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In their seminal work, Lettau, M., and S. Ludvigson, 2001, “Consumption, Aggregate Wealth, and Expected Stock Returns.”  The Journal of Finance  56 (3): 815–49.  https://doi.org/10.1111/0022-1082.00347 , demonstrated that there exists a long-run relationship between consumption, asset holdings, and labor income. They denoted this relationship as  cay  and showed it to be quite successful in predicting the behavior of real stock returns. Their estimation procedure assumes that consumption, asset wealth, and labor income are first-order integrated ( I (1), nonstationary) and that their linear combination forms a zero-order integrated ( I (0), stationary) series. This paper proposes a more general framework in the estimation of the  cay  model by allowing both the series and the long-run equilibrium to be fractionally integrated. We use the recently developed Fractionally Cointegrated VAR (FCVAR) approach to estimate the  cay  model. Results show that: (i) the series are nonstationary but mean-reverting processes, (ii) there exists a long-run equilibrium between consumption, asset wealth, and labor income, (iii) this long-run relationship is a stationary fractionally integrated process, and (iv) the estimated  cay  using the FCVAR approach shows the same desirable forecasting properties as its predecessor.

Consumption, Aggregate Wealth and Expected Stock Returns: An FCVAR Approach