Vintage capital and the dynamics of the AK model

Abstract

ABSTRAeTThis papel' analyzes the equilibrium dynamics of an AK-type endogenous growth model with vintage capital. The inclusion of vintage capital leads to oscillatory dynamics governed by replacement echoes, which additionally influence the intercept of the balanced growth path. These features, which are in sharp contrast to those from the standard AK model, can contribute to explaining the short-run deviations observed bctween investment and growth rates time series. To characterize the convergence properties and the dynamics of the model we develop analytical and numencaJ rnethods that should be of ¡nterest fOl the general resolution of endogenous growth models with vintage capital. RESUMENEn este artículo se analiza la dinámica de uu modelo de crecimiento endógeno de la clase AK en presencia de cosechas de capital (vintage capital). La inclusión en el modelo de una estructura vintage da lugar a una dinámica oscilatoria, vinculada a lo que se conoce como ecos de reemplazo, los cuales a su vez tienen efectos sobre el nivel de la senda de crecimiento equilibrado. Esta propiedad contrasta marcadamente con el comportamiento del modelo AK estándar, y puede contribuir a explicar las desviaciones a corto plazo, que se observan en los datos, ent.re las tasas de inversión y las tasas de crecimiento. Para caracterizar las propiedades de convergencia y la dinámica del modelo se desarrollan métodos analíticos y numéricos que son de interés para la resolución de modelos de crecimiento endógeno con cosechas de capital.

Business cycle fluctuations and learning-by-doing externalities in a one-sector model

“…16 It follows that the share of capital is, as usual, s = 0.3 and the elasticity of capital-labor substitution is σ = 0.5. Such a value for σ is in line with recent empirical estimates which show that σ is in the range of 0.4 − 0.6.…”

“…In the table that follows, we present the Hopf bifurcation value H c and the period of the cycle T computed for various combinations of parameters β and ε e . 16 We have also checked that in a neighborhood of those parameters, the fixed point as defined by (11) exists and satisfies k (t) > 0 and e (t) > 0.…”

“…The main purpose of our paper is to show the existence of a Hopf bi-8 See also Boucekkine et al [16], Boucekkine et al [17] and Fabbri and Gozzi [22]. 9 Benhabib and Rustichini [12] mention the possibility of a Hopf bifurcation in an aggregate model with non-linear utility and vintage capital but do not provide any formal proof of its existence and do not discuss the stability of the bifurcating solutions.…”

Generically distributed investments on flexible projects and endogenous growth

“…Interestingly enough, the dynamic programming approach is used instead of a more "familiar" Pontryagin maximum principle for two reasons: first, there is no result in the literature on the maximum principle which can be directly applied to our problem; second, even in similar cases where some results exist [see, e.g., Boucekkine et al (2005)], it is not possible to find explicitly the optimal strategies, e.g., the value of…”

Optimal investment models with vintage capital: Dynamic programming approach

“…[29,33,37,40]), general equilibrium with vintage capital (see e.g. [15,23] The problem has been already studied by Faggian and by Faggian and Gozzi in the papers [26,27,28,29] in the case of finite horizon, with and without constraints on the control and on the state, yielding a definition of generalized solutions of the associated evolutionary HJB equation. This paper studies instead the infinite horizon case.…”