• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.371-383
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• 2019

Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.193-200
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• 2014

It was recognized by some researchers that the disturbance variance in a censored regression model is frequently underestimated by the maximum likelihood method. This underestimation has implications for the estimation of marginal effects and asymptotic standard errors. For instance, the actual coverage probability of the confidence interval based on a maximum likelihood estimate can be significantly smaller than the nominal confidence level; consequently, a Bayesian estimation is considered to overcome this difficulty. The behaviors of the maximum likelihood and Bayesian estimators of disturbance variance are examined in a fixed effects panel regression model with a limited dependent variable, which is known to have the incidental parameter problem. Behavior under random effect assumption is also investigated.

• The Journal of Industrial Distribution & Business
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• v.12 no.8
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• pp.33-39
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• 2021

Purpose: The influence of age on time preference is not identified in the usual cross-sectional analysis. This study aims to test whether age affects time preference after controlling for the effects of individual heterogeneity including cohort effects. Research design, data and methodology: Drawing on a nationally representative panel dataset of Indonesians, we estimate the effects of age on time preference after controlling for unobserved individual heterogeneity as well as potential cohort effects. We measure time preference exploiting information on two sets of multiple price lists: one for a one-year delay, and the other for a five-year delay. Results: When we controlled for time-invariant individual characteristics, including birth cohort effects in a fixed effects model, the older men and women were more patient in a linear fashion, particularly when the delay was longer. To highlight the importance of controlling for individual fixed effects, we repeated the specification without controlling for individual fixed effects in OLS or censored maximum likelihood regression; we found no relation between age and impatience in men or women and for a one or five-year delay. Conclusions: The older men and women are more patient, and time preferences are correlated with unobserved individual heterogeneity.