BUREAU OF THE CENSUS STATISTICAL RESEARCH DIVISION REPORT SERIES SRD Research Report Number: CENSUS/SRD/RR-91/02 THE EFFECT OF SAMPLING ERROR ON THE TIME SERIES BEHAVIOR OF CONSUMPTION’DATA bY

Much empirical economic research today is executed in the framework of tightly specified time series models that derive from theoretical optimization problems. The results of fitting such models to published time series data are often interpreted as yielding evidence about the values of underlying theoretical parameters. Such conclusions may, however, be sensitive to imperfections in the data. This paper investigates one such imperfection: sampling error in data from the Census Bureau’s Retail Trade Survey (RTS). These data are an important ingredient in the construction of personal consumption expenditures in the national income accounts. We build seasonal time series models for the sampling error in (unb&chmarked) monthly survey estimates that take into account pertinent characteristics of the RTS. To model the signal component we use the “airline model” of Box and Jenkins (1976), augmented by regression terms to account for calendar variation and outliers. This model appears to fit the data well and can be given an economic motivation through a model related to that of Miron (1986), extended to allow for stochastic seasonal tastes. We assess the effects of sampling error by fitting our model to the observed data twice, once allowing for and once ignoring the sampling error component. We find that estimates of the innovation variance and seasonal moving average parameter can be sensitive to even moderate amounts of the type of sampling error present in the retail trade estimates. The nonseasonal moving average parameter estimates turn out to be little affected by the sampling error. We conclude that sampling error should be taken seriously in attempts to derive economic implications by modeling time series data from repeated surveys. .