shifting gears
Appendix 2 Long-term growth model
The Long-term Growth Model (Loayza and Pennings 2018) is based on Solow (1956), Swan (1956), and Hevia and Loayza (2012). The economy consists of a single sector that produces output using physical capital Kt and effective labor ht Lt . At denotes total factor productivity (TFP), which determines the aggregate efficiency of the economy. The relationship between inputs and output is governed by the CobbDouglas production function given by: Yt = At Kt 1−β (ht Lt ) β where βis the aggregate labor share of income, while effective labor is decomposed into human capital per worker ht and the number of workers Lt . The total number of workers can be written as: Lt = ρt ωt Nt where ρt is the participation rate, ωt is the working age to total population ratio, and Nt is the total population. Physical capital in the next period Kt+1 is formed by undepreciated capital (1 − δ) Kt and new investment It : Kt+1 = ( 1 − δ) Kt + It Headline GDP growth gy, t+1 could be decomposed using a log-linear approximation into different growth fundamentals, where gx, t+1 is the growth rate of factor x from t to t+1: 1 − β It [ Y ] t
gy, t+1 = gA,t+1 + β(gh, t+1 + gω, t+1 + gρ, t+1 ) + _ _K _ (1 − β)δ + gN,t+1 Y − t
t
96
