Michael Griebel, Florian Heiss, Jens Oettershagen, Constantin Weiser
arXiv 12 Aug 2019 · Econometrics
arXiv:1908.04110 · PDF · DOI · OpenAlex · Extracted main text
Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators, while empirical and simulation analyzes often find that alternative approximation methods such as quasi-Monte Carlo simulation, Gaussian quadrature, and integration on sparse grids behave considerably better numerically. This paper generalizes the theoretical results widely known for MSL estimators to a general set of maximum approximated likelihood (MAL) estimators. We provide general conditions for both the model and the approximation approach to ensure consistency and asymptotic normality. We also show specific examples and finite-sample simulation results.
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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 | Butler and Moffitt (1982) `A computationally efficient quadrature procedure for the one factor multinomial probit model.' Econometrica 50(3), 761–764 | 0.874 | 5 | 2 | 100% |
| 2 | Davis and Rabinowitz (2007) Methods of Numerical Integration Dover Books on Mathematics Series (Dover Publications) | 0.811 | 4 | 2 | 100% |
| 3 | Bhat (2001) `Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model.' Transportation Research Part B: Met… | 0.737 | 3 | 2 | 100% |
| 4 | Sobol (1967) `The distribution of points in a cube and the approximate evaluation of integrals.' J | 0.737 | 3 | 2 | 100% |
| 5 | Ackerberg, Geweke and Hahn (2009) `Supplement to Comments on ”Convergence Properties of the Likelihood of Computed Dynamic Models”.' Econometrica 77(6), 2009–2017 | 0.644 | 2 | 2 | 100% |
| 6 | Heiss and Winschel (2008) `Likelihood approximation by numerical integration on sparse grids.' J | 0.644 | 2 | 2 | 100% |
| 7 | McFadden and Train (2000) `Mixed MNL models for discrete response.' J | 0.644 | 2 | 2 | 100% |
| 8 | Newey and McFadden (1994) `Large sample estimation and hypothesis testing.' vol. 4 pp. 2111–2245 | 0.644 | 2 | 2 | 100% |
| 9 | Boyd (1984) `Asymptotic coefficients of Hermite function series.' J | 0.644 | 2 | 2 | 100% |
| 10 | Kristensen and Salanié (2017) `Higher-order properties of approximate estimators.' Journal of Econometrics 198(2), 189–208 | 0.644 | 2 | 2 | 100% |
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