Government rhetoric about unbiased policing in both the USA and the UK sits uneasily with the practice of targeting disproportionately for scrutiny individuals belonging to certain minority groups in search of law breakers. Disproportionality may be derived from profiling by group membership, reading evidence of the past to predict future behavior. If that exercise fails adequately to account for diversities within groups, interpretation of evidence becomes contaminated by prejudice, stereotyping individuals because of who they are thought to be and not what they are. If the interpretation of evidence is not clouded by prejudice against or animus towards any group, then profiling contributes to technical efficiency, also called efficiency, according to defenders of profiling. Profiling methods having come under attack for potential conflation of prejudice with probability of criminality, a strand of the literature in economics has emerged claiming to bypass the need to examine the profiling method to devise a statistical test for bias in policing. A test for efficiency as a test for the absence of bias is cleverly crafted not requiring knowledge of data and methods used in profiling. We argue that such a test cannot be a sufficient criterion because of what is missed out by the model. The cost to innocents of being targeted in search for the guilty and external costs which may give rise to endogeneity are ignored in the model. We construct numerical examples to illustrate that efficient strategies suggested by models which do not explicitly scrutinize profiling methods can result in troubled outcomes.