Elasticities of Substitution in Real Business Cycle Models with Home Production

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Date: Nov. 2001
From: Journal of Money, Credit & Banking(Vol. 33, Issue 4)
Publisher: John Wiley & Sons, Inc.
Document Type: Article
Length: 11,673 words

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This paper constructs a simple model of home production that demonstrates the connection between the intertemporal elasticity of substitution in market consumption (IES) and the static elasticity of substitution between home and market consumption (SES). Understanding this connection is important because there is a large body of empirical evidence suggesting that the IES is small, but little evidence on the size of the SES. We use our framework to shed light on the properties of a home production model with a low IES. We find that such a model must have three fundamental properties in order to match key aspects of aggregate U.S. data. First, the steady-state growth rate of technology must be the same across sectors. Second, shocks to technology must be sufficiently positively correlated across sectors. Third, capital must be used more intensively in the market sector than in the home sector. A home production model with these three properties can be surprisingly successful at reconciling the RBC paradigm with evidence for a low IES.

RECENTLY THERE HAS BEEN CONSIDERABLE INTEREST in modifying the standard real business cycle model to include home production. Authors such as Benhabib, Rogerson, and Wright (1991), Greenwood and Hercowitz (1991), Greenwood, Rogerson, and Wright (1995), and Rupert, Rogerson, and Wright (1997) have documented the importance of the home sector in the U.S. economy, and have shown that home production can improve the quantitative performance of the standard model.

In almost all these studies, households derive utility from three "goods": market consumption, home consumption, and leisure. Home consumption is considered to be a substitute for market consumption, as, for example, a home-cooked meal is a substitute for a meal in a restaurant. Leisure is distinct from both these forms of consumption and is modeled in a traditional manner, as time not occupied by home or market production.

In this paper we adopt a different perspective. We argue that households value their leisure time because of what they can do with it. Valued leisure is not the residual time unoccupied by production; after all, time spent in prison is unproductive, but does not generate utility in the same way as time spent at home. From this point of view, it is natural to think that valued leisure is the output from a home production function in which home or leisure time, home capital, and home technology appear just as market time, market capital, and market technology do in the market production function. Accordingly we follow Greenwood and Hercowitz (1991) and use a model in which households derive utility from two "goods": market consumption and home consumption, where the latter replaces the traditional leisure variable.

Even more importantly, we assume that home consumption enters the utility function separably from market consumption. All the home production studies to date have analyzed nonseparable specifications. While this approach has yielded many important insights, we think it is useful to consider a separable alternative. We do this for two reasons. First, the traditional real business cycle literature commonly assumes that...

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Gale Document Number: GALE|A79745674