Maximum Simulated Likelihood Approach Research Articles

Interdependence of rural household welfare measurement in the context of climate variability in Ethiopia

The Ethiopian government and various stakeholders have made significant efforts to improve household consumption, poverty, and food security. However, the results have not met expectations. To ensure that programs are effective, it is critical to have a robust measure of well-being that considers social, economic, institutional and environmental challenges. Previous studies on welfare have focused on a single measurement, but it is important to recognize the interdependence between various well-being indicators to formulate comprehensive interventions and initiatives for rural households in the context of climate change and variability. This paper examines the dynamic link between unidimensional poverty, multidimensional poverty, and food security using panel data from Ethiopia. The interdependency of welfare measurements was estimated using a seemingly unrelated multivariate probit model with a conditional mixed process estimator with full information, a simulated maximum likelihood approach, and the presumption that different metrics can have various policy implications. The chances of interdependence wellbeing status were low for households that were simultaneously food insecure and poor or nonpoor. Multidimensional poverty has a higher success rate than food insecurity or consumption poverty. Unlike unidimensional poverty and food insecurity, multidimensional poverty has a higher chance of to be deprived. Policymakers must consider the synergies and trade-offs of different types of welfare and the dynamic linkage between climate-induced shocks and other covariates with household welfare to minimize households' vulnerability to climate-induced shocks for effective intervention for rural households to obtain a whole picture of wellbeing.

Productivity change and efficiency in the Swiss nursing home industry

ABSTRACT Enhancing nursing home efficiency and productivity is a challenging task for health policy makers due to population ageing trends and increasing healthcare costs. In this study, we analyse nursing home efficiency and productivity using data from the universe of Swiss nursing homes for the period 2007–2015. We estimate a translog cost frontier via generalized true random effects models, which allow to disentangle the transient and the persistent components of inefficiency. In particular, we apply the simulated maximum likelihood approach proposed recently by scholars and then improve our estimates with a Mundlak correction. We find that total factor productivity change has dropped in recent years, and both efficiency components show scope for improvement. However, the marginal gains from transient efficiency measures are potentially larger, and could provide a more valid contribution to reverse the decreasing trend in total factor productivity change.

Acoustic‐based estimates of Cuvier's beaked whale (Ziphius cavirostris) density and abundance along the U.S. West Coast from drifting hydrophone recorders

AbstractAn acoustic survey of Cuvier's beaked whales (Ziphius cavirostris) was conducted off the U.S. West Coast in August and September 2016 using drifting recorder systems with a vertical array of two hydrophones at a depth of ~110 m. Recorders were deployed 22 times to representatively cover a 1,058,000 km2study area from the shelf break to ~556 km offshore. Vertical angles to echolocation pulses were measured using the signal time‐difference‐of‐arrival on the two hydrophones. Echolocation pulses of Cuvier's beaked whales were identified from their arrival angles (always from below the array) and unique acoustic characteristics. The density and abundance of Cuvier's beaked whales were estimated using a group‐based point‐transect analysis with 2 min time snapshots. The area effectively surveyed was estimated using a maximum simulated likelihood approach to fit the observed distribution of signal arrival angles. The acoustic availability of whales during their dive cycle was estimated from the duration of acoustic encounters using a mark‐recapture approach. Overall, Cuvier's beaked whales were present during 0.60% of snapshots, and their estimated average density is 5.12 animals per 1,000 km2(CV= 0.27). Their estimated abundance in the study area is 5,454 individuals (95% credibility intervals: 3,151 to 8,907).

The role of children in the spread of COVID-19: Using household data from Bnei Brak, Israel, to estimate the relative susceptibility and infectivity of children.

