The growth in labor productivity, P, is the driver of real economic
growth. Since 1970, the growth rate, dP/P, in Belgium was on a falling trend. We published
two papers [1,
2] five years
ago. Figure 3 from paper [2] is reproduced below. Our prediction was that the rate of labor
force growth would fall below zero. Here we revisit this prediction and provide
a new projection 5 years ahead. We begin with the model, which is also
described in both papers
Figure 3. Observed and predicted
(from real GDP per capita) change rate of productivity in Belgium. The observed curve is represented by MA(5) of
original version. Model parameters are as follows: A2=$280, N(1959)=150000, B=-1900000, C=0.13, T=5 year.
For the estimation of labor
productivity one needs to know total output (GDP) and the level of employment, E (P=GDP/E),
or total number of working hours, H (P=GDP/H). In the first approximation and for the purposes of our modeling,
we neglect the difference between the employment and the level of labor force
because the number of unemployed is only a small portion of the labor force.
There is no principal difficulty, however, in the subtraction of the
unemployment, which is completely defined by the level of labor force with
possible complication in some countries induced by time lags. The number of
working hours is an independent measure of the workforce. Employed people do
not have the same amount of working hours. Therefore, the number of working
hours may change without any change in the level of employment and vice versa. In
this study, the estimates associated with H
are not used.
Individual productivity
varies in a wide range in developed economies. In order to obtain a
hypothetical true value of average labor productivity one needs to sum up
individual productivity of each and every employed person with corresponding
working time. This definition allows a proper correction when one unit of labor
is added or subtracted and distinguishes between two states with the same
employment and hours worked but with different productivity. Hence, both
standard definitions are slightly biased and represent approximations to the
true productivity. Due to the absence of the true estimates of labor
productivity and related uncertainty in the approximating definitions we do not
put severe constraints on the precision in our modeling and seek only for a
visual fit between observed and predicted estimates.
In this study, we use the estimates of productivity and real GDP per
capita reported by the Conference Board (http://www.conference-board.org/economics/database.cfm).
Recently, we developed a model [3] describing
the evolution of labor force participation rate, LFP, in developed countries as a function of a single defining
variable – real GDP per capita. Natural fluctuations in real economic growth
unambiguously lead to relevant changes in labor force participation rate as expressed
by the following relationship:
= ∫ {dG(t-T))/G(t-T) – A1/G(t-T)}dt (1)
where B1 and C1 are empirical (country-specific) calibration
constants, a1 is empirical (also country-specific) exponent, t0 is the start year of modeling,
T is the time lag, and dt=t2-t1, t1 and t2 are the start
and the end time of the time period for the integration of g(t) = dG(t-T))/G(t-T) – A1/G(t-T)
(one year in our model). Term A1/G(t-T),
where A1 is an empirical constant, represents the evolution
of economic trend. The exponential term defines the change in sensitivity to G due to the deviation of the LFP from its initial value LFP(t0). Relationship (1) fully
determines the behavior of LFP when G is an exogenous variable.
It follows
from (1) that labor productivity can be represented as a function of LFP and G, P~G∙Np/Np∙LFP = G/LFP,
where Np is the working age
population. Hence, P is a function of
G only. Therefore, the growth rate of
labor productivity can be represented using several independent variables.
Because the change in productivity is synchronized with that in G and labor force participation, first
useful form mimics (1):
dP(t)/P(t) = {B2dLFP(t)/LFP(t) + C2}·exp{ a1[LFP(t) - LFP(t0)]/LFP(t0)} (1′)
where B2 and C2 are empirical calibration constants. Inherently, the
participation rate is not the driving force of productivity, but (1′)
demonstrates an important feature of the link between P and LFP – the same
change in the participation rate may result in different changes in the
productivity depending on the level of the LFP.
In order to
obtain a simple functional dependence between P and G one can use two
alternative forms of (1), as proposed in [1]:
dP(t)/P(t) = B4Ns(t-T)+
C4 (2)
where Ns is the number of S-year-olds, i.e. in the specific age
population, B3,…, C4 are empirical constant
different from B2, C2, and a2=a1. In this representation,
we use our finding that the evolution of
real GDP per capita is driven by the change rate of the number of S-year-olds. Relationship (2) links dP/P and Ns directly.
The
following relationship defines dP/P
as a nonlinear function of G only:
N(t2) = N(t1)·{ 2[dG(t2-T)/G(t2-T)
- A2/G(t2-T)] + 1}
(3)
dP(t2)/P(t2) = N(t2-T)/B
+ C (4)
where N(t) is the (formally defined) specific
age population, as obtained using A2
instead of A1; B and C are empirical constants. Relationship (3) defines the evolution
of some specific age population, which is different from actual one.
Productivity
prediction
Here we revisit the case
of Belgium using 5 new readings (between 2007 and 2012). For the prediction, we
use the previously obtained model [2] as described in Figure 3. Figure 3’
displays the measured and predicted rate of productivity growth. The curves are
very close with R2=0.82 for the period between 1967 and 2012. For Belgium,
the range of productivity change varies from 0.05 y-1 in the 1970s
to -0.03 y-1 in 2008 and 2009. As predicted in our previous paper ,
P was rather negative after 2007.
The current rate of productivity
growth is close to 0.0 y-1. The
case of Belgium is characterized by a 5-year lag of the productivity reaction
to the change in GDP. Therefore, we can predict the evolution of dP/P five
years ahead. Figure 3’ shows that the rate of growth in labor productivity will
be positive after 2013. This is a good news.
Figure 3’. Same as in
Figure 3 with 5 new readings.
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