A Model of Housing in the Presence of Adjustment Costs: A Structural Interpretation of Habit Persistence

Abstract

Building on the model of Sanford J. Grossman and Guy Laroque (1990), this paper provides a model of household consumption and portfolio allocation which incorporates the role of housing as both a consumption good and as a component of wealth. The model captures the following features of the household's problem: (a) utility depends, probably nonseparably, on two distinct goods (nondurable consumption and housing); (b) nondurable consumption can be adjusted costlessly, but housing is subject to an adjustment cost; (c) households face housing price risk in the sense that the relative price of housing varies over time; and (d) in addition to the house, the household can invest in a wide variety of financial assets. This single, reasonably tractable, model generates testable implications for portfolio allocation, risk aversion, asset pricing, and the dynamics of nondurable consumption.Because the original Grossman and Laroque model considers a utility function in which the durable good is the sole argument, and thus abstracts completely from nondurable consumption, their analysis cannot address either the potential spillover effects of the adjustment costs of the durable good on the dynamics of nondurable consumption, or the implications for portfolio allocation of housing risk arising from variation in the relative price of housing. In addition to generating implications for issues on which the original Grossman and Laroque model was silent, the housing model delivers a strikingly different message concerning asset pricing. That is, in contrast to the Grossman and Laroque result that the consumption-based Capital Asset Pricing Model (consumption-CAPM) fails, the housing model implies that the consumption-CAPM holds.We assume that the household incurs an adjustment cost when altering the holding of the durable good (or house), although financial assets can be bought and sold costlessly. Consumption of the nondurable good can also be adjusted costlessly. When choosing a new house, the consumer takes into account the fact that the consumption of housing services will be constant at the new level until the subsequent stopping time, when it is again worthwhile to incur the adjustment cost. Thus, the home purchase decision is endogenous and fully rational, but, because of the adjustment cost, infrequent. In this continuous time setting, the household's decision process has a recursive structure; at each instant, the household first decides whether it is optimal to sell the house immediately. On those rare occasions that it is optimal to incur the adjustment cost, the household sells the old house and buys a new one instantaneously. If the household decides that it is not optimal to sell the house immediately, it then determines its optimal holdings of financial assets and optimal level of nondurable consumption conditional on the current housing stock. In essence, because of the adjustment costs associated with the durable good, the current

Explaining house price changes in Greece

“…However, none of these papers is concerned with financial assets. Cocco (2005), Flavin and Yamashita (2002), and Flavin and Nakagawa (2008) consider portfolio choice with exogenous returns in the presence of housing. However, these models are not set in general equilibrium.…”

Risk aversion, risk premia, and the labor margin with generalized recursive preferences

“…These conditions correspond to the criterion α < ρ in (5), emphasized by Epstein and Zin (1989). 19 See also Farmer (1990) and Flavin and Nakagawa (2008), who use essentially the same definition and come to the same conclusions in their dynamic frameworks. 20 The Benveniste-Scheinkman equation (11) holds for generalized recursive preferences as well as expected utility.…”

Portfolio Optimization and Mortgage Choice

“…In this study, we assume that the housing decision is already made and focus, exclusively, on the financing decision. In other studies, the house is viewed as an asset taking part in the portfolio optimization, and utility is measured from housing (see Grossman and Laroque [15]), as well as non-housing goods (see, e.g., Damgaard et al [16], Flavin and Nakagawa [17] and Corradin et al [18]). House price movements are immediately (rather than after retirement only), and sometimes continuously, integrated into consumption.…”