A fall in house prices due to a change in fundamental value redistributes wealth from those long housing (for whom the fundamental value of the house they own exceeds the present discounted value of their planned future consumption of housing services) to those short housing. In a closed economy representative agent model (the special case when the birth rate is zero, of the Yaari-Blanchard OLG model used in the paper), there is no pure wealth effect on consumption from a change in house prices if this represents a change in their fundamental value. When the birth rate is positive, higher fundamental house prices driven by the housing demand of future generations will boost current consumption.
There is a pure wealth effect on consumption from a change in house prices even in the representative agent model, if this reflects a change in the speculative bubble component of house prices.
Two other channels through which a fall in house prices can affect aggregate consumption are (1) redistribution effects if the marginal propensity to spend out of wealth differs between those long housing (the old, say) and those short housing (the young, say) and (2) collateral or credit effects due to the collateralisability of housing wealth and the non-collateralisability of human wealth. A decline in house prices reduces the scope for mortgage equity withdrawal. For given sequences of future after-tax labour income and interest rates, a fall in house prices will then depress consumption in the short run while boosting it in the long run.