One of the significant unanswered questions about COVID-19 epidemiology relates to the role of children in transmission. This study uses data on infections within households in order to estimate the susceptibility and infectivity of children compared to those of adults. The data were collected from households in the city of Bnei Brak, Israel, in which all household members were tested for COVID-19 using PCR (637 households, average household size of 5.3). In addition, serological tests were performed on a subset of the individuals in the study. Inspection of the PCR data shows that children are less likely to be tested positive compared to adults (25% of children positive over all households, 44% of adults positive over all households, excluding index cases), and the chance of being positive increases with age. Analysis of joint PCR/serological data shows that there is under-detection of infections in the PCR testing, which is more substantial in children. However, the differences in detection rates are not sufficient to account for the differences in PCR positive rates in the two age groups. To estimate relative transmission parameters, we employ a discrete stochastic model of the spread of infection within a household, allowing for susceptibility and infectivity parameters to differ among children and adults. The model is fitted to the household data using a simulated maximum likelihood approach. To adjust parameter estimates for under-detection of infections in the PCR results, we employ a multiple imputation procedure using estimates of under-detection in children and adults, based on the available serological data. We estimate that the susceptibility of children (under 20 years old) is 43% (95% CI: [31%, 55%]) of the susceptibility of adults. The infectivity of children was estimated to be 63% (95% CI: [37%, 88%]) relative to that of adults.

Simulated maximum likelihood estimation in joint models for multiple longitudinal markers and recurrent events of multiple types, in the presence of a terminal event

ABSTRACTIn medical studies we are often confronted with complex longitudinal data. During the follow-up period, which can be ended prematurely by a terminal event (e.g. death), a subject can experience recurrent events of multiple types. In addition, we collect repeated measurements from multiple markers. An adverse health status, represented by ‘bad’ marker values and an abnormal number of recurrent events, is often associated with the risk of experiencing the terminal event. In this situation, the missingness of the data is not at random and, to avoid bias, it is necessary to model all data simultaneously using a joint model. The correlations between the repeated observations of a marker or an event type within an individual are captured by normally distributed random effects. Because the joint likelihood contains an analytically intractable integral, Bayesian approaches or quadrature approximation techniques are necessary to evaluate the likelihood. However, when the number of recurrent event types and markers is large, the dimensionality of the integral is high and these methods are too computationally expensive. As an alternative, we propose a simulated maximum-likelihood approach based on quasi-Monte Carlo integration to evaluate the likelihood of joint models with multiple recurrent event types and markers.

The Risk of a Mortality Catastrophe

We develop a continuous-time model for analyzing and valuing catastrophe mortality contingent claims based on stochastic modeling of the force of mortality. We derive parameter estimates from a 105-year time series of U.S. population mortality data using a simulated maximum likelihood approach based on a particle filter. Relying on the resulting parameters, we calculate loss profiles for a representative catastrophe mortality transaction and compare them to the “official” loss profiles that are provided by the issuers to investors and rating agencies. We find that although the loss profiles are subject to great uncertainties, the official figures fall significantly below the corresponding risk statistics based on our model. In particular, we find that the annualized incidence probability of a mortality catastrophe, defined as a 15% increase in aggregated mortality probabilities, is about 1.4%—compared to about 0.1% according to the official loss profiles.

Persistent and transient productive inefficiency: a maximum simulated likelihood approach

The productive efficiency of a firm can be seen as composed of two parts, one persistent and one transient. The received empirical literature on the measurement of productive efficiency has paid relatively little attention to the difference between these two components. Ahn and Sickles (Econ Rev 19(4):461–492, 2000) suggested some approaches that pointed in this direction. The possibility was also raised in Greene (Health Econ 13(10):959–980, 2004. doi: 10.1002/hec.938 ), who expressed some pessimism over the possibility of distinguishing the two empirically. Recently, Colombi (A skew normal stochastic frontier model for panel data, 2010) and Kumbhakar and Tsionas (J Appl Econ 29(1):110–132, 2012), in a milestone extension of the stochastic frontier methodology have proposed a tractable model based on panel data that promises to provide separate estimates of the two components of efficiency. The approach developed in the original presentation proved very cumbersome actually to implement in practice. Colombi (2010) notes that FIML estimation of the model is ‘complex and time consuming.’ In the sequence of papers, Colombi (2010), Colombi et al. (A stochastic frontier model with short-run and long-run inefficiency random effects, 2011, J Prod Anal, 2014), Kumbhakar et al. (J Prod Anal 41(2):321–337, 2012) and Kumbhakar and Tsionas (2012) have suggested other strategies, including a four step least squares method. The main point of this paper is that full maximum likelihood estimation of the model is neither complex nor time consuming. The extreme complexity of the log likelihood noted in Colombi (2010), Colombi et al. (2011, 2014) is reduced by using simulation and exploiting the Butler and Moffitt (Econometrica 50:761–764, 1982) formulation. In this paper, we develop a practical full information maximum simulated likelihood estimator for the model. The approach is very effective and strikingly simple to apply, and uses all of the sample distributional information to obtain the estimates. We also implement the panel data counterpart of the Jondrow et al. (J Econ 19(2–3):233–238, 1982) estimator for technical or cost inefficiency. The technique is applied in a study of the cost efficiency of Swiss railways.

