The macroeconomics of AI capacity: insights from a two-asset growth model

Abstract Specialised AI hardware becomes economically obsolete much faster than conventional capital, so maintaining a given stock of compute requires high replacement investment. This paper studies the implications for growth, adjustment dynamics, and policy in a two-asset growth model in which AI capacity both raises productivity and produces digital services at low marginal cost. Calibrated to advanced economies, the model delivers two distinct adjustment speeds. AI capacity reverts relatively quickly, with a half-life of about seven quarters, while conventional capital adjusts over roughly a decade. When hardware is short-lived, even modest changes in gross spending can produce large swings in measured AI investment, despite only limited movements in the underlying stock. This helps explain the volatility often seen in specialised AI hardware investment cycles. Hardware durability also has first-order welfare effects. In the baseline calibration, a two-percentage-point fall in quarterly depreciation raises welfare by 0.36% in consumption-equivalent terms, while an equal-sized compute tax reduces the steady-state AI stock by around one-fifth.