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General equilibrium, preferences and financial institutions after the crisis

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Abstract

The study is a review of some recent papers in general equilibrium that can be viewed as efforts to better understand the recent financial crisis. We begin by proposing a new set of preferences inspired by the new decision theoretical literature. In our main example, we use the concept of wariness which captures the idea of agents concerned with the worst case scenario. As a consequence, utility functions are weighted sums of a term with discounted future and another which concentrates in the worst period consumption. In this new context, we can have bubbles in a purely classical framework. In the second part of the paper, we change the classical budget set to allow for lack of commitment for the part of the agent. We analyze three different situations where this can happen. In the first one, agents can borrow only with collateral, represented by a durable good. In the second, we study bankruptcy laws where the whole firm is used as collateral, and in the third situation, the agents are punished by exclusion from the market. These three situations have the virtue of being real life based.

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Notes

  1. Joint work with Novinski and Páscoa (Araujo et al. 2011).

  2. Actually, Bewley’s works also cover the case of an uncountable set of commodities.

  3. See Theorem 3.1 in Santos and Woodford (1997) (also the results in Magill and Quinzii 1996) and the example by Bewley (1980) (where a complete markets bubble required an infinite present value of wealth).

  4. Mackey topology in \(\ell ^{\infty }\), for bounded sequences, is the topology of coordinate-wise convergence.

  5. \(U(x) = \min \{\int _{\mathbb {N}}u(x)\mathrm{d}\eta \; : \; \eta \in ba^{1}\) and \(\eta \ge \nu \}\) with \(\nu (A) = \frac{1}{\frac{\delta }{1 - \delta } + \beta }\sum _{t \in A} \delta ^{t}\) if \(A \subsetneq \mathbb {N}\) and \(\nu (\mathbb {N}) = 1\). Thus, we could interpret wariness in this example as a type of ambiguity aversion on a set of discount factors (Schmeidler 1989; Gilboa 1989).

  6. We note that with assumptions of proposition 2, this preferences becomes time consistent along the equilibrium path. For intuitive conditions that guarantee the previous assumptions, and therefore time consistency, see also the working paper with Gama-Torres, Novinski and Páscoa titled On the Role of Money when Agents are Wary.

  7. LIM is a generalized limit, i.e., a continuous linear mapping from \(\ell ^{\infty }\) into \(\mathbb {R}\) such that \(\text {LIM}(x) = \lim _{t}x_{t}\) when this limit exists.

  8. Working paper with Gama-Torres, Novinksi and Páscoa with the same title.

  9. Joint work with Chateauneuf, Gama-Torres and Novinski in the working paper titled General Equilibrium, Risk Loving, Ambiguity and Volatility.

  10. In fact, the difficulties are given by the non-convexity of the preferences; thus, most of the traditional tools are not applicable.

  11. See the working paper Existence and Characterization with Ambiguity Aversion, Ambiguity Loving.

  12. Also see our working paper Existence and Characterization with Ambiguity Aversion, Ambiguity Loving.

  13. Joint work with Chateauneuf and Faro in Araujo et al. (2012a) and in the working paper titled Ambiguous Valuation and Financial Market Imperfections.

  14. Joint work with Kubler and Schommer (Araujo et al. 2012c).

  15. These \(S\) assets \(j\) must satisfy \(C_{j}p_{2}(s) = p_{1}(s)\) for all \(s \in S\).

  16. Joint work with Schommer and Woodford (Araujo et al. 2014).

  17. We dispense with the superscript \(h\) in this discussion, as we discuss the budget constraints of a single household.

  18. Joint work with Ferreira and Funchal (Araujo et al. 2012b).

  19. The Latin American and Caribbean block is composed of Argentina, Bolivia, Brazil, Chile, Colombia, Costa Rica, the Dominican Republic, Ecuador, El Salvador, Guatemala, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Uruguay and Venezuela.

  20. The interest-rate spread confirms the tightness of the Brazilian market: The Brazilian spread (49 %) is more than four times larger than the average spread in Latin American countries (11 %) and more than 12 times larger than the average for OECD countries (3.87 %). All values refer to the 1997–2002 period. See Araujo and Funchal (2005).

  21. Joint work with Santos and Leon (Araujo et al. 2013).

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina, 110, CEP 22460-320, Rio de Janeiro, Brazil

    Aloisio Araujo

  2. EPGE/FGV, Praia de Botafogo, 190, CEP 22250-040, Rio de Janeiro, Brazil

    Aloisio Araujo

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  1. Aloisio Araujo
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Correspondence to Aloisio Araujo.

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This paper is a printed version of the SAET’s presidential lecture in Paris, July 22, 2013.

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Araujo, A. General equilibrium, preferences and financial institutions after the crisis. Econ Theory 58, 217–254 (2015). https://doi.org/10.1007/s00199-014-0840-0

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