Question about both discrete and continuous choice in Dynamic Programming

Forums Questions on specific programs Question about both discrete and continuous choice in Dynamic Programming

This topic contains 1 reply, has 2 voices, and was last updated by Fabian Kindermann November 2, 2020 at 7:38 pm.

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  • #1875

    Shengzhi Mao
    User

    Recently, I found a paper “The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks” (Iskhakov et al., QE, 2017). In this paper, they investigate the retirement (discrete) choice in each period together with consumption (continuous) choice and show the kinks due to the non-convexity problem. In your book, Chapter 10.1.3 Female labor force participation, there exist the discrete choice as well as borrowing constraint. I wonder why there are no discussions about the kinks? Thank you very much!

    #1880

    Fabian Kindermann
    Moderator

    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:

    1. We use linear interpolation, a method that is suitable for dealing with kinks.
    2. 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

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