The Variability and Volatility of Sleep: An ARCHetypal Behavior

Using Dutch time-diary data from 1975-2005 covering over 10,000 respondents for 7 consecutive days each, we show that individuals’ sleep time exhibits both variability and volatility characterized by stationary autoregressive conditional heteroscedasticity: The absolute values of deviations from a person’s average sleep on one day are positively correlated with those on the next day. Sleep is more variable on weekends and among people with less education, who are younger and who do not have young children at home. Volatility is greater among parents with young children, slightly greater among men than women, but independent of other demographics. A theory of economic incentives to minimize the dispersion of sleep predicts that higher-wage workers will exhibit less dispersion, a result demonstrated using extraneous estimates of earnings equations to impute wage rates. Volatility in sleep spills over onto volatility in other personal activities, with no reverse causation onto sleep. The results illustrate a novel dimension of economic inequality and could be applied to a wide variety of human behavior and biological processes.