On the transition dynamics in endogenous recombinant growth models.

This paper constitutes a first attempt at studying the transition dynamics of the Tsur and Zemel (2007) continuous time endogenous growth framework in which knowledge evolves according to the Weitzman (1998) recombinant process. For a specific choice of the probability function characterizing the Weitzman recombinant process, we find a suitable transformation for the state and control variables in the dynamical system diverging to asymptotic constant growth, so that an equivalent 'detrended' system converging to a steady state in the long run can be tackled. Since the dynamical system obtained so far turns out to be analytically intractable, we rely on numerical simulation in order to fully describe the transition dynamics for a set of values of the parameters.Knowledge Production, Recombinant Expansion Process, Endogenous Balanced Growth, Turnpike, Transition Dynamics

The cutoff policy of taxation when CRRA taxpayers differ in risk aversion coefficients and income: a proof.

Under a cutoff policy, taxpayers can either report income as usual and run the risk of being audited, or report a "cutoff" income and hence pay a threshold tax that guarantees not being audited. Whereas the mainstream literature in this field assumes risk neutrality of taxpayers - with some notable exceptions like Chu (1990) and Glen Ueng and Yang (2001) - this paper assumes risk aversion instead: taxpayers have a Constant Relative Risk Aversion (CRRA) utility function and differ in terms of their relative risk aversion coefficient and income. The novel contribution of this work is that, under certain conditions, the cutoff is accepted by taxpayers with intermediate characteristics in terms of income and relative risk aversion. Contrary to the standard result in the literature, a full separation of types (the rich who accept the cutoff versus the poor who refuse it) does not arise. However, our results confirm that the cutoff policy violates equity, as only some taxpayers directly benefit. Nonetheless, the perception of this drawback may in practice be obfuscated because that exclusion does not necessarily affect only the poor.cutoff, tax evasion, relative risk aversion.

On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type.

In this paper we study the existence of bubbles for pricing equilibria in a pure exchange economy à la Lucas, with infinitely lived homogeneous agents. The model is analyzed under fairly general assumptions: no restrictions either on the stochastic process governing dividends’ distribution or on the utilities (possibly unbounded) are required. We prove that the pricing equilibrium is unique as long as the agents exhibit uniformly bounded relative risk aversion. A generic uniqueness result is also given regardless of agent’s preferences. A few ”pathological” examples of economies exhibiting pricing equilibria with bubble components are constructed. Finally, a possible relationship between our approach and the theory developed by Santos and Woodford on ambiguous bubbles is investigated. The whole discussion sheds more insight on the common belief that bubbles are a marginal phenomenon in such models.

Who participates in tax amnesties? Self-selection of risk-averse taxpayers

In this paper we model taxpayer participation in an unanticipated tax amnesty which can be entered by paying a fixed amount. Taxpayers are characterized by a Constant Relative Risk Aversion (CRRA) utility function and differ in relative risk aversion coefficient and in income. With minor changes the same model also describes a FATOTA (Fixed Amount of Taxes or Tax Audit) system. Our results show that amnesties may fail as a self-selective device to fully separate large-scale from small-scale tax evaders and to extract resources from the former. Only taxpayers whose relative risk aversion falls within a given interval participate, while those whose evasion is too small or too large do not enter. The model is used to estimate relative risk aversion and tax evasion of participants in the 1991 and 1994 Italian income tax amnesties.tax amnesty, tax evasion, relative risk aversion, self-selection

Wealth Polarization and Pulverization in Fractal Societies.

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 R&D and we 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 polarized 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 look highly “fractalized”. We also show that a redistribution scheme financed by proportional taxation does not help cure society’s disconnection/polarization; 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.Inequality and Growth; Education; Technological Change; Wealth Polarization/ Pulverization; Iterated Function System; Attractor; Fractal; Cantor Set; Invariant Distribution

Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty

We study a one-sector stochastic optimal growth model, where the utility function is iso-elastic and the production function is of the Cobb-Douglas form. Production is affected by a multiplicative shock taking one of two values. We provide sufficient conditions on the parameters of the model under which the invariant distribution of the stochastic process of optimal output levels is of the Cantor type.

Cantor Type Attractors in Stochastic Growth Models.

We study a one-sector stochastic optimal growth model where production is affected by a shock taking one of two values. Such exogenous shock may enter multiplicatively or additively. A result is presented which provides sufficient conditions to ensure that the attractor of the iterated function system (IFS) representing the optimal policy, is a generalized topological Cantor set. To indicate the role of the strict monotonicity condition on the IFS in this result, examples of attractors, which are not of the Cantor type, are constructed with iterated function systems, whose maps are contractions and satisfy a no overlap property.