Robert Walk and Random Walk Theory

The permanent income hypothesis based on Fischer’s intertemporal choice. It is based on the idea that forward looking individuals base their consumption not only on current income but also on the income they expect to earn in future. Thus, the permanent income hypothesis highlights that consumption depends on expectation in future.
The economist Robert Walk was the first one to derive the implication of rational expectations on consumption. He explained that if the consumer has rational expectations, then changes in consumption over time should be unpredictable. When changes in a variable are unpredictable, the variable is set to follow a random walk. According to Hall, the combination of permanent income hypothesis and rational expectation implies that consumption follows a random walk.
According to permanent income hypothesis, consumer face fluctuating income and try their best to smooth their consumption over time. At any moment, consumers choose consumption based on their current expectation of their life time income
Overtime they change their consumption behavior when they received news that causes them to revise their expectation. For example- a person getting unexpected promotion increases his consumption whereas a person getting unexpected demotion decreases his consumption. In other words, change in consumption reflects surprise about lifetime income. If the consumers are optimally using all the available information, then they should be surprised only the unpredictable or unexpected events. Therefore, changes in consumption are also unpredictable.

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