The Impact of Parenting Style on Children’s Educational Outcomes in the United States

This paper examines the causal link between parenting style and children’s educational outcomes. The existing literature seems to lack any effort to use a nationally representative data from the United States, to properly address endogeneity, or to examine educational outcomes beyond high school level. This paper attempts to mitigate these shortcomings. Drawing upon the National Longitudinal Survey of Youth 1997, it first used OLS and logit regression. It then applied the maximum simulated likelihood approach to get rid of endogeneity, thereby isolating the causal impact of parenting style on children’s educational outcomes. Findings suggested that parenting style mattered for children academic performance. Authoritative parenting style was found to be the best among all types of parenting style. Particularly, relative to uninvolved parents’ children, authoritatively reared children were predicted to have 1.1 more years of schooling and be 18.5, 13.6, and 16.3 percentage points more likely to obtain at least bachelor’s degree, associate’s degree, and high school diploma, respectively. Also, they had 5.5 percentage points less likelihood of being high school dropouts than children reared by uninvolved parents.

A penalized simulated maximum likelihood approach in parameter estimation for stochastic differential equations

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown. We embed the auxiliary importance sampler in a penalized maximum likelihood framework which produces more accurate and computationally efficient parameter estimates. Simulation studies in three different models illustrate promising improvements of the new penalized simulated maximum likelihood method. The new procedure is designed for the challenging case when some state variables are unobserved and moreover, observed states are sparse over time, which commonly arises in ecological studies. We apply this new approach to two epidemics of chronic wasting disease in mule deer.

A Hedonic Valuation of Residential Water Services

AbstractThis paper investigates the economic value of municipal, private, and community‐managed water services in Guatemala through a hedonic analysis of rental housing prices observed in 2006. Hedonic models are jointly estimated with water service choices using a maximum simulated likelihood approach in order to control for potential endogeneity. Findings indicate that the value of piped water depends on the type of water utility. The estimated value of municipal services is at least 15 times as much as the average water bill, while value estimates are not significant for private and community‐managed systems. Value differentials are discussed considering the performance of water utilities and their institutional arrangements.

The composite marginal likelihood (CML) estimation of panel ordered-response models

In the context of panel ordered-response structures, the current paper compares the performance of the maximum-simulated likelihood (MSL) inference approach and the composite marginal likelihood (CML) inference approach. The panel structures considered include the pure random coefficients (RC) model with no autoregressive error component, as well as the more general case of random coefficients combined with an autoregressive error component. The ability of the MSL and CML approaches to recover the true parameters is examined using simulated datasets. The results indicate that the performances of the MSL approach (with 150 scrambled and randomized Halton draws) and the simulation-free CML approach are of about the same order in all panel structures in terms of the absolute percentage bias (APB) of the parameters and econometric efficiency. However, the simulation-free CML approach exhibits no convergence problems of the type that affect the MSL approach. At the same time, the CML approach is about 5–12 times faster than the MSL approach for the simple random coefficients panel structure, and about 100 times faster than the MSL approach when an autoregressive error component is added. As the number of random coefficients increases, or if higher order autoregressive error structures are considered, one can expect even higher computational efficiency factors for the CML over the MSL approach. These results are promising for the use of the CML method for the quick, accurate, and practical estimation of panel ordered-response models with flexible and rich stochastic specifications.

