What are the responsibilities of my teaching assistant?

The responsibilities of the assistants will vary depending on the needs of the course and the wishes of the professor. In the core courses the teaching assistants will hold recitation sections and office hours as well as grade homework assignments and exams. Professors oversee both the material presented in recitation and the grading of all assignments. In the elective courses some assistants will still hold recitation sections and office hours if the professor deems them necessary. Otherwise the assistants will grade.
You should also note that teaching assistants are extremely knowledgeable about the study of economics and the economics department at Columbia. They are a great source of information about the courses, the professors and the choice of courses to fit a variety of goals. They are not necessarily knowledgeable about the requirements of the various economics degrees.