Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

By V. Aguirregabiria, P. Mira. Social Science Research Network, 2002

423 citations recorded by the source corpus.

This paper proposes a procedure for the estimation of discrete Markov decision models and studies its statistical and computational properties. Our method is similar to Rust's Nested Fixed-Point algorithm (NFXP), but the order of the two nested algorithms is swapped. First, we prove that this method produces the maximum likelihood estimator under the same conditions as NFXP. However, our procedure requires significantly fewer policy iterations than NFXP. Second, based on this algorithm, we define a class of sequential consistent estimators, K -stage Policy Iteration (PI) estimators, that encompasses MLE and Holz-Miller, and we obtain a recursive expression for their asymptotic covariance matrices. This presents the researcher with a 'menu' of sequential estimators reflecting a trade-off between efficiency and computational cost. Using actual and simulated data we compare the relative performance of these estimators. In all our experiments, the benefits in efficiency of using a two-stage PI estimator instead of a one-stage estimator (i.e., Hotz-Miller) are very significant. More interestingly, the benefits of MLE relative to two-stage PI are small.

Subfields: Computer Networks and Communications, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/adc498ed4afe131ca510c0a2c064b4e659b383be

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Citations in the corpus

Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition (2016, positive): “Using our framework, the two-step estimators of Aguirregabiria and Mira (2002, 2007), Bajari et al. (2007), Hotz et al. (1994), Pakes et al. (2007), and Pesendorfer and Schmidt-Dengler (2008) can be applied in continuous time. In most empirical studies, the equilibrium will only need to be computed ”
A link based network route choice model with unrestricted choice set (2013, background): “For each trial value of the parameters, and destination (or origin-destination pair 4Another option is, e.g., the swapped nested fixed point algorithm proposed by Aguirregabiria and Mira (2002). if a LS attribute is included) in the sample, the system of linear equations (7) is solved.”
Living Rationally Under The Volcano? An Empirical Analysis Of Heavy Drinking And Smoking (2007, neutral): “Recent applications include Hotz and Miller (1993), Keane and Wolpin (1994, 1997), Rust and Phelan (1997), Gilleskie (1998), Eckstein and Wolpin (1999), Brien, Lillard, and Stern (2000), and Aguirregabiria and Mira (2002). (9)In that sense our paper is similar in spirit to the analysis by Fang and S”
Practical Methods for Estimation of Dynamic Discrete Choice Models (2011, background): “When finite dependence does not hold but the setting is infinite horizon and stationary, Aguirregabiria and Mira (2002) use (26) to construct a CCP repre- sentation, V = I − β d (P (d)λ) * F (d) −1 d P (d) * [U (d) + ǫ * (d)] , solving the matrix inversion and ǫ * (d) portions in a first stage.”
Semiparametric Inference in Dynamic Binary Choice Models, Second Version (2014, methodology): “Several papers used it for testing new methodologies for estimation of dynamic discrete choice models (see Aguirregabiria and Mira (2002), Bajari, Benkard, and Levin (2007), and Norets (2009)).”
Sequential Estimation of Dynamic Discrete Games (2004, methodology): “…guess P̂0 is a consistent estimator, consistency of a NPL fixed-point is straightforward because all elements of the sequence of estimators {θ̂K , P̂K : K ≥ 1} obtained from the NPL algorithm are consistent (see Aguirregabiria and Mira 2002 for a recursive proof in the single agent context).”
Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices (2009, methodology): “…Markov decision models with unobserved heterogeneity, it is possible to obtain an estimator that is higher-order equivalent to the maximum likelihood estimator (MLE) by iterating the nested pseudo-likelihood (NPL) algorithm of Aguirregabiria and Mira (2002) sufficiently many, but finite times.”
Identifying Dynamic Discrete Decision Processes (2002, methodology): “Given that a model is identified: other methods such as maximum likelihood or iterated method of moments (Aguirregabiria and Mira (2000)) could be used for estimation purposes.”
Estimating a Dynamic Adverse-Selection Model: Labour-Force Experience and the Changing Gender Earnings Gap 1968–1997 (2008, background): “However, it still leaves 23This equation is central to estimation in a number of papers including, Hotz et al. (1993); Altug and Miller (1998); Aguirregabiria and Mira (2002); Gayle and Miller (2004); Pesendorfer and Schmidt-Dengler (2003); Bajari, Benkard, and Levin (forthcoming); Pakes,…”
Asymptotic Least Squares Estimators for Dynamic Games (2008, methodology): “We refer the interested reader to the Monte Carlo studies by Hotz and Miller (1994), Aguirregabiria and Mira (2002,2004) and Pakes, Ostrovsky and Berry (2004) for the effect of alternative auxiliary estimators.”
A nested recursive logit model for route choice analysis (2015, methodology): “There are several different ways of estimating a dynamic discrete choice model (Aguirregabiria and Mira, 2010), we adopt the nested fixed point algorithm of Rust (1987). This algorithm combines an outer iterative non-linear optimization algorithm for searching over the parameter space with an inner ”
Measuring the Dynamic Efficiency Costs of Common-Pool Resource Exploitation (2010, methodology): “(1994) and Aguirregabiria and Mira (2002). The first stage is to estimate the equations for stock growth, the evolutions of shrimp price, weather and diesel price independently, and then estimate conditional choice probabilities.”