are associated with large revisions to the original LFP. The root-mean-square forecasting error (RMSFE) of the LFP at a two-year horizon for the period between 1968 and 2006 is 0.28%. This accuracy is slightly larger than that inherent to the original time series (from 0.1% to 0.2%) and, noticeably, obtained using raw data. The elimination of the most obvious (artificial) deviations induced by the revisions to the CPS results in RMSFE=0.2%.