We analyze optimal business tax policy when some firms are able to escape taxation by moving abroad. In contrast to the existing literature, we assume that the true number of mobile firms is ex ante unknown. While the government may learn from the firms' location responses to past tax rate changes, firms may anticipate this and adjust their choices accordingly. We find that incomplete information on mobility substantially affects the properties and the implications of equilibrium policy choices. First, the government may find it optimal to set a tax rate that triggers partial firm migration but full revelation of the true number of mobile firms. Second, we show that, if the firms' outside option is attractive (i.e., relocation cost and foreign tax rates are low), expected tax rates and expected firm migration are higher if the degree of mobility is unknown. Third, there is a positive value of learning, i.e., commitment on future tax rates cannot increase the government's expected revenue. However, if the government can commit to a rule-based learning mechanism, i.e., credibly tie its future tax policy to present policy outcomes, it may obtain a Pareto improvement.