Simulated Likelihood Method Research Articles

A nonlinear dynamic factor model of health and medical treatment.

Quantitative assessments of the relationship between health and medical treatment are of great importance to policy makers. To overcome endogeneity problems we formulate and estimate a tractable dynamic factor model where observed health outcomes are driven by the individual's latent health. The dynamics of latent health reflects both exogenous health deterioration and endogenous health investments. Our model allows us to investigate the effect of medical treatment on current health, as well as on future medical treatment and health outcomes. We estimate the model by maximum simulated likelihood and minimum distance methods using a rich longitudinal data set from Italy obtained by merging a number of administrative archives. These data contain detailed information on medical drug purchase, hospitalization, and mortality for a representative sample of elderly hypertensive patients. Our findings show that the observed autocorrelation in medical treatment reflects both permanent and time-varying observed and unobserved heterogeneity. They also show that medical drug purchase significantly maintains future health levels and prevents transitions to worse health. This suggests that policies aimed at increasing the awareness and the compliance of hypertensive patients help reduce cardiovascular risks and consequent hospitalization and mortality.

Mixed logit model based on nonlinear random utility functions: a transfer passenger demand prediction method on overnight D-trains

In recent years, with the development of high-speed railway in China, the operating mileage and passenger transport capacity have increased rapidly in transportation industry. Due to the high density of trains in the daytime, we usually set up skylights at night (0:00–6:00 am) on high-speed railway for comprehensive maintenance. However, this arrangement contradicts with the operation demand of D-series overnight high-speed trains (overnight D-trains for short). In order to adjust the operation plan of overnight D-trains with skylights coordinately, it is necessary to predict the passenger demand of newly added overnight D-trains. Therefore, in this paper, a mixed logit model based on nonlinear random utility functions for different transport modes is proposed, in order to predict transfer passenger demand. According to Maximum Simulated Likelihood Method, the likelihood function of this mixed logit model is proposed to maximize the overall utility value of different passenger groups while Metropolis–Hastings algorithm is adopted to iteratively solve the probabilities of discrete random variables in utility functions. After that, the unknown distributions of parameters are estimated and the optimal solution of this model is provided by traditional algorithms, basic heuristic algorithms and improved heuristic algorithms including improved fireworks-simulated annealing algorithm proposed in this paper, respectively. Finally, a real-world instance with related data of Beijing–Shanghai corridor is implemented to demonstrate the performance and effectiveness of the proposed approaches.

Panel Stochastic Frontier Model With Endogenous Inputs and Correlated Random Components

In this article, we consider a panel stochastic frontier model in which the composite error term has four components, that is, , where ηi and uit are persistent and transient inefficiency components, τi consists of the random firm effects and vit is the random noise. Two distinguishing features of the proposed model are (i) the inputs are allowed to be correlated with one or more of the error components in the production function; (ii) time-invariant and time-varying components, that is, ( ) and ( ), are allowed to be correlated. To keep the formulation general, we do not specify whether this correlation comes from the correlations between (i) ηi and uit , (ii) τi and uit , (iii) τi and vit , (iv) ηi and vit , or some other combination of them. Further, we also consider the case when the correlation in the composite error arises from the time dependence of . To estimate the model parameters and predict (in)efficiency, we propose a two-step procedure. In the first step, either the within or the first difference transformation that eliminates the time-invariant components is proposed. We then use either the 2SLS or the GMM approach to obtain unbiased and consistent estimators of the parameters in the frontier function, except for the intercept. In the second step, the maximum simulated likelihood method is used to estimate the parameters associated with the distributions of τi and vit , ηi and uit as well as the intercept. The copula approach is used in this step to model the dependence between the time-varying and time-invariant components. Formulas to predict transient and persistent (in)efficiency are also derived. Finally, results from both simulated and real data are provided.

A Kuhn\u2013Tucker model for behaviour in dictator games

We consider a dictator game experiment in which dictators perform a sequence of giving tasks and taking tasks. The data are used to estimate the parameters of a Stone–Geary utility function over own-payoff and other’s payoff. The econometric model incorporates zero observations (e.g. zero-giving or zero-taking) by applying the Kuhn–Tucker theorem and treating zeros as corner solutions in the dictator’s constrained optimisation problem. The method of maximum simulated likelihood (MSL) is used for estimation. We find that selfishness is significantly lower in taking tasks than in giving tasks, and we attribute this difference to the “cold prickle of taking”.

Using Maximum Simulated Likelihood Methods to Overcome Left Censoring: Dynamic Event History Models of Heart Attack Risk in New Zealand

Abstract This paper describes how the risk of experiencing heart attacks varies across gender and ethnicity in New Zealand. We estimate dynamic hazard models using administrative data. We deal with left-censored data using recently developed maximum simulated likelihood methods. The models allow risk to vary with age, previous heart attack history and unobserved individual heterogeneity. We find that the risk of subsequent events is far higher than the risk of the first event, particularly high within 1 year after an event, and that unobserved heterogeneity is important. Generally, male Maoris have the highest risk, followed by female Maoris, then ethnically European males, while ethnically European females have the lowest risk.

