17.5 Robert Hall and the Random-Walk Hypothesis

The permanent-income hypothesis is founded on Fisher’s model of intertemporal choice. It builds on the idea that forward-looking consumers base their consumption decisions not only on their current income but also on the income they expect to receive in the future. Thus, the permanent-income hypothesis highlights that consumption depends on people’s expectations.

Recent research on consumption has combined this view of the consumer with the assumption of rational expectations. The rational-expectations assumption states that people use all available information to make optimal forecasts about the future. You might recall from Chapter 13 that this assumption has potentially profound implications for the costs of stopping inflation. It can also have profound implications for consumption.

The Hypothesis

The economist Robert Hall was the first to derive the implications of rational expectations for consumption. He showed that if the permanent-income hypothesis is correct, and if consumers have rational expectations, then changes in consumption over time should be unpredictable. When changes in a variable are unpredictable, the variable is said to follow a random walk. According to Hall, the combination of the permanent-income hypothesis and rational expectations implies that consumption follows a random walk.


Hall reasoned as follows. According to the permanent-income hypothesis, consumers face fluctuating income and try their best to smooth their consumption over time. At any moment, consumers choose consumption based on their current expectations of their lifetime incomes. Over time, they change their consumption because they receive news that causes them to revise their expectations. For example, a person getting an unexpected promotion increases consumption, whereas a person getting an unexpected demotion decreases consumption. In other words, changes in consumption reflect “surprises” about lifetime income. If consumers are optimally using all available information, then they should be surprised only by events that were entirely unpredictable. Therefore, changes in their consumption should be unpredictable as well.5


The rational-expectations approach to consumption has implications not only for forecasting but also for the analysis of economic policies. If consumers obey the permanent-income hypothesis and have rational expectations, then only unexpected policy changes influence consumption. These policy changes take effect when they change expectations. For example, suppose that today the federal government passes a tax increase to be effective next year. In this case, consumers receive the news about their lifetime incomes when the government passes the law (or even earlier if the law’s passage was predictable). The arrival of this news causes consumers to revise their expectations and reduce their consumption. The following year, when the tax hike goes into effect, consumption is unchanged because no news has arrived.

Hence, if consumers have rational expectations, policymakers influence the economy not only through their actions but also through the public’s expectations of their actions. Expectations, however, cannot be observed directly. Therefore, it is often hard to know how and when changes in fiscal policy alter aggregate demand.


Do Predictable Changes in Income Lead to Predictable Changes in Consumption?

Of the many facts about consumer behaviour, one is impossible to dispute: income and consumption fluctuate together over the business cycle. When the economy goes into a recession, both income and consumption fall, and when the economy booms, both income and consumption rise rapidly.


By itself, this fact doesn’t say much about the rational-expectations version of the permanent-income hypothesis. Most short-run fluctuations are unpredictable. Thus, when the economy goes into a recession, the typical consumer is receiving bad news about his lifetime income, so consumption naturally falls. And when the economy booms, the typical consumer is receiving good news, so consumption rises. This behaviour does not necessarily violate the random-walk theory that changes in consumption are impossible to forecast.

Yet suppose we could identify some predictable changes in income. According to the random-walk theory, these changes in income should not cause consumers to revise their spending plans. If consumers had reason to expect income to rise or fall, they should have adjusted their consumption already in response to that information. Thus, predictable changes in income should not lead to predictable changes in consumption.

Data on consumption and income, however, appear not to satisfy this implication of the random-walk theory. When income is expected to fall by $1, consumption will typically fall at the same time by about $0.50. In other words, predictable changes in income lead to predictable changes in consumption that are roughly half as large.

Why is this so? One possible explanation of this behaviour is that some consumers may fail to have rational expectations. Instead, they may base their expectations of future income excessively on current income. Thus, when income rises or falls (even predictably), they act as if they received news about their lifetime resources and change their consumption accordingly. Another possible explanation is that some consumers are borrowing-constrained and, therefore, base their consumption on current income alone. Regardless of which explanation is correct, Keynes’s original consumption function starts to look more attractive. That is, current income appears to have a larger role in determining consumer spending than the random-walk theory suggests.6 image