Papers by Fabio Privileggi
Compendio di Matematica per l'Economia: un percorso esaustivo ma user-friendly
RePEc: Research Papers in Economics, 2020
We analyze a two-sector stochastic economic growth model of green transition with pollution exter... more We analyze a two-sector stochastic economic growth model of green transition with pollution externalities and foreign capital. The final good is produced by combining dirty and clean inputs, with different implications on pollution accumulation. Pollution negatively affects production capabilities and can be reduced by switching to the clean input. The clean input is produced by using the dirty input and the foreign capital received (in the form of dirty input). Random shocks make the effective economy's ability to transition to green activities highly uncertain, eventually undermining its economic development. Such a setting gives rise to a dynamic system represented by a three dimensional affine iterated function system. We show that the economy's steady state is represented by an invariant measure supported on a compact set, characterizing its fractal nature and showing that its attractor may be a distorted Sierpiński tetrahedron.
Matematica per le scienze economiche e sociali, Volume 1: Funzioni di una Variabile
RePEc: Research Papers in Economics, 2001
You may download, copy and otherwise use the AAM for non-commercial purposes provided that your l... more You may download, copy and otherwise use the AAM for non-commercial purposes provided that your license is limited by the following restrictions: (1) You may use this AAM for non-commercial purposes only under the terms of the CC-BY-NC-ND license. (2) The integrity of the work and identification of the author, copyright owner, and publisher must be preserved in any copy.
Stochastic Optimal Growth Through State-Dependent Probabilities
Journal of Public Economic Theory, Dec 5, 2017
Mainstream endogenous growth models assume that new knowledge is embodied into new intermediate o... more Mainstream endogenous growth models assume that new knowledge is embodied into new intermediate or final goods, monopolistically supplied by the patent holder. Recent technological progress, however, often gives rise to pure intellectual contents, such as software codes or business models, directly usable in the production of final goods. Once a content of this type has been produced, it is in fixed supply, that is, the inventor can only rent it out (or sell it) or not; hence the quantity restriction typical of monopoly cannot arise, while competition is viable (Chantrel et al., 2012; Marchese and Privileggi, 2014). We show that, however, as long as the inventor owning a patent can control through license activation devices the access to the intellectual content of the workers using her invention in the final goods production, monopolistic exploitation becomes viable and will occur. It turns out that in this framework both the level of wages and of consumption and the rate of growth of the economy are smaller than in the first best, while with elastic labor supply also labor employment is negatively impacted. This implies that some standard public policies devised for correcting inefficiencies in development can perform poorly in this framework.
Economic Theory
We analyze the role of disease containment policy in the form of treatment in a stochastic econom... more We analyze the role of disease containment policy in the form of treatment in a stochastic economic-epidemiological framework in which the probability of the occurrence of random shocks is state-dependent, namely it is related to the level of disease prevalence. Random shocks are associated with the diffusion of a new strain of the disease which affects both the number of infectives and the growth rate of infection, and the probability of such shocks realization may be either increasing or decreasing in the number of infectives. We determine the optimal policy and the steady state of such a stochastic framework, which is characterized by an invariant measure supported on strictly positive prevalence levels, suggesting that complete eradication is never a possible long run outcome where instead endemicity will prevail. Our results show that: (i) independently of the features of the state-dependent probabilities, treatment allows to shift leftward the support of the invariant measure;...
Annals of Operations Research
We analyze the implications of infectious diseases and social distancing in an extended SIS frame... more We analyze the implications of infectious diseases and social distancing in an extended SIS framework to allow for the presence of stochastic shocks with state dependent probabilities. Random shocks give rise to the diffusion of a new strain of the disease which affects both the number of infectives and the average biological characteristics of the pathogen causing the disease. The probability of such shock realizations changes with the level of disease prevalence and we analyze how the properties of the state-dependent probability function affect the long run epidemiological outcome which is characterized by an invariant probability distribution supported on a range of positive prevalence levels. We show that social distancing reduces the size of the support of the steady state distribution decreasing thus the variability of disease prevalence, but in so doing it also shifts the support rightward allowing eventually for more infectives than in an uncontrolled framework. Nevertheless, social distancing is an effective control measure since it concentrates most of the mass of the distribution toward the lower extreme of its support.
