This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dube et al. (2012) find the bound on the errors of...
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This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dube et al. (2012) find the bound on the errors of the NFP estimates computed by contraction mappings (NFP/CTR) has the order of the square root of the inner loop tolerance. Under our assumptions, we theoretically derive an upper bound on the numerical bias in the NFP/CTR, which has the same order of the inner loop tolerance. We also discuss that, compared with NFP/CTR, NFP using Newton's method has a smaller bound on the estimate error. (C) 2016 Elsevier B.V. All rights reserved.
We propose two Mathematical Programming with Equilibrium Constraints (MPEC) formulations: the MPEC-Sparse and the MPEC-Dense to estimate a class of separable matching models. We compare MPEC with the nestedfixed-Poin...
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We propose two Mathematical Programming with Equilibrium Constraints (MPEC) formulations: the MPEC-Sparse and the MPEC-Dense to estimate a class of separable matching models. We compare MPEC with the nestedfixed-point (NFXP) algorithm-a well-received method in the literature of structural estimation. Using both simulated and actual data, we find that MPEC is more robust than NFXP in terms of convergence and solution quality. In terms of computing time, MPEC-Dense is 9 to 20 times faster than NFXP in simulations. For practitioners, MPEC is considerably simpler to program.
Evidence suggests that municipal water utility administrators in the western US price water significantly below its marginal cost and, in so doing, inefficiently exploit aquifer stocks and induce social surplus losses...
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Evidence suggests that municipal water utility administrators in the western US price water significantly below its marginal cost and, in so doing, inefficiently exploit aquifer stocks and induce social surplus losses. This paper empirically identifies the objective function of those managers, measures the deadweight losses resulting from their price-discounting decisions, and recovers the efficient water pricing policy function from counterfactual experiments. In doing so, the estimation uses a "continuous-but-constrained-control" version of a nested fixed-point algorithm in order to measure the important intertemporal consequences of groundwater pricing decisions.
Consider the following “inverse stochastic control” problem. A statistician observes a realization of a controlled stochastic process $\{ d_t ,x_t \} $ consisting of the sequence of states $x_t$, and decisions $d_t$...
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Consider the following “inverse stochastic control” problem. A statistician observes a realization of a controlled stochastic process $\{ d_t ,x_t \} $ consisting of the sequence of states $x_t$, and decisions $d_t$ of an agent at times $t = 1, \cdots ,T$. The null hypothesis is that the agent’s behavior is generated from the solution to a Markovian decision problem. The inverse problem is to use the data $\{ d_t ,x_t \} $ to go backward and “uncover” the agent's objective function U, and his beliefs about the law of motion of the state variables p. The problem is complicated by the fact that the statistician generally only observes a subset $x_t$ of the state variables $(x_t ,\eta _t )$ observed by the agent. This paper formulates the inverse problem as a problem of statistical inference, explicitly accounting for unobserved state variables$\eta _t $, in order to produce a nondegenerate and internally consistent statistical model. Specifically, the functions U and p are assumed to depend on a vector of unknown parameters $\theta $ known by the agent but not by the statistician. The agent’s preferences and expectations are uncovered by finding a parameter vector $\hat \theta $ that maximizes the likelihood function for the observed sample of data. The difficulty is that neither the dynamic programming problem nor the associated likelihood function has an a priori known functional form. In general the solution is only described recursively via Bellman’s “principle of optimality.” This paper derives a nestedfixed-point maximum likelihood algorithm that computes e and the associated value function $V_{\hat \theta } $ for a class of discrete control processes$(d_t ,x_t )$, where the control variable $d_t$ is restricted to a finite set of alternatives. Given M independent realizations of $(d_t ,x_t )$ for T time periods, it is shown that 8 converges to the true parameter $\theta ^ * $ with probability 1 and has an asymptotic Gaussian distribution as M (or the number of
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