Corrigenda: An Asymptotic of the Distribution of the Limited Information Maximum Likelihood Estimate of a Coefficient in a Simultaneous Equation System

The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently estimated by Liu and Breen's formula. The effect of conditioning on a second-order asymptotic ancillary statistic, i.e., the smallest characteristic root associated with the LIML estimation, is analyzed by means of an asymptotic expansion of the distribution as well as the exact distribution. The smallest root helps to give an intuitively appealing measure of precision of the LIML estimator.

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Comparing Single-Equation Estimators in a Simultaneous Equation System

Econometric Theory ◽

10.1017/s026646660001135x ◽

1986 ◽

Vol 2 (1) ◽

pp. 1-32 ◽

Cited By ~ 21

Author(s):

T. W. Anderson ◽

Naoto Kunitomo ◽

Kimio Morimune

Keyword(s):

Maximum Likelihood ◽

Least Squares ◽

Maximum Likelihood Estimator ◽

Equation System ◽

Single Equation ◽

Ordinary Least Squares ◽

Limited Information ◽

Likelihood Estimator ◽

Mean Squared Errors ◽

Simultaneous Equation System

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k-class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as modifications of the limited information maximum likelihood estimator and several Bayes' estimators. Many inequalities between the asymptotic mean squared errors and concentrations of probability are given. Among medianunbiasedestimators, the limited information maximum likelihood estimator dominates the median-unbiased fixed k-class estimator.

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Third-Order Efficiency of the Extended Maximum Likelihood Estimators in a Simultaneous Equation System

Econometrica ◽

10.2307/1911730 ◽

1985 ◽

Vol 53 (1) ◽

pp. 177 ◽

Cited By ~ 22

Author(s):

Kei Takeuchi ◽

Kimio Morimune

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimators ◽

Equation System ◽

Simultaneous Equation ◽

Third Order ◽

Simultaneous Equation System

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The Links between the Companies Market Price Quality and that of its Management and Business Quality: A System Panel Data Approach

GIS Business ◽

10.26643/gis.v11i6.3383 ◽

2016 ◽

Vol 11 (6) ◽

pp. 28-38

Author(s):

Dinis Daniel Santos ◽

Elias Soukiazis

Keyword(s):

Panel Data ◽

Business Performance ◽

Market Price ◽

Equation System ◽

Simultaneous Equation ◽

System Equation ◽

Simultaneous Equation System ◽

Management Quality ◽

The Relationship

This work uses a simultaneous equation system approach to analyze the relationship between the management and business quality of companies and their market price quality. Using panel data we found that both the management and the business quality of companies positively influence the market price quality of the studied American companies. Additionally, variables like the actual position of the company price quality compared to the industry average, being on the top or the bottom, or the beta value of a company, also influence the market price quality of the respective company. It is shown that the system equation approach is the most appropriate to explain the linkages between price, business, and management quality providing consistent estimates. Also, using ratings to express the three core variables in the system is the most adequate way to define the quality characteristics in terms of price, management, and business performance of the companies considered in this study.

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Box-Cox Transformations

10.1093/oso/9780198505044.003.0010 ◽

2017 ◽

Author(s):

Russell Cheng

Keyword(s):

Maximum Likelihood ◽

Normal Form ◽

Maximum Likelihood Estimate ◽

Likelihood Estimate ◽

Grouped Data ◽

Numerical Example ◽

Alternative Method ◽

Modified Likelihood

This chapter examines the well-known Box-Cox method, which transforms a sample of non-normal observations into approximately normal form. Two non-standard aspects are highlighted. First, the likelihood of the transformed sample has an unbounded maximum, so that the maximum likelihood estimate is not consistent. The usually suggested remedy is to assume grouped data so that the sample becomes multinomial. An alternative method is described that uses a modified likelihood similar to the spacings function. This eliminates the infinite likelihood problem. The second problem is that the power transform used in the Box-Cox method is left-bounded so that the transformed observations cannot be exactly normal. This biases estimates of observational probabilities in an uncertain way. Moreover, the distributions fitted to the observations are not necessarily unimodal. A simple remedy is to assume the transformed observations have a left-bounded distribution, like the exponential; this is discussed in detail, and a numerical example given.

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