Simulation of σ_K: A Calibrated Schumpeterian Vintage Model with Export to Low-Wage Countries

1. The model and its parameters Consider three vintages of capital: K_prod (the most recent Schumpeterian wave, fully productive), K_res (the previous wave, still in production but depreciated), and K_sterile (the oldest wave, amortised and exported to a low-wage country). At each period, a new wave replaces the previous one. The definition is σ_K = K_sterile / (K_prod + K_res + K_sterile). The calibration uses three documented sources. First, the OECD Measuring Capital manual indicates that for machinery and equipment, a service life of about fifteen years is standard, with geometric depreciation profiles where roughly 10% of the initial value remains at the end of the service life . Second, the BEA depreciation rates, widely used in the literature, give economic depreciation rates ranging from about 5% per year for long-lived assets (ships, railway equipment: 27–28 years of service life) to about 15–16% per year for construction machinery and agricultural tractors (8–9 years) . Third, French national accounts use log-normal mortality laws combined with linear depreciation, approximated by geometric profiles for capital services; for "other machinery and equipment," the implicit geometric decay is in the same order of magnitude