Suppose I have two regressors, task availability (Xa) and task participation (Xp), and a DV Y. One can only participate in a task if it is available, but one can choose not to participate even if a task is available. Baseline model Y ~ Xa, should be the total effect of task availability. Y ~ Xa + Xa * Xp, adds the effect of participation. Now, if the interaction model is the true model, would Y ~ Xa be biased, because of omitted variable problem? That is, the total effect cannot be estimated using the baseline model?