Consumption smoothing - Alchetron, The Free Social Encyclopedia

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.

Model

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)

E t being the mathematical expectation conditional on all information available in t δ = 1 / β − 1 being the agent's rate of time preference r t = R t − 1 ≥ δ being the real rate of interest in t u being the strictly concave one-period utility function c t being the consumption in t y t = w t being the earnings in t A t being the assets, apart from human capital, in t .

agents choose the consumption path that maximizes:

E 0 ∑ t = 0 ∞ β t [ u ( c t ) ]

Subject to a sequence of budget constraints:

A t + 1 = R t + 1 ( A t + y t − c t )

The first order necessary condition in this case will be:

β E t R t + 1 u ′ ( c t + 1 ) u ′ ( c t ) = 1

By assuming that R t + 1 = R = β − 1 we obtain, for the previous equation:

E t u ′ ( c t + 1 ) = u ′ ( c t )

Which, due to the concavity of the utility function, implies:

E t [ c t + 1 ] = c t

Thus, rational agents would expect to achieve the same consumption in every period.

Hall also showed that for a quadratic utility function, the optimal consumption is equal to:

c t = [ r 1 + r ] [ E t ∑ i = 0 ∞ ( 1 1 + r ) i y t + i + A t ]

This expression shows that agents choose to consume a fraction of their present discounted value of their human and financial wealth.

Empirical evidence

Robert Hall (1978) estimated the Euler equation in order to find evidence of a random walk in consumption. The data used are US National Income and Product Accounts (NIPA) quarterly from 1948 to 1977. For the analysis the author does not consider the consumption of durable goods. Although Hall argues that he finds some evidence of consumption smoothing, he does so using a modified version. There are also some econometric concerns about his findings.

Wilcox (1989) argue that liquidity constraint is the reason why consumption smoothing does not show up in the data. Zeldes (1989) follows the same argument and finds that a poor household's consumption is correlated with contemporaneous income, while a rich household's consumption is not.

References

Consumption smoothing Wikipedia

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Contents

Model

Empirical evidence

References