Abstract
If decision costs lead agents to update consumption every D periods, then econometricians will find an anomalously low correlation between equity returns and consumption growth (Lynch 1996). We analytically characterize the dynamic properties of an economy composed of consumers who have such delayed updating. In our setting, an econometrician using an Euler equation procedure would infer a coefficient of relative risk aversion biased up by a factor of 6D. Hence with quarterly data, if agents adjust their consumption every D =4 quarters, the imputed coefficient of relative risk aversion will be 24 times greater than the true value. High levels of risk aversion implied by the equity premium and violations of the Hansen-Jagannathan bounds cease to be puzzles. The neoclassical model with delayed adjustment explains the consumption behavior of shareholders. Once limited participation is taken into account, the model matches most properties of aggregate consumption and equity returns, including new evidence that the covariance between ln(Ct+h/Ct) and Rt+1 slowly rises with h.
Highlights
Consumption growthcovaries only weakly with equity returns,which seems to implythatequities are not veryrisky.investorshave historicallyreceived a very large premium for holding equities
Since only a fraction1/D of households adjust in the firstplace, the aagpgprreogxaimteactoevlayr1ixan1c/ebDeatswleaerngeeqasuiittywroeutludrnbesanifdacllohnosuusmehpotilodnsgardojuwsttheids instantaneously.The Euler equation forthe instantaneous-adjustment model implies that the coefficientof relativeriskaversion is inversely related to the covariance between equity returns and consumption growth
We assume thattheeconomyhas twolinearproductiontechnologies:a risk-freetechnologyand a riskytechnology(i.e., equities)
Summary
Consumption growthcovaries only weakly with equity returns,which seems to implythatequities are not veryrisky.investorshave historicallyreceived a very large premium for holding equities. Grossman and Laroque (1990) argued that adjustment costs might answer the equity-premiumpuzzle If it is costlyto change consumption, households will not respond instantaneouslyto changes in asset prices. Since only a fraction1/D of households adjust in the firstplace, the aagpgprreogxaimteactoevlayr1ixan1c/ebDeatswleaerngeeqasuiittywroeutludrnbesanifdacllohnosuusmehpotilodnsgardojuwsttheids instantaneously.The Euler equation forthe instantaneous-adjustment model implies that the coefficientof relativeriskaversion is inversely related to the covariance between equity returns and consumption growth. If an econometricianused this Euler equation to impute the coefficientof relativeriskaversion, and he used data fromour delayed adjustmenteconomy,he would imputea coefficienotfrelativeriskaversion thatwas 6D timestoo large.
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