Simulation-based Estimation Method Research Articles

Unsupervised mixture estimation via approximate maximum likelihood based on the Cramér - von Mises distance

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate numerically an intractable normalizing constant. In such a setup, simulation-based estimation methods are an appealing alternative. The approximate maximum likelihood estimation (AMLE) approach is employed. It is a general method that can be applied to mixtures with any component densities, as long as simulation is feasible. The focus is on the dynamic lognormal-generalized Pareto distribution, and the Cramér - von Mises distance is used to measure the discrepancy between observed and simulated samples. After deriving the theoretical properties of the estimators, a hybrid procedure is developed, where standard maximum likelihood is first employed to determine the bounds of the uniform priors required as input for AMLE. Simulation experiments and two real-data applications suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.

Distribution-free estimation of individual parameter logit (IPL) models using combined evolutionary and optimization algorithms

When estimating random coefficients models from choice data, decisions relating to the multivariate density function assumed to describe preference heterogeneity across the population raise questions about stochastic (in)dependence between preference dimensions, uni- vs. multi-modality, potential point masses, bounds and/or constraints on support regions, among other concerns. Parametric representations of population distributions have generally implied uncomfortable compromises to achieve estimation tractability. It would seem preferable to sidestep such issues by estimating individual preferences in a distribution-free manner, but this freedom of form implies a large number of parameters since we lose the parsimony enabled by parametric densities and must deal directly with estimation of individual decision maker preferences. I propose a hybrid distribution-free estimator for individual parameter logit models that uses a genetic algorithm as first stage, the solution from which becomes a starting point for a gradient-based search to obtain the final posterior maximum likelihood estimates of individual preferences. This estimator is described in detail, its parameter recovery capability is tested with Monte Carlo data generation simulations, and a case study is developed in some detail to illustrate its use in policy analysis. The estimator can be applied to both stated and revealed preference data, requiring only that sufficient choice replications be available for individual observation units consistent with extant estimation methods. Computational experience shows the estimator to require CPU times comparable to extant simulation-based estimation methods, meaning that its use is practical for the exploration of the parameter space through multiple trials.

An Adversarial Approach to Structural Estimation

We propose a new simulation-based estimation method, adversarial estimation, for structural models. The estimator is formulated as the solution to a minimax problem between a generator (which generates synthetic observations using the structural model) and a discriminator (which classifies if an observation is synthetic). The discriminator maximizes the accuracy of its classification while the generator minimizes it. We show that, with a sufficiently rich discriminator, the adversarial estimator attains parametric efficiency under correct specification and the parametric rate under misspecification. We advocate the use of a neural network as a discriminator that can exploit adaptivity properties and attain fast rates of convergence. We apply our method to the elderly’s saving decision model and show that including gender and health profiles in the discriminator uncovers the bequest motive as an important source of saving across the wealth distribution, not only for the rich.

A simulation-based estimation method for bias reduction

ABSTRACTModels are often built to evaluate system performance measures or to make quantitative decisions. These models sometimes involve unknown input parameters that need to be estimated statistically using data. In these situations, a statistical method is typically used to estimate these input parameters and the estimates are then plugged into the models to evaluate system output performances. The output performance estimators obtained from this approach usually have large bias when the model is nonlinear and the sample size of the data is finite. A simulation-based estimation method to reduce the bias of performance estimators for models that have a closed-form expression already exists in the literature. In this article, we extend that method to more general situations where the models have no closed-form expression and can only be evaluated through simulation. A stochastic root-finding problem is formulated to obtain the simulation-based estimators and several algorithms are designed. Furthermore, we give a thorough asymptotic analysis of the properties of the simulation-based estimators, including the consistency, the order of the bias, the asymptotic variance, and so on. Our numerical experiments show that the experimental results are consistent with the theoretical analysis.

A meta-analysis of health-related quality of life after primary treatment for prostate cancer as measured by the Expanded Prostate Cancer Index Composite.

39 Background: Health-related quality of life (HRQoL) outcomes are important in treatment selection for prostate cancer. The Expanded Prostate Cancer Index Composite (EPIC) is a validated and widely-utilized HRQoL survey which accounts for newer radiotherapeutic, surgical, and hormonal treatment methods. We present a meta-analysis of patient reported HRQoL outcomes collected with EPIC and compare HRQoL trends with radiation therapy, surgery, or active surveillance as primary treatment. Methods: The PubMed database was systematically searched for all studies which presented data directly derived from the use of EPIC on patients with prostate cancer prior to 07/09/2014. All eligible studies were selected for either inclusion and analysis or exclusion based on pre-determined criteria. The data from included studies was compiled and a simulation-based estimation method using Approximate Bayesian Computation was performed to obtain missing standard deviation estimate. A longitudinal meta-analysis was conducted to estimate EPIC-profiles for each component using Bayesian p-spline method. Results: Over 4,000 studies were searched, 152 were deemed eligible, and 39 were included. The calculated mean summary score estimates are shown in the attached table. Conclusions: In the urinary domain, radical prostatectomy (RP) has lower acute scores than active surveillance (AS) or radiation therapy (RT) without long-term difference. In the bowel domain, RT has lower scores than AS or RP acutely and long-term. In the sexual domain, RT and RP have lower acute scores than AS. RP has lower scores than RT without long-term difference. In the hormonal domain, little difference was noted between modalities. [Table: see text]