Metodi Ricorsivi Per L'Ottimizzazione Dinamica Stocastica
1993/1994VI Ciclo1964Versione digitalizzata della tesi di dottorato cartacea
University of Wollongong Research Online
Environmental shocks and sustainability in a basic economy-environment model
Journal of Public Economic Theory, 2021
Our paper intersects two topics in growth theory: the growth maximizing government size and the r... more Our paper intersects two topics in growth theory: the growth maximizing government size and the role of Social Capital in development. We modify a simple OLG framework by introducing two key features: a production functionà la Barro (1990) together with the possibility that public officials stole a fraction of public resources under their own control. As underlined by the literature on corruption, Social Capital affects positively public officials' probability of getting caught stealing. Therefore, in our endogenous growth model such probability is taken as a proxy of Social Capital. We find that maximum growth rates are compatible with Big Government size, measured both in terms of expenditures and public officials, when associated with high levels of Social Capital.
Matematica per le scienze economiche e sociali, Volume 2: Algebra lineare, funzioni di più variabili e ottimizzazione statica
Discrete & Continuous Dynamical Systems - B, 2021
We analyze a purely dynamic model of public debt stabilization under ambiguity. We assume that th... more We analyze a purely dynamic model of public debt stabilization under ambiguity. We assume that the debt to GDP ratio is described by a random variable, and thus it can be characterized by investigating the evolution of its density function through iteration function systems on mappings. Ambiguity is associated with parameter uncertainty which requires policymakers to respond to such an additional layer of uncertainty according to their ambiguity attitude. We describe ambiguity attitude through a simple heuristic rule in which policymakers adjust the available vague information (captured by the empirical distribution of the debt ratio) with a measure of their ignorance (captured by the uniform distribution). We show that such a model generates fractal-type objects that can be characterized as fixed-point solutions of iterated function systems on mappings. Ambiguity is a source of unpredictability in the long run outcome since it introduces some singularity features in the steady stat...
SSRN Electronic Journal, 2015
Mainstream endogenous growth models assume that new knowledge is embodied into new intermediate o... more Mainstream endogenous growth models assume that new knowledge is embodied into new intermediate or final goods, monopolistically supplied by the patent holder. Recent technological progress, however, often gives rise to pure intellectual contents, such as software codes or business models, directly usable in the production of final goods. Once a content of this type has been produced, it is in fixed supply, that is, the inventor can only rent it out (or sell it) or not; hence the quantity restriction typical of monopoly cannot arise, while competition is viable (Chantrel et al., 2012; Marchese and Privileggi, 2014). We show that, however, as long as the inventor owning a patent can control through license activation devices the access to the intellectual content of the workers using her invention in the final goods production, monopolistic exploitation becomes viable and will occur. It turns out that in this framework both the level of wages and of consumption and the rate of growth of the economy are smaller than in the first best, while with elastic labor supply also labor employment is negatively impacted. This implies that some standard public policies devised for correcting inefficiencies in development can perform poorly in this framework.
Mathematics and Computers in Simulation, 2015
This paper concludes the study of transition paths in the continuous-time recombinant endogenous ... more This paper concludes the study of transition paths in the continuous-time recombinant endogenous growth model by providing numerical methods to estimate the threshold initial value of capital (a Skiba-type point) above which the economy takes off toward sustained growth in the long run, while it is doomed to stagnation otherwise. The model is based on the setting first introduced by Tsur and Zemel and then further specified by Privileggi, in which knowledge evolves according to the Weitzman recombinant process. We pursue a direct approach based on the comparison of welfare estimations along optimal consumption trajectories either diverging to sustained growth or converging to a steady state. To this purpose, we develop and test three algorithms capable of numerically simulating the initial Skiba-value of capital, each corresponding to initial stock of knowledge values belonging to three different ranges, thus covering all possible scenarios.
