Fabio Privileggi

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 a 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.

Taxpayers' Attitudes Toward Risk and Amnesty Participation: Economic Analysis and Evidence for the Italian Case

This paper provides a simple model, based on expected utility theory, for rationalizing taxpayers reaction to an unexpected amnesty offer. The model is estimated through a deterministic approach, with reference to data pertaining to the 1991 and 1994 Italian tax amnesties. Results seem sound and suggest that standard critiques to the use of expected utility theory for describing taxpayer behavior do not apply when participation in amnesties is considered. However, the model fails in explaining the behavior of full compliers (who refuse the amnesty). Their behavior can be better rationalized by resorting to the expected utility with rank dependent probability approach.

Agent's liability versus principal's liability when attitudes toward risk differ

This paper studies through an agency model the problem of concealing an illegal activity which benefits the principal. The agent can exert an effort that negatively affects the likelihood of detection. We model such behavior with the assumption that the principal is risk neutral while the agent is risk averse. Two opposite legal regimes are considered: in the first, only the principal is strictly liable; in the second, only the agent is. We show that shifting the liability upon the agent, while the monetary sanction and the probability of detection are kept constant, reduces the principals net benefit, thus favoring deterrence of wrongdoing. However, the agents effort in cheating can either increase or decrease. For a specific model we are able to characterize cases in which a reduction in cheating prevails, and shifting the liability upon the agent has clear-cut beneficial effects on compliance.

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.

Fractal steady states instochastic optimal control models

The paper is divided into two parts. We first extend the Boldrin and Montrucchio theorem[5] on the inverse control problem to the Markovian stochastic setting. Given a dynamicalsystem xt+1 = g(xt , zt ), we find a discount factor β* such that for each 0 < β < β* a concaveproblem exists for which the dynamical system is an optimal solution. In the second part,we use the previous result for constructing stochastic optimal control systems having fractalattractors. In order to do this, we rely on some results by Hutchinson on fractals and self‐similarities.A neo‐classical three‐sector stochastic optimal growth exhibiting the Sierpinskicarpet as the unique attractor is provided as an example.

Environmental shocks and sustainability in a basic economy-environment model

We study a stochastic, discrete-time, economy-environment integrated model, where human activity affects the evolution of pollution over time. We assume that exogenous i.i.d. environmental shocks determine the rate of pollution transfer. We show that the pollution to capital ratio dynamics can be read as an iterated function system converging to an invariant distribution supported on a (asymmetric) Cantor set, and that human intervention aiming at offsetting the environmental impact of economic activities is needed to ensure sustainability.

On the transition dynamics in endogenous recombinant growth models

Tsur and Zemel (2007) developed an endogenous growth model in which balanced long-run growth is obtained by assuming that the stock of knowledge evolves according toWeitzman’s (1998) recombinant expansion process and is used, together with physical capital, as input factor by competitive firms in order to produce a unique physical good. At each instant new knowledge is produced by an independent R&D sector directly controlled by a “regulator” who aims at maximizing the discounted utility of a representative consumer over an infinite horizon. The optimal resources required for new knowledge production are obtained by the regulator in the form of a tax levied on the consumers. The economy, thus, envisages two sectors, a competitive one devoted to the production of the unique physical good, and a regulated R&D sector in which the public good “knowledge” is being directly financed by the regulator and produced according toWeitzman’s production function.

Endogenous Recombinant Growth and Intellectual Property Rights

We show that, even in a framework in which monopolistic exploitation of patents does not occur, patents still give rise to serious drawbacks. We build on Weitzman’s (1998) recombinant growth model which provides a stylized but clear description of the formation of knowledge externalities. In our framework a benevolent government buys immediately new patents in a competitive market and releases their contents for free. We show that inefficiencies nevertheless arise and welfare can be improved by correcting the market price through a tax-subsidy scheme. We characterize the (asymptotic) steady state equilibrium, and some properties of the transitional path. We show that if certain conditions are met, then the economy will converge to its (asymptotic) balanced growth path, and along such a path growth will be independent of the policy parameter; conversely, transition dynamics are affected by the choice of the policy parameter. We then quantitatively analyze the effect of different policy interventions on welfare, and show that stricter tax (weaker appropriability) regimes lead to higher social welfare.

Endogenous Recombinant Growth Through Market Production of Knowledge and Intellectual Property Rights

We analyze the relationship between economic growth, knowledge production and intellectual property rights. Economists and historians underline different aspects as possible causes of knowledge accumulation; the former stress the role of incentive mechanisms while the latter the autonomous progress of science. We construct a unified theory allowing for the presence of markets and the autonomous accumulation of knowledge by introducing intellectual property right policies in an endogenous recombinant growth model. In this framework a benevolent government should reallocate resources from the final to the knowledge production sector and implement a tax-subsidy scheme in order to correct for the inefficiencies generated by the process. We characterize the (asymptotic) steady state equilibrium, and some properties of the transitional path. We show that if certain conditions are met, then the economy will converge to its (asymptotic) balanced growth path, and along such a path growth will be independent of the government policy; conversely, transition dynamics and the capital to knowledge ratio are affected by the choice of the tax-subsidy parameter. We then quantitatively analyze the effect of different policy interventions on welfare, and show that welfare is increasing in the policy parameter and a strictly positive policy level may be required to avoid stagnation.

Takeoff vs. stagnation in endogenous recombinant growth models

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.