Building proxies that capture time-variation in expected returns using a VAR approach

I use the consumer's budget constraint to derive a relationship between stock market returns, the residuals of the trend relationship among consumption, aggregate wealth and labour income, and three major sources of risk: future changes in the housing consumption share, future labour income growth and future consumption growth. I model the joint dynamics of changes in the housing consumption share, consumption-growth, wealth growth, income growth, asset returns, consumption-wealth ratio and dividend-price ratio, and show that asset returns largely reflect expectations about long-run risk. On the other hand, unexpected shocks play a negligible role in the context of forecasting future asset returns. Combining the intertemporal budget constraint and the forecasting properties of an informative Vector Autoregression (VAR), one can, therefore, generate the predictability of many economically motivated variables developed in the literature on asset pricing, and accommodate the implications of a wide class of optimal models of consumer behaviour without imposing a functional form on preferences.