Figure 2. Indices of Per Capita Real GDP and Hours.
Our trend is just a well-defined statistic, where a statistic is a real valued
function. Hodrick and Prescott’s (1980) trend statistic mimics well the
smooth curve that economists fit through the data. The family of trends we
considered is one-dimensional. The one in the family that we used is the first
one we considered. Later we learned that the actuaries use this family of
smoothers, as did John von Neumann when he worked on ballistic problems
for the U.S. government during World War II.2 A desirable feature of this
definition is that with the selection of smoothing parameters for quarterly
time series, there are no degrees of freedom and the business cycle statistics
are not a matter of judgment. Having everyone looking at the same set of
statistics facilitated the development of business cycle theory by making
studies comparable.
One set of key business cycle facts are that two-thirds of business cycle
fluctuations are accounted for by variations in the labor input, one-third by
variations in total factor productivity, and virtually zero by variations in the
capital service input. The importance of variation in the labor input can be
seen in Figure 1.
This is in sharp contrast to the secular behavior of the labor input and output,
which is shown in Figure 2. Secularly, per capita output has a strong upward
trend, while the per capita labor input shows no trend.
A second business cycle fact is that consumption moves procyclically; that
is, the cyclical component of consumption moves up and down with the
cyclical component of output. A third fact is that in percentage terms, invest-
2 See Stigler’s (1978) history of statistics.