Rivista di Matematica per le Scienze Economiche e Sociali, 1995
A notion of …nitely optimal plan for intertemporal optimization problems as a necessary condition... more A notion of …nitely optimal plan for intertemporal optimization problems as a necessary condition for optimality is introduced. Under interiority of a feasible plan and di¤erentiability of the return function, such a plan satis…es the stochastic analogue of deterministic Euler-Lagrange conditions, which become also su¢ cient conditions under concavity of the return function. Then, under more general assumptions, a su¢ cient criterion of optimality based on competitive plans supported by price systems and transversality conditions is discussed. Di¤erently from the current literature, no restrictive hypotheses on the probability measure of the random shocks are assumed.
Computational Economics, 2011
This paper provides a step further in the computation of the transition path of a continuous time... more This paper provides a step further in the computation of the transition path of a continuous time endogenous growth model discussed by Privileggi (2010)-based on the setting first introduced by Tsur and Zemel (2007)-in which knowledge evolves according to the Weitzman (1998) recombinant process. A projection method, based on the least squares of the residual function corresponding to the ODE defining the optimal policy of the 'detrended' model, allows for the numeric approximation of such policy for a positive Lebesgue measure range of values of the efficiency parameter characterizing the probability function of the recombinant process. Although the projection method's performance rapidly degenerates as one departs from a benchmark value for the efficiency parameter, we are able to numerically compute time-path trajectories which are sufficiently regular to allow for sensitivity analysis under changes in parameters' values.
Research Papers in Economics, 2021
We establish novel results on generalized fractal operators with condensation and apply them in t... more We establish novel results on generalized fractal operators with condensation and apply them in the analysis of a macroeconomic-epidemiological model characterized by deep uncertainty under the assumption that it is impossible to quantify with certainty the exact number of current and future infectives. The setting is simple: the level of prevalence of a communicable disease determines the size of the healthy labor force, affecting output and consumption; health policy is publicly funded via income taxation but the availability of resources is endogenously determined since depending on disease prevalence. Since the high degree of uncertainty is reflected also in the policymakers' choice of the policy tools to limit the spread of the disease, we investigate how the peculiarities of different policymakers (a shortsighted vs far-sighted approach) affect the asymptotic invariant distribution of macroeconomic activity. Specifically, we exploit the condensation term of the fractal operator to characterize the consequence of shortsighted policies. Through numerical simulations we find that, as we would expect, far-sighted policies lead to asymptotic invariant probability distributions concentrating more mass on high levels of aggregate consumption together with small numbers of infectives, while the invariant distribution reached through shortsighted policies, besides concentrating more mass on low levels of aggregate consumption together with large numbers of infectives, exhibits an additional layer of (uniform) uncertainty generated by the condensation term.
In this paper we investigate wealth inequality/polarization properties related to the geometry of... more In this paper we investigate wealth inequality/polarization properties related to the geometry of the support of the limit distribution of wealth in economies characterized by equal opportunities and uninsurable individual risk. We work out two simple successive generation models, one with stochastic human capital accumulation and one with R&D, and prove that intense technological progress makes the support of the wealth distribution converge to a fractal Cantor-like set. Such limit distribution implies the disappearance of the middle class, with a “gap ” between two wealth clusters that widens as the growth rate becomes higher. Hence, we claim that in a highly meritocratic world in which the payoff of the successful individuals is high enough, and in which social mobility is strong, societies tend to become unequal and polarized. We also show that a redistribution scheme financed by proportional taxation does not help cure society’s inequality/polarization – on the contrary, it mig...
In this paper we study the geometrical properties of the support of the limit distributions of in... more In this paper we study the geometrical properties of the support of the limit distributions of income/wealth in economies with uninsurable individual risk, and how they are affected by technology and preference parameters and by policy variables. We work out two simple successive generation models with stochastic human capital accumulation and with RD on the contrary, it might increase it. Finally we show that these results are not confined to our analytically worked out examples but are easily extended to a widely used class of macroeconomic and growth models.
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Papers by Fabio Privileggi