  The Household Pulse Survey (HPS), recently released by the U.S. Census
Bureau, gathers timely information about the societal and economic impacts of
coronavirus. The first phase of the survey was quickly launched one month after
the beginning of the coronavirus pandemic and ran for 12 weeks. To track the
immediate impact of the pandemic, individual respondents during this phase were
re-sampled for up to three consecutive weeks. Motivated by expected job loss
during the pandemic, using public-use microdata, this work proposes unit-level,
model-based estimators that incorporate longitudinal dependence at both the
response and domain level. In particular, using a pseudo-likelihood, we
consider a Bayesian hierarchical unit-level, model-based approach for both
Gaussian and binary response data under informative sampling. To facilitate
construction of these model-based estimates, we develop an efficient Gibbs
sampler. An empirical simulation study is conducted to compare the proposed
approach to models that do not account for unit-level longitudinal correlation.
Finally, using public-use HPS micro-data, we provide an analysis of "expected
job loss" that compares both design-based and model-based estimators and
demonstrates superior performance for the proposed model-based approaches.
