Limited-information Likelihood Research Articles

R&D contribution in TFP growth of Greek industry: A limited information likelihood approach

ABSTRACTWe provide a novel panel model to decompose total factor productivity (TFP) growth in the Greek industry at the firm level while we tackle the contribution of R&D. We, therefore, opt for parametric methodology that provides statistical inference and would validate the results. Our modeling departs from prior strong assumptions such as error terms across firms being independent. In fact, we provide a novel limited information maximum likelihood (LIML) estimation method that adequately deals with the issue of endogeneity and model misspecification. We demonstrate that our model detects variability in terms of TFP growth components across industries and firms. Our results show that R&D would enhance TFP of Greek firms, albeit the crisis has had a detrimental impact. Financial ratios such as liquidity and solvency ratios also affect TFP as we demonstrate that both would enhance TFP. The solvency ratio is important as it provides an estimate of whether the firm can cope with debt. We also note variability across small versus medium and large firms and report that small firms are more productive and spend more of their revenues on R&D. In terms of policy, our evidence warrants higher R&D spending to enhance TFP growth, though R&D funding is a concern.

ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models

We develop novel methods for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Computation which build likelihoods based on limited information. The proposed estimators and filters are computationally attractive relative to standard likelihood-based versions since they rely on low-dimensional auxiliary statistics and so avoid computation of high-dimensional integrals. Despite their computational simplicity, we find that estimators and filters perform well in practice and lead to precise estimates of model parameters and latent variables. We show how the methods can incorporate intra-daily information to improve on the estimation and filtering. In particular, the availability of realized volatility measures help us in learning about parameters and latent states. The method is employed in the estimation of a flexible stochastic volatility model for the dynamics of the S&P 500 equity index. We find evidence of the presence of a dynamic jump rate and in favor of a structural break in parameters at the time of the recent financial crisis. We find evidence that possible measurement error in log price is small and has little effect on parameter estimates. Smoothing shows that, recently, volatility and the jump rate have returned to the low levels of 2004–2006.

Bayesian Analysis in Moment Inequality Models

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any δ -contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior. Our simulation evidence indicates that the Bayesian approach has advantages over frequentist methods, in the sense that, with a proper choice of the prior, the posterior provides more information about the true parameter inside the identified region.We also address the problem of moment and model selection. Our optimality criterion is the maximum posterior procedure and we show that, asymptotically, it selects the true moment/model combination with the most moment inequalities and the simplest model.

Posterior consistency of nonparametric conditional moment restricted models

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter $g_0$. We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior with nonshrinking variance. In addition, $g_0$ is allowed to be only partially identified in the frequentist sense, and the parameter space does not need to be compact. The posterior is regularized using a slowly growing sieve dimension, and it is shown that the posterior converges to any small neighborhood of the identified region. We then apply our results to the nonparametric instrumental regression model. Finally, the posterior consistency using a random sieve dimension parameter is studied.

Posterior Consistency of Nonparametric Conditional Moment Restricted Models

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite dimensional parameter g0. We estimate it in a quasi-Bayesian way based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thintail prior (a prior that has very thin tail outside a growing bounded set), and (iii) normal prior with non-shrinking variance. In addition, g0 is allowed to be only partially identified, and the parameter space does not need to be compact. The posterior is regularized using a slowly-growing sieve dimension, and it is shown that the posterior converges to any small neighborhood of the identified region. We then apply our results to the nonparametric instrumental regression model. Finally, the posterior consistency using a random sieve dimension parameter is studied.

Bayesian analysis in moment inequality models

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any δ-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior. Our simulation evidence indicates that the Bayesian approach has advantages over frequentist methods, in the sense that, with a proper choice of the prior, the posterior provides more information about the true parameter inside the identified region. We also address the problem of moment and model selection. Our optimality criterion is the maximum posterior procedure and we show that, asymptotically, it selects the true moment/model combination with the most moment inequalities and the simplest model.

