Dennis Kristensen, Patrick K. Mogensen, Jong Myun Moon, Bertel Schjerning
arXiv 10 Apr 2019 · Econometrics · publishedJournal of Econometrics (2020) · 3 citations (OpenAlex)
arXiv:1904.05232 · PDF · DOI · OpenAlex · Extracted main text
We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators defining the two functions. The random Bellman operators, and therefore also the corresponding solutions, are generally non-smooth which is undesirable. To circumvent this issue, we introduce a smoothed version of the random Bellman operator and solve for the corresponding smoothed value function using sieve methods. We show that one can avoid using sieves by generalizing and adapting the `self-approximating' method of Rust (1997) to our setting. We provide an asymptotic theory for the approximate solutions and show that they converge with root-N-rate, where $N$ is number of Monte Carlo draws, towards Gaussian processes. We examine their performance in practice through a set of numerical experiments and find that both methods perform well with the sieve method being particularly attractive in terms of computational speed and accuracy.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Rust, J (1997) Using randomization to break the curse of dimensionality | 1.000 | 14 | 6 | 100% |
| 2 | Pal, J. and J. Stachurski (2013) Fitted value function iteration with probability one contractions | 1.000 | 10 | 4 | 100% |
| 3 | Rust, J (1987) Optimal replacement of gmc bus engines: An empirical model of harold zurcher | 1.000 | 6 | 3 | 100% |
| 4 | Arcidiacono, P., P. Bayer, F. A. Bugni, and J. James (2013) Approximating high-dimensional dynamic models: Sieve value function iteration | 0.843 | 3 | 3 | 100% |
| 5 | Rust, J (1988) Maximum likelihood estimation of discrete control processes | 0.811 | 4 | 2 | 100% |
| 6 | Munos, R. and C. Szepesvari (2008) Finite-time bounds for fitted value iteration | 0.737 | 3 | 2 | 100% |
| 7 | van der Vaart, A. W. and J. A. Wellner (1996) Weak Convergence and Empirical Processes | 0.644 | 4 | 2 | 50% |
| 8 | Keane, M. and K. I. Wolpin (1994) The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte carlo evidence | 0.511 | 2 | 1 | 100% |
| 9 | Bowman, A., P. Hall, and T. Prvan (1998) Bandwidth selection for the smoothing of distribution functions | 0.405 | 1 | 1 | 100% |
| 10 | Brumm, J. and S. Scheidegger (2017) Using adaptive sparse grids to solve high-dimensional dynamic models | 0.405 | 1 | 1 | 100% |
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