  A principal can propose a project to an agent, who then decides whether to
accept. Their payoffs from launching the project depend on an unknown binary
state. The principal can obtain more precise information about the state
through a test at no cost, but crucially, it is common knowledge that she can
falsify the test result. In the most interesting case where players have
conflicted interests, the optimal test is a binary lemon-detecting test. We
also find that coordination is possible when the principal is pessimistic but
not when the agent is pessimistic. Moreover, when the agent has private
information about the state, a single binary lemon-detecting test remains
optimal even though the principal has the option to screen the agent by
providing a menu of tests. Our finding is consistent with observed tests in
real practice.
