This paper develops models for sampling error covariance matrices of estimates of age group poverty rates, median income, and per capita income from the Current Population Survey's (CPS) March Supplement. (Not part of the normal CPS estimation procedures, the covariances for 1989 to 1993 were estimated by Bob Fay using vplex , a variance estimation program (Fay 1989). The ultimate objective is to use the sampling error models developed here, in combination with models for the time series of poverty rates and income measures, to improve estimates of the “true" (unobserved) state poverty rates and income measures.

Our models account for three features of the CPS sampling error covariance structure: (1) differences in the variances by state (through random state effects): (2) dependence of variances on sample size and on the level of the estimates (through a generalized variance function, GVF); and (3) sampling error correlations over time (through an autoregressive-moving-average (ARMA) time series model). Section 2 describes our general modelling approach. Then, in Section 3, we discuss details of the model development for the CPS application.