Folklore Theorems, Implicit Maps, and Indirect Inference

The delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics. Extensions of these methods are provided for sequences of functions that are commonly encountered in applications and where the usual methods sometimes fail. Important examples of failure arise in the use of simulation-based estimation methods such as indirect inference. The paper explores the application of these methods to the indirect inference estimator (IIE) in first order autoregressive estimation. The IIE uses a binding function that is sample size dependent. Its limit theory relies on a sequence-based delta method in the stationary case and a sequence-based implicit continuous mapping theorem in unit root and local to unity cases. The new limit theory shows that the IIE achieves much more than (partial) bias correction. It changes the limit theory of the maximum likelihood estimator (MLE) when the autoregressive coefficient is in the locality of unity, reducing the bias and the variance of the MLE without affecting the limit theory of the MLE in the stationary case. Thus, in spite of the fact that the IIE is a continuously differentiable function of the MLE, the limit distribution of the IIE is not simply a scale multiple of the MLE, but depends implicitly on the full binding function mapping. The unit root case therefore represents an important example of the failure of the delta method and shows the need for an implicit mapping extension of the continuous mapping theorem.

A simple method for time scaling value-at-risk: Let the data speak for themselves

New empirical and data-based scaling factors are introduced to scale the 1-day value-at-risk (VaR) to 5- and 10-day VaR. The method relies on the estimation of the ratio of the high quantiles of the aggregated data to the daily data. Using real data sets, the new scaling factors are compared with the commonly used benchmark of square-root-of-time scaling, and a more complex simulation-based estimation method. The results indicate that the empirical scaling factors outperform against the square-root-of-time scaling and are competitive with the simulation-based method.

Provider networks and primary‐care signups: do they restrict the use of medical services?

This article analyzes the effect of gatekeeper and network restrictions on use of health-care services using simulation-based estimation methods. Data from the Community Tracking Survey (1996-1997) show significant evidence of selection into plans with gatekeeper and/or network restrictions. Enrollees in plans with networks of physicians have fewer office-based visits to non-physician medical professionals, but more emergency room visits and hospital stays. Individuals in plans that require signups with a primary-care provider have more visits to non-physician providers of care, more surgeries and hospital stays but substantially fewer emergency room visits. Enrollees of plans that do not pay for out-of-network services have more office-based and emergency room visits, but less surgeries and hospitalizations.

Learning by Doing vs. Learning About Match Quality: Can We Tell Them Apart?

Understanding the accumulation of match-specific capital is crucial in shedding light on the reasons for the prevalence of long-term employ- ment relationships and on the welfare consequences of turnover in the labor market. One of the most important source of match-specific capital is human capital acquired through match-specific learning. Such learn- ing can take on two distinct forms. In the first case, workers accumulate match-specific human capital through learning-by-doing. In the second case, a worker and a firm in an employment relationship learn about the quality of the match over time, thereby acquiring valuable information. I construct a structural model that embeds these two learning explana- tions. I show that it is possible to distinguish the two explanations given turnover data on employing firms coupled with data on workers. Such data now exist in the form of matched employer-employee data sets. I use a matched French data set to estimate the structural model using the Efficient Method of Moments, a simulation-based estimation method. I find that, while learning-by-doing could be present in the first few months of an employment relationship, learning about match quality dominates at tenures above half a year. This finding has important consequences for economists' understanding of the sources of match-specific capital and for the desirability of policies that alter the incentives for turnover for workers of different tenure.

A NONPARAMETRIC SIMULATED MAXIMUM LIKELIHOOD ESTIMATION METHOD

Existing simulation-based estimation methods are either general purpose but asymptotically inefficient or asymptotically efficient but only suitable for restricted classes of models. This paper studies a simulated maximum likelihood method that rests on estimating the likelihood nonparametrically on a simulated sample. We prove that this method, which can be used on very general models, is consistent and asymptotically efficient for static models. We then propose an extension to dynamic models and give some Monte-Carlo simulation results on a dynamic Tobit model.We thank Jean-Pierre Florens, Arnoldo Frigessi, Christian Gouriéroux, Jim Heckman, Guy Laroque, Oliver Linton, Nour Meddahi, Alain Monfort, Eric Renault, Christian Robert, Neil Shephard, and two referees for their comments. Remaining errors and imperfections are ours. Parts of this paper were written while Bernard Salanié was visiting the University of Chicago, which he thanks for its hospitality.

Structural change tests for simulated method of moments

Simulation-based estimation methods have become more widely used in recent years. We propose a set of tests for structural change in models estimated via simulated method of moments (see Duffe and Singleton (Econometrica 61 (1993) 929). These tests extend the work of Andrews (Econometrica 61 (1993) 821), Ghysels et al. (J. Econom. 82 (1997) 209) and Sowell (Econometrica 64 (1996) 1085; Tests for Violation of Moment Conditions, Manuscript, Graduate School of Industrial Administration, Carnegie mellon University) which covered generalized method of moments estimators not involving simulation. We derive the asymptotic distributions of various tests. We show that the number of simulations does not affect the asymptotic distribution under the null but adversely influences local asymptotic power. A Monte-Carlo investigation of the finite sample size and power reveals that a relatively small number of simulations suffices to obtain tests with desirable small sample size and power properties.

Indirect Inference, Nuisance Parameter, and Threshold Moving Average Models

We analyze the modifications that occur in indirect inference when a nuisance parameter is not identified under the null hypothesis. We develop a testing procedure adapted to this simulation-based estimation method, and detail its use for detecting the threshold effect in threshold moving average models with contemporaneous and lagged asymmetries. In contrast to existing threshold models, these models allow taking into account the presence of asymmetric effects of current and lagged random shocks. We use them to measure the persistence of shocks to U.S. output.