Automation and Aging in General Equilibrium: AI Capital, Fertility, and the Return to Capital

This paper develops a general equilibrium overlapping-generations model with endogenous fertility, in which firms accumulate both physical and artificial intelligence (AI) capital, and uses it to study the macroeconomic transmission of two structural disturbances: an AI technology shock and a longevity shock. The AI shock acts as a capital-demand disturbance: it raises all rates of return, most sharply the return to AI capital, reallocates investment from physical to AI capital, and produces a front-loaded output expansion that decays monotonically. The longevity shock acts as a saving-supply disturbance: it deepens the aggregate capital stock, compresses returns and the real interest rate, and generates hump-shaped, persistent dynamics. The two shocks move fertility in opposite directions: AI raises it modestly through an income effect, while longevity lowers it by strengthening the life-cycle saving motive and the cost of childrearing. A forecast-error variance decomposition attributes most aggregate volatility to the longevity shock, while the AI shock dominates the variance of the return to AI capital. Fertility is strongly countercyclical and almost perfectly negatively correlated with hours worked, placing household time allocation at the center of the mechanism. Robustness checks across the capital share, the shock persistence, and the utility specification show that only an empirically implausible labor-AI elasticity reverses the wage and fertility signs. A welfare analysis finds the AI shock welfare-improving under complementarity, whereas longevity produces a short-run welfare loss that recedes as capital deepening raises wages, since households initially compress consumption and fertility to finance a longer retirement.