A simulation evaluation of the maximum approximate composite marginal likelihood (MACML) estimator for mixed multinomial probit models

This paper evaluates the ability of the maximum approximate composite marginal likelihood (MACML) estimation approach to recover parameters from finite samples in mixed cross-sectional and panel multinomial probit models. Comparisons with the maximum simulated likelihood (MSL) estimation approach are also undertaken. The results indicate that the MACML approach recovers parameters much more accurately than the MSL approach in all model structures and covariance specifications. The MACML inference approach also estimates the parameters efficiently, with the asymptotic standard errors being, in general, only a small proportion of the true values. As importantly, the MACML inference approach takes only a very small fraction of the time needed for MSL estimation. In particular, the results suggest that, for the case of five random coefficients, the MACML approach is about 50 times faster than the MSL for the cross-sectional random coefficients case, about 15 times faster than the MSL for the panel inter-individual random coefficients case, and about 350 times or more faster than the MSL for the panel intra- and inter-individual random coefficients case. As the number of alternatives in the unordered-response model increases, one can expect even higher computational efficiency factors for the MACML over the MSL approach. Further, as should be evident in the panel intra- and inter-individual random coefficients case, the MSL is all but practically infeasible when the mixing structure leads to an explosion in the dimensionality of integration in the likelihood function, but these situations are handled with ease in the MACML approach. It is hoped that the MACML procedure will spawn empirical research into rich model specifications within the context of unordered multinomial choice modeling, including autoregressive random coefficients, dynamics in coefficients, space–time effects, and spatial/social interactions.

The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models

The likelihood functions of multinomial probit (MNP)-based choice models entail the evaluation of analytically-intractable integrals. As a result, such models are usually estimated using maximum simulated likelihood (MSL) techniques. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and practically infeasible as the number of dimensions of integration rises. In this paper, we introduce a maximum approximate composite marginal likelihood (MACML) estimation approach for MNP models that can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler procedure relative to simulation techniques, and has the advantage of substantial computational time efficiency relative to the MSL approach. The paper provides a “blueprint” for the MACML estimation for a wide variety of MNP models.

Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach via Particle Filtering

In this paper we provide a unified methodology for conducting likelihood-based inference on the unknown parameters of a general class of discrete-time stochastic volatility (SV) models, characterized by both a leverage effect and jumps in returns. Given the nonlinear/non-Gaussian state-space form, approximating the likelihood for the parameters is conducted with output generated by the particle filter. Methods are employed to ensure that the approximating likelihood is continuous as a function of the unknown parameters thus enabling the use of standard Newton-Raphson type maximization algorithms. Our approach is robust and efficient relative to alternative Markov Chain Monte Carlo schemes employed in such contexts. In addition it provides a feasible basis for undertaking the nontrivial task of model comparison. Furthermore, we introduce new volatility model, namely SV-GARCH which attempts to bridge the gap between GARCH and stochastic volatility specifications. In nesting the standard GARCH model as a special case, it has the attractive feature of inheriting the same unconditional properties of the standard GARCH model but being conditionally heavier-tailed; thus more robust to outliers. It is demonstrated how this model can be estimated using the described methodology. The technique is applied to daily returns data for S&P 500 stock price index for various spans. In assessing the relative performance of SV with leverage and jumps and nested specifications, we find strong evidence in favour of a including leverage effect and jumps when modelling stochastic volatility. Additionally, we find very encouraging results for SV-GARCH in terms of predictive ability which is comparable to the other models considered.

Assessing the Effect of Current Account and Currency Crises on Economic Growth

Several empirical studies are concerned with measuring the effect of currency and current account crises on economic growth. Using different empirical models this paper serves two aspects. It provides an explicit assessment of country specific factors influencing the costs of crises in terms of economic growth and controls via a treatment type model for possible sample selection governing the occurrence of crises in order to estimate the impact on economic growth correctly. The applied empirical models allow for rich intertemporal dependencies via serially correlated errors and capture latent country specific heterogeneity via random coefficients. For accurate estimation of the treatment type model a simulated maximum likelihood approach employing efficient importance sampling is used. The results reveal significant costs in terms of economic growth for both crises. Costs for reversals are linked to country specific variables, while costs for currency crises are not. Furthermore, shocks explaining current account reversals and growth show strong significant positive correlation.

