Dear Shengzhi Mao,

sorry of the very, very late response. I moved to a new home with my family and therefore I am running big time behind my schedule.

Regarding your question: You are absolutely right. Whenever we have a discrete choice problem, there is the issue of the policy functions not being differentiable anymore. It might even happen that they exhibit a discontinuity.

We are aware of this problem, but the discussion in Iskhakov et al. requires a very high level of computational and theoretical knowledge. In the course of writing the book we decided that, for educational reasons, we should not dive into this topic. We also think that our solution to the problem is (maybe with some shortcomings) an accurate enough description of the discrete choice problem. This is for two reasons:

- We use linear interpolation, a method that is suitable for dealing with kinks.
- We interpolate expected values in the intertemporal choice problem, and not individual policy functions. Expectation formation washes out some of the problems with kinks, as at different future states of the world, kinks occur at different points of the state space.

But you are absolutely right. Our choice of computational method can be improved to deal more explicitly with the kinks in our optimization problem.

I hope this clarifies things. Let me know if you have any further questions.

Best,

Fabian