Bayesian measurement of productivity and efficiency in the presence of undesirable outputs: crediting electric utilities for reducing air pollution

Abstract Many studies have measured productivity change and efficiency when an undesirable output is a by-product. We flexibly treat the bad as a technology shifter of an input distance function and model a system of nonlinear equations subject to endogeneity. Theory dictates that we impose monotonicity on all inputs, outputs, and the bad. Since a Bayesian full-information likelihood approach can easily be misspecified, we utilize the Kim (J. Econometrics 107 (2002) 175) limited-information likelihood (LIL) derived by minimizing the entropy distance subject to the moment conditions from the Generalized Method of Moments (GMM) estimator. This represents an extension of the Bayesian Method of Moments approach of Zellner and Chen (Macroeconom. Dyn. 5 (2001) 673), Zellner and Tobias (Int. Econom. Rev. 42 (2001) 121), and Zellner (in: Bayesian Analysis in Econometrics and Statistics: The Zellner View and Papers, Edward Elgar, Cheltenham, 1997; J. Econometrics 83 (1998) 185) which uses entropy maximization but does not incorporate a specific likelihood. Using Bayes’ Theorem we combine traditional priors with the LIL, which has a mode at the standard multiple-equation GMM estimator, yielding a limited-information posterior distribution. We generalize the approach of Kim (J. Econometrics 107 (2002) 175) by incorporating an unknown covariance matrix in a Gibbs sampling framework and applying the methodology to nonlinear equations. This allows us to estimate shadow prices, technical efficiency, and productivity change for a panel of electric utilities, yielding results that differ substantially from those obtained using standard GMM.

Limited information likelihood and Bayesian analysis

In this paper, we study how to embed the optimal generalized method of moments (GMM) estimate in a likelihood-based inference framework and the Bayesian framework. First, we derive a limited information likelihood (LIL) under some moment-based limited information available in GMM based on entropy theory of I-projection theory. Second, we study a limited information Bayesian framework in which the posterior is derived from the LIL and a prior. As the LIL enables us to incorporate GMM or related inference methods in the likelihood-based inference framework, it allows us a rich set of practical applications in the Bayesian framework in which the posterior is obtained from a likelihood and a prior. Our results are primarily large sample results as inference in the underlying GMM framework is usually justified in asymptotics. Investigation of large sample properties of the posterior derived from the LIL reveals an interesting relation between the Bayesian and the classical distribution theories.

Limited Information Likelihood Analysis Of Survey Data

Summary Analysts of survey data are often interested in modelling the population process, or superpopulation, that gave rise to a ‘target’ set of survey variables. An important tool for this is maximum likelihood estimation. A survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst. In this circumstance, sample inclusion probabilities, which are typically available, provide information which needs to be incorporated into the analysis. We consider the case where these inclusion probabilities can be modelled in terms of a linear combination of the design and target variables, and only sample values of these are available. Strict maximum likelihood estimation of the underlying superpopulation means of these variables appears to be analytically impossible in this case, but an analysis based on approximations to the inclusion probabilities leads to a simple estimator which is a close approximation to the maximum likelihood estimator. In a simulation study, this estimator outperformed several other estimators that are based on approaches suggested in the sampling literature.

Information Source Utilization and Teachers' Attributes in Physical Education: A Preliminary Test of a Rational Paradigm

This study sought to provide empirical evidence concerning physical education information-seeking patterns of elementary teachers at the primary level. It also investigated the relationship between information use patterns and teachers' attributes. A model based on simple utilitarian concepts explaining information use patterns was developed and tested. The basic assumption of the model was that the use of information sources would increase as the perceived benefits of the information derived increased, and the costs of retrieving and using the information decreased. Subjects for the study were elementary school teachers from the Vancouver school system in British Columbia, Canada (N = 86). Simultaneous equation procedures employing limited information likelihood estimators were used to test the model. The results of the study indicated that sources of information internal to the school system dominated utilization patterns. Among these, curriculum support material and discussion with colleagues were highly favored, suggesting that teachers at these grade levels rely heavily upon the experience of others in the same system and the support of very specific resource materials about physical education activities. The research also showed that those who felt they knew more and claimed to enjoy teaching actively sought to acquire more knowledge from more sources than those who knew less. Finally, the study demonstrated that models based on simple assumptions of rationality can predict decisions concerning information utilization.