Consumption smoothing
Consumption smoothing is the economic concept used to express the desire of people to have a stable path of consumption. Since Milton Friedman's permanent income theory (1956) and Modigliani and Brumberg (1954) life-cycle model, the idea that agents prefer a stable path of consumption has been widely accepted. This idea came to replace the perception that people had a marginal propensity to consume and therefore current consumption was tied to current income.
Friedman's theory argues that consumption is linked to the permanent income of agents. Thus, when income is affected by transitory shocks, for example, agents' consumption should not change, since they can use savings or borrowing to adjust. This theory assumes that agents are able to finance consumption with earnings that are not yet generated, and thus assumes perfect capital markets. Empirical evidence shows that liquidity constraint is one of the main reasons why it is difficult to observe consumption smoothing in the data.
In 1978, Robert Hall formalized Friedman's idea. By taking into account the diminishing returns to consumption, and therefore, assuming a concave utility function, he showed that agents optimally would choose to keep a stable path of consumption.
With (cf. Hall's paper)
agents choose the consumption path that maximizes:
Subject to a sequence of budget constraints:
The first order necessary condition in this case will be:
By assuming that we obtain, for the previous equation:
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