Autori
Privileggi, FabioMarsiglio, SimoneMendivil, FranklinLa Torre, DavideTitolo
Self-Similar Measures in Multi-Sector Endogenous Growth Models.Periodico
Università degli studi di Torino. Dip. Di Economia e Statistica Cognetti de Martiis. Working paper seriesAnno:
2015 - Volume:
2 - Fascicolo:
9 - Pagina iniziale:
1 - Pagina finale:
30 We analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic
Lucas-Uzawa (1988) model and an extended three-sector version as in La Torre and Marsiglio (2010).
As in the case of sustained growth the optimal dynamics of the state variables are not stationary, we focus on the
dynamics of the capital ratio variables, and we show that, through appropriate log-transform ations, they can be
converted into affine iterated function systems converging to an invariant distribution supported on some fractal
set. This proves that also the steady state of endogenous growth models i.e., the stochastic balanced growth path
equilibrium—might have a fractal nature. We also provide some sufficient conditions under which the associated
self-similar measures turn out to be either singular or absolutely continuous (for the three-sector model we only
consider the singularity).
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