The aim of this paper is to assess an alternative method of estimating the amount of profit shifting and corporate income tax revenue losses. We propose a nonstandard methodology to refine the measurement of profit shifting beyond the traditional semi-elasticity procedure. A four-stage Data Envelopment Analysis (DEA) is used to estimate the relative technical efficiency of profits before taxation reported by foreign-owned companies in Czechia. The efficiency gap resulting from the difference between the first-stage and third-stage technical efficiency scores represents the level of profit shifting. Using the statutory and average effective corporate income tax rates, we calculate the amount of corporate income tax revenue losses attributable to profit shifting. The estimated mean level of profit shifting by foreign subsidiaries involved in the manufacturing and service sectors between 2009 and 2016 is over 570 million EUR, and the mean amount of tax losses exceeds 100 million EUR. In relative terms, profit shifting leads to a decrease in total corporate income tax revenues of 2% in Czechia. Foreign-owned companies involved in the manufacturing sector are less efficient than foreign-owned companies from services industries in terms of relative technical efficiency scores, while companies involved in the service sector have a considerably high efficiency gap with respect to companies involved in the manufacturing sector.