4.1.2Contribution to Output and Productivity Growth

After testing for the sign and significance of the output elasticity of IT capital, I will measure the contribution of this type of capital to output and productivity growth. Considering equation 4.14 in growth rates leads to

gr(Yits) = γt-1+λi+νs+ sKNIT gr(KNITits) + sKIT gr(KITits) + sL gr(Lits) + μits(4.16)

The contribution to output growth from IT capital is measured by sKITgr(KITits) where gr stands for “growth rate” measured as the ratio of the difference between variables at time t and t-1, divided by the value at time t-1. Many authors use first log differences to measure growth rates, but I believe the previous formula is more accurate.⁴ Variable s represents the income share of inputs (previously defined by equation 3.5), and in equilibrium it is equal to the input’s marginal product times its share of output. Finally, μ represents the error term.

Following Oliner and Sichel (2000), equation 4.16 is divided on both sides by Lits to estimate the labor productivity growth contribution of a given input. The authors also control for labor quality by adding variable gr(q), where q could represent years of experience or education:

gr(Yits/Lits) = γt-1+λi+νs+ α0 gr(KNITits/Lits)+ α1 gr(KITits/Lits) + αL gr(q) + μits(4.17)

Thus, growth in labor productivity depends on growth in TFP (which is captured by various fixed effects (γt-1 + λi+ νs), capital deepening (growth in KNIT/L and KIT/L) and change in labor quality gr(q).