This paper adresses the generation of test cases for testing the conformance of a black-box implementation with respect to its specification, in the context of reactive systems. We aim at extending the principles and algorithms of model-based testing à la ioco for recursive specifications that can be modeled by Push-Down Systems (PDS). Such specifications may be more compact than non-recursive ones and are more expressive. The generated test cases are selected according to a test purpose, a (set of) scenario of interest that one wants to observe during test execution. The test generation method we propose in this paper is based on program transformations and a coreachability analysis, which allows to decide whether and how the test purpose can still be satisfied. However, despite the possibility to perform an exact analysis, the inability of test cases to inspect their own stack prevents it from using fully the coreachability information. We discuss this partial observation problem, its consequences, and how to minimize its impact.