The Effects of Domestic and International Remittances on Food Insecurity in Low- and Middle-Income Countries

Despite food insecurity being a key policy priority for aid organisations and governments around the world, the effects of remittances on food insecurity in low- and middle-income countries are largely unknown. Using data from the 2014–15 waves of the Gallup World Poll, and the first global experiential measure of food insecurity, we examine the impacts of receiving domestic, international, and both (domestic and international) remittances on individual-level food insecurity in 92 low- and middle-income countries. We estimate a series of endogenous multinomial treatment effects models, using both two-stage residual inclusion and maximum simulated likelihood methods. Results show domestic and international remittances have differential impacts on the probability of being food insecure. Controlling for endogeneity, we find that domestic, international, and combinations of both remittances decrease food insecurity. However, international remittances have a much greater impact than domestic remittances. Results also show heterogeneous effects of remittances across economic development rankings, where remittances provide greater protection against experiencing food insecurity in lower-income countries than in middle-income countries. These findings highlight the importance of migration and remittance flows as mechanisms for reducing food insecurity. This has potentially important policy implications for those seeking to reduce global hunger to achieve the SDG targets.

An Expectation-Maximization Algorithm to Estimate the Integrated Choice and Latent Variable Model

As computing capability has grown dramatically, the transport choice model has rigorously included latent variables. However, integrated latent and choice variable (ICLV) models are hampered by a serious problem that is caused by the maximum simulated likelihood method. The method cannot properly reproduce the true coefficients, which is a problem that is often referred to as a lack of empirical identification. In particular, the problem is exacerbated particularly when an ICLV model is calibrated based on cross-sectional data. An expectation-maximization (EM) algorithm has been successfully employed to calibrate a random coefficient choice model, but it has never been applied to the calibration of an ICLV model. In this study, an EM algorithm was adapted to calibrate an ICLV model, and it successfully reproduced the true coefficients in the model. The main contribution of adopting an EM algorithm was to simplify the calibration procedure by decomposing the procedure into three well known econometric problems: a weighted linear regression, a weighted discrete choice problem, and a weighted ordinal choice problem. Simulation experiments also confirmed that an EM algorithm is a stable method for averting the problem of lack of empirical identification.

Maximum simulated likelihood estimation of the panel sample selection model

ABSTRACTHeckman's (1976, 1979) sample selection model has been employed in many studies of linear and nonlinear regression applications. It is well known that ignoring the sample selectivity may result in inconsistency of the estimator due to the correlation between the statistical errors in the selection and main equations. In this article, we reconsider the maximum likelihood estimator for the panel sample selection model in Keane et al. (1988). Since the panel data model contains individual effects, such as fixed or random effects, the likelihood function is more complicated than that of the classical Heckman model. As an alternative to the existing derivation of the likelihood function in the literature, we show that the conditional distribution of the main equation follows a closed skew-normal (CSN) distribution, of which the linear transformation is still a CSN. Although the evaluation of the likelihood function involves high-dimensional integration, we show that the integration can be further simplified into a one-dimensional problem and can be evaluated by the simulated likelihood method. Moreover, we also conduct a Monte Carlo experiment to investigate the finite sample performance of the proposed estimator and find that our estimator provides reliable and quite satisfactory results.

Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses

The distributional transform (DT) is amongst the computational methods used for estimation of high-dimensional multivariate normal copula models with discrete responses. Its advantage is that the likelihood can be derived conveniently under the theory for copula models with continuous margins, but there has not been a clear analysis of the adequacy of this method. We investigate the small-sample and asymptotic efficiency of the method for estimating high-dimensional multivariate normal copula models with univariate Bernoulli, Poisson, and negative binomial margins, and show that the DT approximation leads to biased estimates when there is more discretization. For a high-dimensional discrete response, we implement a maximum simulated likelihood method, which is based on evaluating the multidimensional integrals of the likelihood with randomized quasi Monte Carlo methods. Efficiency calculations show that our method is nearly as efficient as maximum likelihood for fully specified high-dimensional multivariate normal copula models. Both methods are illustrated with spatially aggregated count data sets, and it is shown that there is a substantial gain on efficiency via the maximum simulated likelihood method.

