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This paper empirically examines the long-run relationship between consumption, asset wealth and labor income (i.e.,  cay ) in the United States through the lens of a quantile cointegration approach. The advantage of using this approach is that it allows for a nonlinear relationship between these variables depending on the level of consumption. We estimate the coefficients using a Phillips–Hansen type fully modified quantile estimator to correct for the presence of endogeneity in the cointegrating relationship. To test for the null of cointegration at each quantile, we apply a quantile CUSUM test. Results show that: (i) consumption is more sensitive to changes in labor income than to changes in asset wealth for the entire distribution of consumption, (ii) the elasticity of consumption with respect to labor income (asset wealth) is larger at the right (left) tail of the consumption distribution than at the left (right) tail, (iii) the series are cointegrated around the median, but not in the tails of the distribution of consumption, (iv) using the estimated  cay  obtained for the right (left) tail of the distribution of consumption improves the long-run (short-run) forecast ability on real excess stock returns over a risk-free rate.

Consumption, aggregate wealth and expected stock returns: a quantile cointegration approach