Is Consumption Too Smooth? Long Memory and the Deaton Paradox

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Abstract
Under common ARIMA representations of income, the permanent-income hypothesis predicts that the volatility of consumption should be larger than the volatility of unanticipated shocks to income; this prediction is not supported by the data. We examine whether this apparent excess smoothness of consumption is the result of the ARIMA representation's implicit restrictions on low-frequency dynamics. By using a generalized long-memory stochastic representation, we construct confidence intervals for the long-run impulse response of income in the absence of such low-frequency restrictions. These intervals are quite wide and include regions in which excess smoothness vanishes.

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