Simulated maximum likelihood estimation for discrete choices using transformed simulated frequencies

Many existing methods of simulated likelihood for discrete choice models require additive errors that have normal or extreme value distributions. This paper focuses on a situation where the model does not admit such additive errors so that the popular method of GHK or logit estimation is not applicable. This paper proposes a new method of simulated likelihood that is free from simulation bias for each finite number of simulations, and yet flexible enough to accommodate various model specifications beyond those of additive normal or logit errors. The method begins with the likelihood function involving simulated frequencies and finds a transform of the likelihood function that identifies the true parameter for each finite simulation number. The transform is explicit, containing no unknowns that demand an additional step of estimation. The estimator achieves the efficiency of MLE when the simulation number increases fast enough. This paper presents and discusses results from Monte Carlo simulation studies of the new method.

On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood

The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived conveniently under the theory for copula models with continuous margins, but there has not been a clear analysis of the adequacy of this method. We investigate the asymptotic and small-sample efficiency of two variants of the method for estimating the multivariate normal copula with univariate binary, Poisson, and negative binomial regressions, and show that they lead to biased estimates for the latent correlations, and the univariate marginal parameters that are not regression coefficients. We implement a maximum simulated likelihood method, which is based on evaluating the multidimensional integrals of the likelihood with randomized quasi-Monte Carlo methods. Asymptotic and small-sample efficiency calculations show that our method is nearly as efficient as maximum likelihood for fully specified multivariate normal copula-based models. An illustrative example is given to show the use of our simulated likelihood method.

Doing R&D in a Closed or Open Mode: Dynamics and Impacts on Productivity

On the one hand, firms prefer to perform R&D in an open mode (letting R&D be performed extramurally or even selling their R&D services) to benefit from knowledge spillovers and complementarities between internal and external R&D. On the other hand, they may also like to perform R&D in a closed mode (funding and executing their R&D intramurally) to minimize outgoing externalities. We examine the dynamic process by which firms change the way of doing R&D and how these strategic choices of doing R&D affect their productivity growth. This study is based on the Statistics Canada Research and Development in Canadian Industry survey (RDCI), which collects data on R&D performed in the business sector in Canada. The paper is based on data for the period 1997 to 2006. The panel dimension of the data allows to control for unobserved characteristics of R&D performers by estimating a multinomial Logit model with unobserved heterogeneities using maximum simulated likelihood (MSL) method.

Maximum Simulated Likelihood and Expectation-Maximization Methods to Estimate Random Coefficients Logit with Panel Data

The random coefficients logit model allows a more realistic representation of agents’ behavior. However, the estimation of that model may involve simulation, which may become impractical with many random coefficients because of the curse of dimensionality. In this paper, the traditional maximum simulated likelihood (MSL) method is compared with the alternative expectation-maximization (EM) method, which does not require simulation. Previous literature had shown that for cross-sectional data, MSL outperforms the EM method in the ability to recover the true parameters and estimation time and that EM has more difficulty in recovering the true scale of the coefficients. In this paper, the analysis is extended from cross-sectional data to the less volatile case of panel data to explore the effect on the relative performance of the methods with several realizations of the random coefficients. In a series of Monte Carlo experiments, evidence suggested four main conclusions: (a) efficiency increased when the true variance–covariance matrix became diagonal, (b) EM was more robust to the curse of dimensionality in regard to efficiency and estimation time, (c) EM did not recover the true scale with cross-sectional or with panel data, and (d) EM systematically attained more efficient estimators than the MSL method. The results imply that if the purpose of the estimation is only to determine the ratios of the model parameters (e.g., the value of time), the EM method should be preferred. For all other cases, MSL should be used.

A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix

When the dimension of the vector of estimated parameters increases, simulation based methods become impractical, because the number of draws required for estimation grows exponentially with the number of parameters. In simulation methods, the lack of empirical identification when the number of parameters increases is usually known as the “curse of dimensionality” in the simulation methods. We investigate this problem in the case of the random coefficients Logit model. We compare the traditional Maximum Simulated Likelihood (MSL) method with two alternative estimation methods: the Expectation–Maximization (EM) and the Laplace Approximation (HH) methods that do not require simulation. We use Monte Carlo experimentation to investigate systematically the performance of the methods under different circumstances, including different numbers of variables, sample sizes and structures of the variance–covariance matrix. Results show that indeed MSL suffers from lack of empirical identification as the dimensionality grows while EM deals much better with this estimation problem. On the other hand, the HH method, although not being simulation-based, showed poor performance with large dimensions, principally because of the necessity of inverting large matrices. The results also show that when MSL is empirically identified this method seems superior to EM and HH in terms of ability to recover the true parameters and estimation time.

Inferring beliefs as subjectively imprecise probabilities

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.