Estimation in generalised linear mixed models with binary outcomes by simulated maximum likelihood

Fitting multilevel models to discrete outcome data is problematic because the discrete distribution of the response variable implies an analytically intractable log-likelihood function. Among a number of approximate methods proposed, second-order penalised quasi-likelihood (PQL) is commonly used and is one of the most accurate. Unfortunately, even the second-order PQL approximation has been shown to produce estimates biased toward zero in certain circumstances. This bias can be marked especially when the data are sparse. One option to reduce this bias is to use Monte-Carlo simulation. A bootstrap bias correction method proposed by Kuk has been implemented in MLwiN. However, a similar technique based on the Robbins-Monro (RM) algorithm is potentially more efficient. An alternative is to use simulated maximum likelihood (SML), either alone or to refine estimates identified by other methods. In this article, we first compare bias correction using the RM algorithm, Kuk’s method and SML. We find that SML performs as efficiently as the other two methods and also yields standard errors of the bias-corrected parameter estimates and an estimate of the log-likelihood at the maximum, with which nested models can be compared. Secondly, using simulated and real data examples, we compare SML, second-order Laplace approximation (as implemented in HLM), Markov Chain Monte-Carlo (MCMC) (in MLwiN) and numerical integration using adaptive quadrature methods (in Stata’s GLLAMM and in SAS’s proc NLMIXED). We find that when the data are sparse, the second-order Laplace approximation produces markedly lower parameter estimates, whereas the MCMC method produces estimates that are noticeably higher than those from the SML and quadrature methods. Although proc NLMIXED is much faster than GLLAMM, it is not designed to fit models of more than two levels. SML produces parameter estimates and log-likelihoods very similar to those from quadrature methods. Further our SML approach extends to handle other link functions, discrete data distributions, non-normal random effects and higher-level models.

Estimation of stochastic frontier production functions with input-oriented technical efficiency

This paper deals with estimation of input-oriented (IO) technical inefficiency using a stochastic production frontier model. Econometrically the model is similar to a class of models that arise in specifying technical inefficiency in cost-minimizing and profit-maximizing frameworks. The standard maximum likelihood (ML) method that is used to estimate output-oriented (OO) technical efficiency cannot be applied to estimate these models. We use a simulated ML approach to estimate the IO production function and compare results from the IO and OO models, mainly to emphasize the point that estimated efficiency, returns to scale, technical change, etc., differ depending on whether one uses the model with IO or OO technical inefficiency.

Computational Issues in the Sequential Probit Model: A Monte Carlo Study

We discuss computational issues in the sequential probit model that have limited its use in applied research. We estimate parameters of the model by the method of simulated likelihood and by Bayesian MCMC algorithms. We provide Monte Carlo evidence on the relative performance of both estimators. Given the numerical difficulties associated with the estimation procedures, we advise the applied researcher to use both stochastic optimization algorithms in the Simulated Maximum Likelihood approach as well as Bayesian MCMC algorithms to check the compatibility of the results.

Computational Issues in the Sequential Probit Model: A Monte Carlo Study

We discuss computational issues in the sequential probit model that have limited its use in applied research. We estimate parameters of the model by the method of simulated likelihood and by Bayesian MCMC algorithms. We provide Monte Carlo evidence on the relative performance of both estimators. Given the numerical difficulties associated with the estimation procedures, we advise the applied researcher to use both stochastic optimization algorithms in the Simulated Maximum Likelihood approach as well as Bayesian MCMC algorithms to check the compatibility of the results.

A statistical model for orientation mechanism

A variance components model with response variable depending on both fixed effects of explanatory variables and random components is specified to model longitudinal circular data, in order to study the directional behaviour of small animals, as insects, crustaceans, amphipods, etc. Unknown parameter estimators are obtained using a simulated maximum likelihood approach. Issues concerning log-likelihood variability and the related problems in the optimization algorithm are also addressed. The procedure is applied to the analysis of directional choices under full natural conditions ofTalitrus saltator from Castiglione della Pescaia (Italy) beaches.