In conducting an investigation into the specification of partial static equilibrium factor demand models, this paper isolates: (1) the endogeneity of output and quasi-fixed factor levels; (2) the choice of omitted share equation; and (3 ) the presence of serial correlation (when using time series data) as the specification issues that most affect the existing empirical literature. The impact of specification changes are studied via a series of experiments conducted on an illustrative data set and are found to have significant effects on: parameter estimates and model diagnostics; departures between observed and full equilibrium levels of quasi- fixed factors; and price elasticities. As a consequence, caveats must be attached to several previous studies and care must be taken by future researchers in addressing using such models.