arXiv 9 Dec 2021 · Econometrics
arXiv:2112.04637 · PDF · DOI · OpenAlex · Extracted main text
I suggest an enhancement of the procedure of Chiong, Hsieh, and Shum (2017) for calculating bounds on counterfactual demand in semiparametric discrete choice models. Their algorithm relies on a system of inequalities indexed by cycles of a large number $M$ of observed markets and hence seems to require computationally infeasible enumeration of all such cycles. I show that such enumeration is unnecessary because solving the "fully efficient" inequality system exploiting cycles of all possible lengths $K=1,\dots,M$ can be reduced to finding the length of the shortest path between every pair of vertices in a complete bidirected weighted graph on $M$ vertices. The latter problem can be solved using the Floyd--Warshall algorithm with computational complexity $O\left(M^3\right)$, which takes only seconds to run even for thousands of markets. Monte Carlo simulations illustrate the efficiency gain from using cycles of all lengths, which turns out to be positive, but small.
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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 | Chiong, K., Y.-W. Hsieh, and M. Shum (2017) Counterfactual estimation in semiparametric discrete choice models | 1.000 | 6 | 3 | 100% |
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