Solow system driven by $\alpha$-stable L\'evy process

Abstract

This paper empirically implements a Solow-type growth model driven by $\alpha$-stable L\'evy shocks with time-varying capital elasticity. We extend the framework with an $\alpha$-stable L\'evy process, thereby capturing three stylized facts of severe macroeconomic fluctuations: heavy-tailed distributions, jump discontinuities, and infinite variance. We derive the stationary distribution of the capital deviation process, obtain its conditional characteristic function in closed form, and provide an integral representation that explicitly reveals a dual mean-reversion structure separating investment gestation lags from endogenous feedback. We design an estimation strategy based solely on well-defined objective functions that respects the probabilistic properties of L\'evy-driven data and circumvents the non-existence of variance. We apply the framework to Argentine quarterly data from 2004 to 2023, with time-varying capital elasticity calibrated from Penn World Table labor shares. Our estimates show that the L\'evy specification delivers structural parameters substantially closer to external PWT benchmarks than the Gaussian Ornstein-Uhlenbeck counterpart and substantially improves crisis-period tracking without sacrificing performance in tranquil periods. Cross-country evidence from Colombia and the United States confirms that the quarterly capital adjustment speed $\eta \approx 0.05$ exhibits striking stability across vastly different volatility regimes. Robustness checks across tail index specifications demonstrate that the L\'evy framework consistently outperforms the Ornstein-Uhlenbeck benchmark for a broad range of empirically relevant tail indices. These findings establish the L\'evy specification as a robust generalization of the Gaussian benchmark, offering a more credible tool for forecasting and structural parameter estimation in both emerging and advanced economies.