The representative-agent framework has endowed macroeconomists with powerful microeconomic tools. Unfortunately, it has also blurred the distinction between statements that are valid at the individual level and those that apply to the aggregate. In this paper I argue that probability theory puts strong restrictions on the joint behavior of a large number of units that are less than fully synchronized. Many fallacies arise from disregarding these restrictions. For example, asymmetric factor adjustment costs at the firm level need not imply asymmetric responses of aggregate employment flows to positive and negative shocks.