Developing Imputation Models for the Services Sectors Portion of the Economic Census

The editing software used by the Economic Census offers a variety of imputation options, many of which employ statistical models. In prior censuses, the services sectors portion of the Economic Census has relied on industry average imputation as its primary statistical imputation model. This ratio imputation method uses weighted least squares estimates for no-intercept simple linear regression models as imputation parameters. The weighted regression method currently used compensates for heteroscedasticity (unequal error variances). The industry average imputation method used by the services sectors portion of the Economic Census assumes the following weighted regression model for each basic data item Y: Yij = βi Xij + ξij, ξij ~ (0, Xij σ), i.e., var(ξij) = σij = Xij σ, where j indexes the establishments within industry i that satisfy the ratio edit li ≤ Yij/Xij ≤ ui. Thompson and Sigman (1996) and Huang (1984) demonstrate the plausibility of this model for the services sectors data. The best linear unbiased estimator (B.L.U.E) of βi (the industry average) for this model is the weighted least square estimate with weight of 1/Xij, so that ∑ (Draper and Smith, 1981, p.111). ∑ ∑ ∑ = j ij j ij j ij ij j ij ij ij X Y X w Y X w / / 2