Macroeconomics


-5 Robert Hall and the Random-Walk



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Ebook Macro Economi N. Gregory Mankiw(1)

17-5

Robert Hall and the Random-Walk

Hypothesis

The permanent-income hypothesis is based on Fisher’s model of intertemporal

choice. It builds on the idea that forward-looking consumers base their con-

sumption 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 assump-

tion states that people use all available information to make optimal forecasts

about the future. As we saw in Chapter 13, this assumption can have profound

implications for the costs of stopping inflation. It can also have profound impli-

cations for the study of consumer behavior.

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 expec-

tations 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 consump-

tion over time. At any moment, consumers choose consumption based on their

current expectations of their lifetime incomes. Over time, they change their con-

sumption because they receive news that causes them to revise their expecta-

tions. For example, a person getting an unexpected promotion increases

consumption, whereas a person getting an unexpected demotion decreases con-

sumption. In other words, changes in consumption reflect “surprises” about life-

time income. If consumers are optimally using all available information, then

they should be surprised only by events that were entirely unpredictable. There-

fore, changes in their consumption should be unpredictable as well.

4

Implications



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 expec-

tations. For example, suppose that today Congress passes a tax increase to be

effective next year. In this case, consumers receive the news about their lifetime

incomes when Congress passes the law (or even earlier if the law’s passage was

predictable). The arrival of this news causes consumers to revise their expecta-

tions and reduce their consumption. The following year, when the tax hike goes

into effect, consumption is unchanged because no news has arrived.

C H A P T E R   1 7

Consumption

| 517

4

Robert E. Hall, “Stochastic Implications of the Life Cycle–Permanent Income Hypothesis: The-



ory and Evidence,’’ Journal of Political Economy 86 (December 1978): 971–987.


518

|

P A R T   V I



More on the Microeconomics Behind Macroeconomics

Hence, if consumers have rational expectations, policymakers influence the

economy not only through their actions but also through the public’s expectation

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 behavior, 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 econo-

my 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 unpre-

dictable. 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 con-

sumption rises. This behavior does not necessarily violate the random-walk the-

ory 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 expected income to rise or fall, they should

have adjusted their consumption already in response to that information. Thus, pre-

dictable changes in income should not lead to predictable changes in consumption.

Data on consumption and income, however, appear not to satisfy this impli-

cation of the random-walk theory. When income is expected to fall by $1, con-

sumption will on average 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 behavior is that some con-

sumers may fail to have rational expectations. Instead, they may base their expec-

tations 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 explana-

tion is that some consumers are borrowing-constrained and, therefore, base their

consumption on current income alone. Regardless of which explanation is cor-

rect, Keynes’s original consumption function starts to look more attractive. That

is, current income has a larger role in determining consumer spending than the

random-walk hypothesis suggests.

5



CASE STUDY



5

John Y. Campbell and N. Gregory Mankiw, “Consumption, Income, and Interest Rates: Reinterpret-

ing the Time-Series Evidence,” NBER Macroeconomics Annual (1989): 185–216; Jonathan Parker, “The

Response of Household Consumption to Predictable Changes in Social Security Taxes,” American Eco-



nomic Review 89 (September 1999): 959–973; and Nicholas S. Souleles, “The Response of Household

Consumption to Income Tax Refunds,” American Economic Review 89 (September 1999): 947–958.





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