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Page #1Page #2Page #3Page #4Page #5Page #6Page #7Page #8Page #9Page #10Page #11Page #12Page #13Page #14Page #15Page #16Page #17Page #18Page #19Page #20Page #21Page #22Page #23Page #24Page #25Page #26Page #27Page #28Page #29Page #30Household Portfolio Allocations, Life Cycle E®ects andAnticipated In°ation¤Matthew ChambersDepartment of EconomicsTowson UniversityTowson, Maryland 21252Don E. SchlagenhaufDepartment of EconomicsFlorida State UniversityTallahassee, Florida 32306February 2003AbstractStocks, bonds and money play di®erent roles in an individual's portfolio. We ex-amine data from various Wealth Supplements of the PSID and document portfoliopatterns over the life cycle. In order to account for observed holding patterns, we con-struct a stochastic overlapping generation model. In the model, individuals are ex anteidentical, but are subject an uncertain life expectancy and income uncertainty. Indi-viduals attempt to smooth consumption by holding on money, bonds and real capital.We show that the model is able to replicate life cycle portfolio allocations. Becausemoney holding patterns are age dependent, we use the model to examine the portfolioe®ects of in°ation. We ¯nd that in°ation has modest e®ects on household portfoliocompositions. The largest e®ects occur for households between age 45 and age 65.¤We have bene¯ted from the comments of Carlos Garriga, S. Chaterjee, AyseµImrohoro¸glu, Ed Prescott,and especially Eric Young. An earlier version of this paper was presented at the 2001 Meeting of the Societyfor Economic Dynamics.1. IntroductionIn recent years, there has been a great amount of interest in trying to understand householdportfolio behavior over the life cycle. The motivation for this interest, in part, comes fromthe aging of the baby boom generation and the implications of aging for social securitysystems and the level of private and national savings. A substantial theoretical literaturehas considered age-related patterns of asset allocation in terms of the standard portfoliochoice paradigm.1Recently, the question of the relationship between age and portfolioallocation has been investigated empirically. Canner, Mankiw, and Weil (1997) examinewhether investors who are more risk averse, such as older individuals, hold more risklessassets in their portfolios. Such behavior does not appear to be consistent with the mutualfund separation theorem. Poterba and Samwick (2000) examine saving behavior from ademographic perspective and ¯nd that the composition of an individual's portfolio variesover the life cycle.In this paper we examine the Wealth Supplements to the PSID and document how cur-rency, bond and stock holding varies with wealth levels as well as an agent's life cycle.Stockholding is characterized by a humped shaped pattern over the life cycle with the peakoccurring in the mid ¯fties. In contrast, money plays a very important role for young andold individuals. Our data suggest that the fraction of the portfolio allocated to money has a"U-shaped" life cycle pattern. The life cycle pattern of bond holding in the portfolio seemsto increase with age until retirement. Because we ¯nd that portfolio composition dependson age, we construct a stochastic overlapping generation general equilibrium model whereindividuals live in an uncertain environment and attempt to smooth consumption throughsavings. Individuals have access to three savings vehicles to insure against income °uctu-ations - real capital, government bonds, and money. Markets are incomplete as negativepositions are not possible in each asset. Money is also required for consumption purposes.Aggregate shocks are not present in the model. We calibrate and solve our model numer-ically. We ¯nd that the model can account for most of the observed portfolio allocationpatterns. Since money holdings play an important role in the portfolio of younger and olderindividuals, we use the model to examine how alternative (anticipated) in°ation levels im-pact individuals portfolio allocation decisions. We ¯nd that increased in°ation has modeste®ects on household portfolios. As in°ation increases, households reallocate their portfoliosby decreasing money holdings, and increasing stock holdings. These e®ects are particularlystrong for households between ages 45 and 65. This pattern is robust to aggregate assetlevels as well as portfolio shares. Bond holdings are hardly a®ected by increased in°ation.These portfolio e®ects can be translated into aggregate e®ects. Aggregate stock holdingsand consumption increase with higher in°ation. Since the rate of return on money falls withincreased in°ation, we also ¯nd that aggregate money holdings fall with in°ation. Giventhat consumption and money holdings move in opposite directions, precautionary moneyholdings fall signi¯cantly as in°ation rises. We also ¯nd signi¯cant changes in aggregateprices at di®erent levels of anticipated in°ation. We ¯nd that as the rate of in°ation in-creases, the rate of return on stocks falls, the discount price of bonds rises, the price level1Some of the papers that have examined the theoretical implications of age for portfolio allocationsare Bodie, Merton and Samuelson(1992), Campbell, Cocco, Gomes, and Maenhout(1999), Gakidis(1997),Hochguertel(1998), Kimball(1993), and Samuelson(1989,1990).3on goods increases, and the budget balancing income tax rate increases. The increase in theprice of the discount bonds implies that the risk-free interest rate and the level of anticipatedin°ation are inversely related.2It is interesting to compare our results to Chatterjee and Corbae (1992). They study aneconomy where individuals live two periods and are faced with di®erent endowments. Agentshave access to money and costly credit to smooth consumption. Their paper analyticallystudies the individual's decision to participate in the costly credit or bond market. They ¯ndthat changes in the money growth rate have a negative e®ect on real interest rates becauseof changes in asset type holdings. The real interest rate change results in a redistribution ofwealth. Our model is much more general than their model and our numerical work allowsus to examine the quantitative size of their redistribution channel.This paper is organized into four sections. In the ¯rst section, we report the results froman analysis of a data set we developed from Wealth Supplements to the PSID. This data setallows us to examine how individuals or family


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