Questions: The Random Walk Hypothesis of Consumption (Hall)
4 questions to test your understanding
Score: 0 / 4
Question 1 Multiple Choice
A worker learns today that her salary will rise by 20% in two years. Under Hall's random walk hypothesis, when should her consumption change?
AOnly when the raise arrives in two years
BToday, when the news arrives, and not again when the raise is paid
CGradually over the two years
DNever, because consumption follows a random walk
Consumption responds to news about lifetime resources. The announcement raises permanent income today, so consumption rises today. When the raise is actually paid, nothing new is learned, so consumption should not jump again.
Question 2 Multiple Choice
Under quadratic utility with the real interest rate equal to the rate of time preference, which equation describes optimal consumption?
AC_{t+1} = C_t exactly
BE_t[C_{t+1}] = C_t
CC_t = Y_t
DE_t[C_{t+1}] = (1 + r)Y_t
Quadratic utility makes marginal utility linear in consumption. With r equal to the discount rate, the Euler equation u′(C_t) = E_t[u′(C_{t+1})] reduces to C_t = E_t[C_{t+1}]. Consumption is expected to stay the same, but actual consumption next period can differ because of new information.
Question 3 True / False
Finding that last year's income growth predicts this year's consumption growth is evidence against the strict form of Hall's hypothesis.
TTrue
FFalse
Answer: True
Last year's income was known when last year's consumption was chosen. If it still predicts consumption growth, consumers did not fully use available information, or could not act on it. This pattern is called excess sensitivity of consumption to predictable income.
Question 4 Short Answer
Why does Hall's result make consumption changes hard to predict even though consumers plan carefully?
Think about your answer, then reveal below.
Model answer: A forward-looking consumer sets consumption today using all information about expected lifetime resources. Anything predictable is therefore already reflected in today's consumption, and consumption changes only when unexpected news arrives. Since news is by definition unpredictable, so are the changes.
The logic matches efficient-markets reasoning for asset prices: if a change could be forecast, optimizing agents would already have acted on it.