In the previous post we demonstrated that the level of unemployment could hardly influence real economic growth because the portion of people out of labor force changes in a much wider range (by a factor of 5) and still does not affect the real growth. Here we present a quantitative model explaining the long-term change in the labor force participation rate, LFP, which, obviously, defines the portion of people not in labor force. In this blog, we presented similar models for Canada and Italy but without appropriate math.

We first try to model

*dLFP/LFP*as a nonlinear function of real GDP per capita,*G,*and tested a simple relationship:*dLFP(t)/LFP(t) = D*(1)

_{1}[dG(t-T)/G(t-T) - A_{2}/G(t-T)] +D_{2}where

*D*and_{1}*D*are empirical constants, and_{2}*A*is also an empirical. The time interval is_{2}*dt*=1 year, and thus, omitted in the equation. The intuition behind this model is that it is real economic that drives the change in LFP. The evolution of LFP depends on the difference between the observed rate of growth and the potential rate of growth defined by a reciprocal function of G, A_{2}/G.Figure 1 depicts the measured LFP and that predicted from real GDP per capita using equations (2) and (3). Both variables are borrowed from the Total Economy Database provided by the Conference Board. All in all, the model describes the evolution of LFP in the US since 1964 with an extremely high accuracy. In the mainstream economics, there is no other model of LFP predicting its evolution with a compatible accuracy. Moreover, the predicted curve leads by 2 years (T=2) that allows forecasting at a 2 year horizon. (See our post in January 2011 on the short term LFP prediction.)

Al in all, the rate of participation in labor force depends only on the evolution of real GDP per capita two years ago. Therefore, the level and rate of unemployment, as a part of labor force, plays no role in real economic growth. At least empirical facts say so.

Figure 1. Measured and predicted LFP in the US, where

*A*= $360 (1990 US dollars) is empirical constant. T=2 years._{2}