Stefano Bosi

Indeterminacy and Endogenous Fluctuations With Arbitrarily Small Liquidity Constraint

The empirical relevance of indeterminacy and sunspot fluctuations has been often questioned on the basis of the implausibly high degrees of increasing returns to scale or unconventional calibrations for the fundamentals required. In this paper we study a one-sector economy with partial cash-in-advance constraint on consumption expenditures and show how such phenomena are by contrast quite pervasive: In fact, their scope improves as soon as the liquidity constraint is set smaller and smaller and finally, for amplitudes of the liquidity constraint small enough, they are bound to prevail for whatever fundamentals specification.

Mortality Differential and Growth: What do we Learn From the Barro-Becker Model?

The model of endogenous fertility by Barro and Becker (1989) is augmented by taking into account the heterogeneity of households in terms of capital endowments, mortality, and costs per surviving child. There exists a unique balanced growth path where the population growth rates of all dynasties are equal. An increase in mortality raises the time cost per surviving child, and enhances economic growth, while reducing parity and demographic growth. The mechanism rests on the quantity-quality trade-off of having children, summarized by the adjustment of the average rearing cost of a surviving child.

On existence, efficiency and bubbles of Ramsey equilibrium with borrowing constraints

We address the fundamental issues of existence and efficiency of a Ramsey equilibrium with heterogenous discounting, elastic labor supply and borrowing constraints. In the first part, we prove the equilibrium existence in a truncated bounded economy through a fixed-point argument by Gale and Mas-Colell (1975). This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. The proof of existence is eventually given for an infinite-horizon economy as a limit of a sequence of truncated economies. Our general approach is suitable for applications to other models with different market imperfections. In the second part, we show the impossibility of bubbles in a productive economy and we give sufficient conditions for equilibrium efficiency.

Animal spirits in cash-in-advance economies

The possibility of indeterminacy and sunspot fluctuations in dynamic rational expectations models has been often questioned on empirical grounds, for such models are widely believed to rely on implausibly high degrees of increasing returns to scale and/or other controversial calibrations of economic fundamentals. In this paper, we study the occurrence of such phenomena in a standard (one-sector) optimal growth model with endogenous labor supply and a partial cash-in-advance constraint on consumption purchases. We show that, under standard preferences and constant returns to scale in production, indeterminacy typically prevails for an arbitrarily small amplitude of the liquidity constraint. We also analyze the cyclical properties of the model submitted to technological and beliefs disturbances and observe that it performs as well as comparable indeterminate models in the literature.

Endogenous business cycles: Capital–labor substitution and liquidity constraint

It is well known from the literature that the introduction of financial constraints in economies with infinite-lived agents can be responsible for the occurrence of multiple equilibria and en- dogenous fluctuations. However, the question of the persistence of such phenomena when the constraints are progressively relaxed remains open. By departing from Cazzavillan, Lloyd-Braga and Pintus (1996) framework with heterogeneous agents and positive externalities in aggregate capital and labor, we show that endogenous fluctuations can persist for a wide range of the financial constraint.

Asset bubbles and efficiency in a generalized two-sector model

We consider a multi-sector infinite-horizon general equilibrium model. Asset supply is endogenous. The issues of equilibrium existence, efficiency, and bubble emergence are addressed. We show how different assets give rise to very different rational bubbles. We also point out that efficient bubbly equilibria may exist.

On the optimal control of pollution in a human capital growth model

Abstract On the one hand, the adoption of polluting technologies can enhance the factor productivity; on the other hand, pollution lowers the stock of human capital by weakening physical and mental performances, and shortening the life expectancy at the end. To capture the impact of pollution on economic growth, we compute the optimal policy in a continuous-time endogenous growth model à la Lucas (1988). The concavity properties we consider, not only ensure the uniqueness of solution but also play a fundamental role in comparative statics and local dynamics.

Natural cycles and pollution

In this paper, we study a competitive Ramsey model where a pollution externality, coming from production, impairs a renewable resource which affects the consumption demand. A proportional tax, levied on the production level, is introduced to finance public depollution expenditures. In the long run, two steady states may coexist, the one with a low resource level, the other with a high level. Interestingly, a higher green tax rate lowers the resource level of the low steady state, giving rise to a Green Paradox (Sinn, 2008). Moreover, the green tax may be welfareimproving at the high steady state but never at the low one. Therefore, at the latter, it is optimal to reduce the green tax rate as much as possible. Conversely, the optimal tax rate is positive when the economy experiences the high steady state. This rate is unique. In the short run, the two steady states may collide and disappear through a saddle-node bifurcation. Since consumption and natural resources are substitutable goods, a limit cycle may arise around the high stationary state. To the contrary, this kind of cycles never occur around the low steady state whatever the resource effect on consumption demand. Finally, focusing on the class of bifurcations of codimension two, we find a Bogdanov-Takens bifurcation.

OPTIMAL IMMIGRATION POLICY: WHEN THE PUBLIC GOOD IS RIVAL

In this model, we characterize optimal immigration and fiscal policies in presence of a rival public good and heterogeneous discounting. Surprisingly, even if the government is benevolent towards natives only, it is optimal to keep borders open. Indeed, in the long run, patient natives hold the whole stock of capital, while impatient immigrants work. Moreover, since capital intensity is stationary, capital per native, consumption and the public good increase with the number of (immigrant) workers. This positive effect offsets the disutility deriving from the congestion of the public good. Howevern when we account for the costs associated to cultural heterogeneity, we find that it is optimal to regulate immigration inflows. We also interpret the long-run sensitivity of the optimal policy mix with respect to the fundamentals.

Indeterminacy and business-cycle fluctuations in a two-sector monetary economy with externalities

We consider a two-sector economy with money-in-the-utility-function and sector-specific externalities. We provide conditions on technologies leading to the existence of local indeterminacy for any value of the interest rate elasticity of money demand, provided the elasticity of intertemporal substitution in consumption is large enough. Moreover, we show that the occurrence of multiple equilibria is intimately linked with the existence of a flip bifurcation and period-two cycles.