References and Literature

The neoclassical growth model under uncertainty, presented in Section 17.1, was first analyzed by Brock and Mirman (1972). Because the analysis of the social planner’s problem is considerably easier than the study of equilibrium growth under uncertainty, most analyses in the literature look at the social planner’s problem and then appeal to the Second Welfare Theorem.

The first systematic analysis of competitive equilibrium under uncertainty is provided in Lucas and Prescott (1971) and Mehra and Prescott (1979). Sargent and Ljungqvist (2004, Chapter 12) provides a good textbook treatment. The material in Section 17.2 is similar to that in Sargent and Ljungqvist but is more detailed and provides a few additional results.

The Real Business Cycle literature is enormous and the treatment in Section 17.3 only scratches the surface. The classic papers in this literature are Kydland and Prescott (1982) and Long and Plosser (1983). Sargent and Ljungqvist (2004) again provides a good introduc­tion.

Section 17.4 presents the incomplete markets model first introduced by Truman Bewley (1977, 1980, 1986). This model has now become one of the workhorse models of macro­economics and has been used for analysis of business cycle dynamics, income distribution, 690

optimal fiscal policy, monetary policy, and asset pricing. A more modern treatment is pro­vided in Aiyagari (1994), though the published version of the paper does not contain any of the mathematical analysis. The reader is referred to Bewley (1977, 1980) and to the working paper version, Aiyagari (1993), for more details on some of the propositions stated in Section 17.4 as well as a proof of existence of a stationary equilibrium, which I did not provide in the text. Krusell and Smith (1998, 1999, 2005), among others, have used this model for busi­ness cycle analysis and have also provided new quantitative tools for the study of incomplete market economies.

Section 17.5 is a simple stochastic extension of the baseline overlapping generations model. I am not aware of any similar treatment, though none of the material in this section is new or difficult.

Section 17.6 builds on Acemoglu and Zilibotti (1997) and more details on some of the results stated in that section are provided in Acemoglu and Zilibotti (1997). Evidence on the relationship between economic development and volatility is provided in Acemoglu and Zilibotti (1997), Imbs and Wacziarg (2003), and Koren and Tenreyro (2007). Ramey and Ramey (1994) also provide related evidence, though they emphasize the effect of volatility on growth using cross-country regression analysis. As noted above, the concept of decentralized equilibrium used in this model is not Arrow-Debreu. Instead it imposes price-taking behavior in all open markets and determines the set of open markets via a free entry condition. This type of equilibrium concept is commonly used in general equilibrium theory, for example, Hart (1980), Makowski (1980), and Allen and Gale (1991). Koren and Tenreyro (2007) present a generalization of the Acemoglu and Zilibotti (1997) model. Acemoglu and Zilibotti (1997) also contain an analysis of international capital flows in a similar framework and this analysis is extended in Martin and Rey (2002).

17.9.