Solving Macroeconomic Models with Homogeneous Technology and Logarithmic Preferences

Bethmann, Dirk

doi:10.1111/1467-8454.12004

Cited by 5 publications

(8 citation statements)

References 16 publications

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“…The results highlighted in Proposition 1 are pretty standard in the literature (see Bethmann, 2007Bethmann, , 2013La Torre et al, 2011). It is also very well-known that the Uzawa-Lucas (1988) framework, because of the linearity in the production of (new) human capital, may generate sustained long-run growth.…”

Section: Absolutely Continuous Vs Singular Self-similar Measuresmentioning

confidence: 56%

“…By applying the Verification principle, it is possible to obtain an analytical expression for the value function of the above problem, and consequently derive explicitly the optimal dynamics of physical and human capital (see also Bethmann, 2007Bethmann, , 2013.…”

Section: Absolutely Continuous Vs Singular Self-similar Measuresmentioning

confidence: 99%

“…6 In this framework the planner has to choose consumption, c t , and the share of human capital to allocate into physical, u t , and knowledge, v t , production, taking into account the presence of random shocks, which affect both physical and technological capital production. The technological knowledge, a t , evolves over time because of newly produced knowledge: a t+1 = y a t .…”

Section: A Three-sector Modelmentioning

confidence: 99%

See 2 more Smart Citations

Self-similar measures in multi-sector endogenous growth models

Torre¹,

Marsiglio²,

Mendivil³

et al. 2015

Chaos, Solitons & Fractals

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We analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Uzawa-Lucas (1965, 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-transformations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some (possibly fractal) compact 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). AbstractWe analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Uzawa-Lucas (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-transformations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some (possibly fractal) compact set. This proves that also the steady state of endogenous growth modelsi.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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Section: Absolutely Continuous Vs Singular Self-similar Measuresmentioning

confidence: 56%

Section: Absolutely Continuous Vs Singular Self-similar Measuresmentioning

confidence: 99%

Section: A Three-sector Modelmentioning

confidence: 99%

See 1 more Smart Citation

Self-similar measures in multi-sector endogenous growth models

Torre¹,

Marsiglio²,

Mendivil³

et al. 2015

Chaos, Solitons & Fractals

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show abstract

“…In presence of shocks on the exponents of the Cobb-Douglas production functions it becomes difficult to pursue the usual "guess-and -verify" approach (Bethmann, 2007(Bethmann, , 2013 …”

Section: Economic Growth and Stochastic Factor Sharesmentioning

confidence: 99%

Fractal attractors and singular invariant measures in two-sector growth models with random factor shares

Torre

Marsiglio

Mendivil

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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We analyze a multi-sector growth model subject to random shocks affecting the two sector-specific production functions twofold: the evolution of both productivity and factor shares is the result of such exogenous shocks. We determine the optimal dynamics via Euler-Lagrange equations, and show how these dynamics can be described in terms of an iterated function system with probability. We also provide conditions that imply the singularity of the invariant measure associated with the fractal attractor. Numerical examples show how specific parameter configurations might generate distorted copies of the Barnsley's fern attractor.

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“…Proof of Proposition 1. To apply the Guess and verify method (see, e.g., Bethmann, 2007;2013), the linearity of the terms inside the logarithm in (14) suggests the following form for the value function:…”

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confidence: 99%

On the economic growth and environmental trade-off: a multi-objective analysis

Marsiglio

Privileggi

2019

Ann Oper Res

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We develop a multicriteria approach, based on a scalarization technique, in order to analyze the trade off between economic growth and environmental outcomes in a framework in which the economy and environment relation is bidirectional. On the one hand, economic growth by stimulating production activities gives rise to emissions of pollutants which deteriorate the environment. On the other hand, the environment affects economic activities since pollution generates a production externality determining how much output the economy can produce and reducing welfare. In this setting we show that optimality dictates an initial overshooting followed by economic degrowth and rising pollution. This implies that independently of the relative importance of economic and environmental factors, it is paradoxically optimal for the economy to asymptotically reach the maximum pollution level that the environment is able to bear.

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Solving Macroeconomic Models with Homogeneous Technology and Logarithmic Preferences

Cited by 5 publications

References 16 publications

Self-similar measures in multi-sector endogenous growth models

Self-similar measures in multi-sector endogenous growth models

Fractal attractors and singular invariant measures in two-sector growth models with random factor shares

On the economic growth and environmental trade-off: a multi-objective analysis

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