MONETARY POLICY AND ENDOWMENT RISK IN A LIMITED PARTICIPATION MODEL

Abstract

I. INTRODUCTION An asset market segmentation model is constructed in this paper to study the risk-sharing role of monetary policy. Economic agents face uninsurable endowment risk when there is limited asset market participation. Because an initial money injection goes first to those who can access the asset market, money is nonneutral and monetary policy redistributes consumption across agents. Thus, monetary policy plays a risk-sharing role that provides crude insurance. Limited participation models that capture nonneutralities of money were initially developed by Grossman and Weiss (1983) and Rotemberg (1984) and followed by Lucas (1990), Fuerst (1992), and Chatterjee and Corbae (1992). Recently, Alvarez and Atkeson (1997), Alvarez, Lucas, and Weber (2001), and Alvarez, Atkeson, and Kehoe (2002) have made important contributions, but they focus on the implications of liquidity effects, asset prices, and the exchange rate instead of the risk-sharing implications of monetary policy. My model is built on Alvarez, Lucas, and Weber (2001). There are two types of households: traders who participate in the asset market and nontraders who do not. These types are determined exogenously. In each period, traders receive constant endowments, whereas nontraders face uninsurable endowment shocks. In the asset market, the government injects money through open market operations and traders initially receive the money injection. In equilibrium, money is nonneutral and monetary policy redistributes consumption between traders and nontraders. The government money injection increases traders' consumption and decreases nontraders' consumption because traders get the money injection through the asset market whereas nontraders suffer from inflation. If nontraders all receive the same endowment shock, then monetary policy is a perfect risk-sharing tool that can smooth out consumption across traders and nontraders. However, if nontraders receive idiosyncratic endowment shocks, then monetary policy is not enough to perfectly insure nontraders. Although monetary policy does not achieve a Pareto optimal allocation, it can mitigate the dispersion of consumption across nontraders. The optimal money growth rate can be positive or negative depending on the endowment distribution. The Friedman rule is not optimal in general. There is a set of limited participation literature where the asset market is endogenously segmented: Chatterjee and Corbae (1992), Alavarez, Atkeson, and Kehoe (2002), Chiu (2004), and Chiu and Molico (2007). Although endogenous asset market segmentation is useful in some contexts, for this paper nothing is lost by assuming exogenous segmentation, and much is gained in simplicity. Models of the redistributional effects of monetary policy include Levine (1991), Shi (1999), Berentsen, Camera, and Waller (2005), and Molico (2006). The models studied by Levine (1991) and Mollico (2006) are particularly relevant. Levine (1991) studies an incomplete markets environment where positive money growth implemented through lump-sum transfers can be optimal. Molico (2006) studies a search environment and shows, similarly, that positive inflation with lump-sum transfers can be welfare-enhancing, but not at high rates of inflation. In both the Levine (1991) and Molico (2006) environments, there is an insurance role for monetary policy, much as in the environment studied in this paper. The model here has the virtue of being much more tractable than either the Levine (1991) or Molico (2006) models. Furthermore, a novelty here is to study an insurance role for monetary policy in the context of market segmentation, where the agents who received the first-round effects of monetary policy do not wish to share risk among themselves. The key risk-sharing problem has to do with risk sharing between asset market participants and nonparticipants. The remainder of the paper is organized as follows. …