Growth in labour productivity can be attributed to two distinct components, which are often but
not always complementary: a within-sector effect, where technological improvements increase
productivity in a given economic activity, holding the capital-labour ratio in that sector constant,
and a between-sector effect, where more labour is allocated to productive economic activities.5
The following function captures the decomposition of aggregate labour productivity growth over
the given period (t − k to t) into these two components respectively, where θi,t represents the
sectoral share of employment in sector i at time t for the n sectors, Yt is overall productivity at
time t, yi,t represents productivity in sector i at time t, and Δ captures the change in a given
variable from t