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Extrapolation and interpolation

Interpolation and extrapolation are used to prepare the first approximations of the state estimates of some of the components of personal income for the years in which direct source data are unavailable. Both procedures use the data for these components for benchmark years-the years for which the best data are available-and both frequently use other data that are related to the benchmark-year data for the components.

Interpolation is used to derive the first approximation of the estimates for years that are between benchmark years. For example, if data for wages and salaries for an industry were available only from the decennial censuses of population but employment data were available annually from another source, the first approximations of wages and salaries for 1981-89 are interpolated from the state data for wages and salaries 1980 and for 1990, the two census benchmark years, and from the data for employment for 1980-90.

Extrapolation is used to derive the first approximations for the years that are beyond the most recent benchmark year. For example, the first approximations of wages for 1991-1999 might be extrapolated from the census benchmark data for 1990 and from the employment data for 1990-1999. The estimates based on extrapolation are usually superseded by revised estimates when benchmark data become available for a more current year. For the preceding example, the estimates for 1991-1999 would be superseded by estimates based on interpolation when census benchmark data became available for 2000.