Empirical Proxies for the Consumption-Wealth Ratio

Campbell (1993) has employed a log-linearized approximation to an aggregate budget constraint to show how the ratio of consumption to total (human and non-human) wealth summarizes agents’ expectations concerning both future labor income and future asset returns. A problem with implementing this approach empirically is the unobservability of human wealth. Recently, Lettau and Ludvigson (2001a) have operationalized Campbell’s approach by approximating the log of total wealth with a linear combination of the log of labor income and the log of observable non-human wealth. If valid, this framework implies that the log-levels of consumption, assets, and labor income will be cointegrated. We demonstrate, however, that standard tests fail to reject the hypothesis of no cointegration once one employs measures of consumption, assets, and labor income that are jointly consistent with an underlying budget constraint. We also show that deviations of consumption, assets, and income from an estimated common trend are unable to predict future excess returns on stocks out of sample once theoretically consistent measures are used. ∗Corresponding author. Mailing address: Mail Stop 80, 20th and C Streets NW, Washington, DC 20551. E-mail: [email protected]. ∗∗E-mail: [email protected]. We are grateful to Martin Lettau and an anonymous referee for comments on earlier drafts of this paper. The views expressed are our own and do not necessarily reflect the views of the Board of Governors, the staff of the Federal Reserve System, or the Central Bank of Ireland.