Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits nonzero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

A seasonal commodity is one that either (1) is not available during certain seasons or (2) is always available but its prices or quantities fluctuate with the season or time of year. The existence of type-1 seasonal commodities in consumer preference functions means that the usual economic approach to index number theory cannot be applied to construct a short-term month-to-month or quarter-to-quarter consumer price index. We postulate various separability assumptions on intertemporal preferences that can be used to justify various seasonal index number formulas. One of our approaches leads to an index number solution to the problem of seasonal adjustment.

This paper studies the problems of measuring economic growth under conditions of high inflation. Traditional bilateral index number theory implicitly assumes that variations in the price of a commodity within a period can be ignored. To justify this assumption under conditions of high inflation, the accounting period must be shortened to a quarter, a month, or possibly a week. However, once the accounting period is less than a year, the problem of seasonal commodities is encountered; i.e., in some subannual periods, many seasonal commodities will be unavailable and hence the usual bilateral index number theory cannot be applied. The paper systematically reviews the problems of index number construction when there are seasonal commodities and high inflation. Various index number formulas are justified from the viewpoint of the economic approach to index number theory by making separability assumptions on consumers' intertemporal preferences. We find that accurate economic measurement under conditions of high inflation is very complex.