Julio Davila

Constrained Efficiency in the Neoclassical Growth Model With Uninsurable Idiosyncratic Shocks

We investigate the welfare properties of the one-sector neoclassic growth model with uninsurable idiosyncratic shocks. We focus on the constrained efficiency notion of the general equilibrium literature, and we demonstrate constrained inefficiency for our model. We provide a characterization of constrained efficiency that uses the first-order condition of a constrained planners problem that points to the margins of relevance for whether capital is too high or too low : the income composition of the (consumption) poor. We calibrate our benchmark model parameters governing idiosyncratic risks to the U.S. earnings and wealth distribution, and for this distribution the income of the poor is mainly composed of labor earnings. We compute the constrained-efficient allocations -including transition dynamics- for our model economy, and we conclude that the long-run capital stock in a laissez faire world is not only too low, but much too low. We also show that one can find parameterizations with different qualitative features : in one case, the steady-state capital stock is too high, and in another case no steady state exists.

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.

The rationality of expectations formation

Abstract Rational expectations are not required to follow from beliefs that explain well history, but just to correctly foresee the future. As a consequence, at a rational expectations equilibrium, the agents’ expectations may follow from beliefs that explain poorly the observed history, even among those rationalizing their choices. This paper shows, firstly, that if agents hold rationally formed expectations instead – in the sense of following from beliefs that explain history better than any other beliefs justifying their choices – then allocations unsupported by rational expectations can be shown to be equilibrium outcomes. By means of this result, it is established, secondly, that adding the common knowledge of the rationality of the formation of expectations to that of the rationality of choices and of market clearing, still does not suffice to guarantee rational expectations. Finally, the rationally formed expectations equilibria produced in this paper exhibit a sunspot-like volatility that, interestingly enough, do not rely on an explicit sunspot mechanism.

Competitive Bargaining Equilibrium

We propose a simple bargaining procedure, the equilibrium of which converges to the Walrasian allocation as the agents become increasingly patient. We thus establish that the competitive outcome obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. This procedure has therefore important implications for policy applications compared to standard bargaining rules.

On the connection between correlated equilibria and sunspot equilibria

The issue of the connection between correlated equilibria of Maskin-Tirole (1987) economies and finite markovian stationary sunspot equilibria of overlapping generations economies is reconsidered in this paper.The conjecture stated in Maskin-Tirole (1987) about the existence of a close connection between correlated equilibria of market games modelling economies with asymmetric information about an extrinsic uncertainty and finite markovian stationary sunspot equilibria of related overlapping generations economies is reconsidered in this paper. It is shown that there is no robust example of an overlapping generations economy with a non-negligible set of finite markovian stationary sunspot equilibria which can be identified with correlated equilibria of the corresponding economy a la Maskin-Tirole, and vice versa. This result qualifies the conjectured connection between the two equilibrium concepts in these two frameworks.

Is Bargaining over Prices Efficient

We consider the problem of two agents bargaining over the relative price of two goods they are endowed with. They alternatingly exchange price offers and the utilities are discounted. The recipient of an offer can either accept it and choose the quantities to be traded, or reject and counteroffer a different relative price. We study the set of equilibria as discounting frictions vanish and find that: (1) any generic economy has bargaining equilibria that are inefficient even as discounting frictions vanish; and (2) a bargaining equilibrium converging to a Walrasian outcome exists for some robust types of convergence of the discount factors, but it does not exist for other equally robust convergences. Moreover, in case there exists a bargaining equilibrium converging to a Walrasian outcome, then there is necessarily a multiplicity of them. As a consequence, unlike in Rubinsteins (1982) alternating-offer bargaining, the equilibrium outcome of this set-up is not generically unique and efficient.

Cycles and sunspot: The Poincaré-Hopf approach

This paper deals with the existence of stationary sunspot equilibria (SSE) of finite order in an n-commodity economy. We first provide a simple condition that is sufficient for the existence of SSE associated with any given Markov matrix. This condition encompasses and extends previous results by Guesnerie (Journal of Economic Theory, 1986, 40, 103–128) and Chiappori and Guesnerie (in: Economic complexity, chaos, sunspots, bubbles and nonlinearity, 189, CUP). Also, we consider the order of the corresponding SSE (i.e. the cardinality of their support), and we show that almost all of these are of maximum order. Finally, we study the links between SSE and cycles, and find that the existence of cycles of order 2 detected by our condition implies that of SSE arbitrarily close to cycles of order k for any even k — although cycles of order k may not exist in such models.

Implementing the best steady state with savings in unbacked risky assets

This paper shows, in an overlapping generations economy a la Diamond (1965), that when savings in an unbacked asset (e.g. at money) bear some risk of becoming suddenly worthless, the market does not implement the best steady state attainable with that asset. Nonetheless, in the absence of an absolutely riskless at money and excluding resorting to redistributive scal policies that would allow to attain the rst-best steady state, this best monetary steady state can be implemented as a competitive equilibrium with the adequate policy of taxes on returns to capital, subsidies to returns to monetary savings, and lump-sum transfers. The policy is, at the steady state, balanced every period and non-redistributive.

Time and Uncertainty in Overlapping Generations Economies

This paper shows the general reversibility of every perfect foresight equilibrium of an overlapping generations economy. It then shows and characterizes the existence of reversible sunspot equilibria in these economies as well, which seems to be at odds with our intuition about the irreversibility of a tree of events. Although the paper establishes also that such reversible stochastic equilibria constitute a negligible subset of all the equilibria of their class, their mere existence may be considered somewhat puzzling for this intuition. Journal of Economic Literature

Output Externalities On Total Factor Productivity

The impact that output has on future total factor productivity —i.e. the dynamic complementarities shown to be empirically relevant in Cooper and Johri (1997)— is not internalized by competitive agents. As a result, the allocation that a planner would choose cannot be reached as a competitive equilibrium outcome (neither for infinitely-lived agents nor for overlapping generations): the market return to savings and wage rate are too low. The planner’s allocation can nonetheless be implemented by a fiscal policy subsidizing as needed the returns to savings and the wage rate. The exact policy differs depending on whether just past investment or total output influences productivity: in the first case only capital returns need to be subsidized, while in the second case labor income needs to be subsidized too. The policy is balanced period-by-period by means of a lump-sum tax.