Fitting Fully Observed Recursive Mixed-process Models with cmp

At the heart of many econometric models are a linear function and a normal error. Examples include the classical small-sample linear regression model and the probit, ordered probit, multinomial probit, tobit, interval regression, and truncated-distribution regression models. Because the normal distribution has a natural multidimensional generalization, such models can be combined into mul-tiequation systems in which the errors share a multivariate normal distribution. The literature has historically focused on multistage procedures for fitting mixed models, which are more efficient computationally, if less so statistically, than maximum likelihood. Direct maximum likelihood estimation has been made more practical by faster computers and simulated likelihood methods for estimating higher-dimensional cumulative normal distributions. Such simulated likelihood methods include the Geweke–Hajivassiliou-Keane algorithm (Geweke, 1989, Econometrica 57: 1317–1339; Hajivassiliou and McFadden, 1998, Econometrica 66: 863–896; Keane, 1994, Econometrica 62: 95–116). Maximum likelihood also facilitates a generalization to switching, selection, and other models in which the number and types of equations vary by observation. The Stata command cmp fits seemingly unrelated regressions models of this broad family. Its estimator is also consistent for recursive systems in which all endogenous variables appear on the right-hand sides as observed. If all the equations are structural, then estimation is full-information maximum likelihood. If only the final stage or stages are structural, then estimation is limited-information maximum likelihood. cmp can mimic a score of built-in and user-written Stata commands. It is also appropriate for a panoply of models that previously were hard to estimate. Heteroskedasticity, however, can render cmp inconsistent. This article explains the theory and implementation of cmp and of a related Mata function, ghk2(), that implements the Geweke–Hajivassiliou–Keane algorithm.

ACTIVE LABOR MARKET PROGRAMS AND REGIONAL MOBILITY OF LABOR: EVIDENCE FROM THE SWEDISH RECESSION, 1994-1995

This paper addresses the impact of active labor market programs on interregional migration in Sweden. The purpose of the study is to determine the extent to which the programs, which provide training and labor market assistance to jobless individuals, induce participants to migrate. Analysis is based on data registers compiled in 1994 and 1995 by Statistics Sweden and the Labor Market Board of Sweden. The paper specifies and estimates a two-equation model of participation and subsequent migration. The model, which is estimated by the method of maximum simulated likelihood, accounts for the role of program participation as an endogenous choice variable in the decision to migrate. In an attempt to capture the effect of migrant self-selection, the estimation approach also controls for unobserved heterogeneity in the participation and migration equations. Results of the study indicate a significant positive impact of participation on subsequent mobility for males. This result is robust with respect to alternative specifications of the migration equation and alternative formulations of the model for program participation. For females, the evidence of program impacts is mixed and it appears to be sensitive to the statistical formulation of the model. (JEL J38, J61)

Confessions of an internet monopolist: demand estimation for a versioned information good

We investigate profit- maximizing versioning plans for an information goods monopolist. The analysis employs data obtained from a web-based field experiment in which potential buyers were offered information goods in varied price-quality configurations. Maximum simulated likelihood (MSL) methods are used to estimate parameters describing the distribution of utility function parameters across potential buyers of the good. The resulting estimates are used to examine the impact of versioning on seller profits and market efficiency.

Parameter Estimation of the Mixed Logit Model and Its Application

The mixed Logit model is flexible for application because the coefficients associated with the attributes of the utility variables could be distributed in normal, lognormal, SB, and other types. On the basis of Beijing's resident daily travel survey, a mixed Logit model is presented and calibrated in this paper. The method of maximum simulated likelihood, in which quasi-random number sequences of shuffled Halton and the MLHS (modified latin hypercube sampling) are used for simulation, is developed to estimate the coefficients, and hence to determine suitable distributions for them. The estimated values give clear explanations to the factors influencing the resident's mode choice behavior.

Estimating Fully Observed Recursive Mixed-Process Models with Cmp

At the heart of many econometric models is a linear function and a normal error. Examples include the classical small-sample linear regression model and the probit, ordered probit, multinomial probit, Tobit, interval regression, and truncated distribution regression models. Because the normal distribution has a natural multidimensional generalization, such models can be combined into multi-equation systems in which the errors share a multivariate normal distribution. The literature has historically focused on multi-stage procedures for estimating mixed models, which are more efficiently computationally, if less so statistically, than maximum likelihood (ML). But faster computers and simulated likelihood methods such as the Geweke, Hajivassiliou, and Keane (GHK) algorithm for estimating higher dimensional cumulative normal distributions have made direct ML estimation practical. ML also facilitates a generalization to switching, selection, and other models in which the number and types of equations vary by observation. The Stata module CMP fits Seemingly Unrelated Regressions (SUR) models of this broad family. Its estimator is also consistent for recursive systems in which all endogenous variables appear on the right-hand-sides as observed. If all the equations are structural, then estimation is full-information maximum likelihood (FIML). If only the final stage or stages are, then it is limited-information maximum likelihood (LIML). CMP can mimic a dozen built-in Stata commands and several user-written ones. It is also appropriate for a panoply of models previously hard to estimate. Heteroskedasticity, however, can render it inconsistent. This paper explains the theory and implementation of cmp and of a related Mata function, ghk2(), that implements the GHK algorithm.