The aggregate consumption function
The model for aggregate consumption in B&N satisfies the criteria we listed in Section 2.3. They provide a model in which cointegration analysis establishes that the linear relationship
cht = constant + 0.56yht + 0.27wht, (2.6)
is a cointegrating relationship and that the cointegration rank is one. Hence, while the individual variables in (2.6) are assumed to be non-stationary and integrated, the linear combination of the three variables is stationary with a constant mean showing the discrepancy between consumption and its long-run equilibrium level 0.56yht +0.27wht. Moreover, income and wealth are weakly exogenous for the cointegration parameters. Hence, the equilibrium correction model for Acht satisfies the requirements of valid conditioning. Finally, the cointegration parameters appears to be invariant. The estimated marginal models for income and wealth show evidence of structural breaks. The joint occurrence of a stable conditional model (the consumption function) and unstable marginal models for the conditional variables is evidence of within sample invariance of the coefficients of the conditional model and hence super exogenous conditional variables (income and wealth). The result of invariance is corroborated by Jansen and Terasvirta (1996), using an alternative method based on smooth transition models.
The empirical consumption function in B&N has proven to be relatively stable for more than a decade, in particular this applies to the cointegration part of the equation. Thus, it is of particular interest to compare it with rival models in the literature.