future income is resolved, they will be able to choose the appropriate level of consumption. Hence, one can expect that, intertemporally, the option value of waiting for consumers is increasing in the weight of durable goods in the consumer expenditure function and it is also higher the longer the irreversibility of their purchase.

The adjustment mechanism that governs the purchases of consumption goods is critical for understanding why durables consumption in particular will overreact under uncertainty. In early work on this topic Bernanke (1984, 1985) uses a rule that implies a regular adjustment with which the consumers close the gap between their desired and actual levels of durables stock. However, this type of behavior is not consistent with the data in which adjustments happen only infrequently. This observation has led subsequent studies to address the shortcoming of Bernanke by modelling the adjustment mechanism via the (S,s) model framework first used by Arrow et al. (1951) in the context of inventories adjustment, e.g. Lam (1991); Attanasio (2000); Eberly (1994); Bertola et al. (2005). In the standard textbook (S,s) model, inventories are allowed to vary between two target levels of stock, the upper, S, and the lower, s. Applied to consumer spending, the upper band S and the lower band s refer to the maximum and minimum stock of consumption goods a household desires to hold relative to their income. The consumer increases spending when stocks fall to the lower target level and reduces it when they reach the upper level. In this framework, the existence of transaction costs associated with purchases of durables leads to an irregular adjustment particularly for this category of goods.

Lam (1991) considers a situation when the consumer uses a threshold criterion instead of adjusting the stock regularly in small increments to close the gap between desired and actual level of durables. In his model the consumers buy or sell durables when the stock exceeds a certain lower or upper threshold, but do not act otherwise. He shows that households adjust stocks infrequently and expenditures react more to large income shocks than to small shocks. Furthermore, desired stocks are not very sensitive to transitory income, upward adjustments happen quicker than downward adjustments and thresholds levels vary across households. He attributes the different speed of adjustment to imperfections in resale markets while the threshold heterogeneity across households is a consequence of liquidity constraints. When households are faced with a lack of access to credit or excessively expensive finance, the upper threshold level increases as they are unable to adjust their durables stock to the desired higher level. The low threshold on the other hand will be small because if the desired stock is lower than the actual stock, households might be tempted to resell their durables in order to be able to purchase the nondurables they cannot access due to credit constraints.

Attanasio (2000) provides additional insights into the relationship of the adjustment bands and consumer income. He models the purchases of cars by US households as an (S,s) rule defining his thresholds in terms of the ratio of durables to non-durables. Using a large microeconomic dataset he directly estimates the (S,s) parameters and finds that desired ratio of durables is lower for households with lower income. In addition, he also find evidence that the (S,s) bands are large. This implies pervasive inertial behavior and potentially high relevance for the determination of aggregate expenditure. Unfortunately, as shown by the paper itself, explicitly deriving aggregate implications proves difficult.

Such aggregate implications are attempted in Eberly (1994). Similarly to Attanasio (2000), this paper 6