Balanced growth and empirical proxies of the consumption-wealth ratio

Empirical proxies of the aggregate consumption-wealth ratio in terms of a cointegrating relationship between consumption (c), asset wealth (a) and labour income (y), commonly referred to as cay-residuals, play an important role in recent empirical research in macroeconomics and finance. This paper shows that the balanced-growth assumption made in deriving cay implies a second cointegrating relationship between the three variables; the three great ratios c - a, c - y and a - y should all be individually stationary In U.S. data I find evidence for this second cointegrating relationship once I control for deterministic trends and a structural break. The fact that cay is a linear combination of two stationary great ratios has a number of important implications. First, without additional identifying restrictions, the residual from a cointegrating regression can no longer be interpreted as an approximation of the aggregate consumption-wealth ratio. I discuss an identifying assumption that may still allow to do so. Secondly, predictive regressions of asset prices on a combination of two stationary great ratios, must do at least as well as regressions on cay alone. Still, cay proves remarkably robust as an indicator of aggregate asset price cycles. The findings here also inform a recent debate about the role of look-ahead bias in cay: in order to identify transitory components in asset prices, households do not need to identify the parameters of the cay-relation at all.