Consistent moment estimators of regression coefficients in the presence of errors in variables

This paper examines the possibilities of moment estimators of regression coefficients in the errors-in-variables problem suggested by Geary (1942) and others [Scott (1950) and Drion (1951)]. This approach yields consistent estimators of regression coefficients based on uni- and bi-variate moments (or cumulants) of third or higher order. These are computationally simple and need milder assumptions than the standard techniques, viz., ML and IV estimation. After a review of past investigations, this paper proposes new moment estimators and compares the asymptotic efficiencies of six estimators proposed earlier or here and of the OLS estimator. The case where the true regressor is lognormally distributed receives considerable attention in this communication.     

Cost and Production Duality: The Case of the Regulated Firm

This paper examines a generalization of cost-production duality for regulated firms. It derives an equivalency between the production function and conditional factor demands for the case where the firm's optimization problem is subject to a set of additional (regulatory) constraints. This procedure is extended to an optimization problem within a dynamic framework which leads to the recovery of the firm's technology.     

Tendency towards normality of linear combinations of random variables

IfX andY are two random variables with the same means and variances, thenX is said to be nearer normal thanY if the absolute values of its cumulants are smaller than the corresponding cumulants ofY. Using this definition, it is shown that a linear combination of a finite number of independent identically distributed random variables is always nearer normal than its constituents, but that this is not necessarily true if not-identically distributed or not-independent variables are used. Some consequences of the results are reached for the testing of normality of time series and for the assumptions frequently made by social scientists about the distribution of their data.     

Estimation of technical change and TFP growth based on observable technology shifters

Journal of Productivity Analysis - This paper models and estimates total factor productivity (TFP) growth parametrically. The model is a generalization of the traditional production function model...     

Price-endogenized Input–Output Model: A General Equilibrium Analysis of the Production Sector of the Japanese Economy

This paper considers a generalization of the open Leontief model, by endogenizing the input coefficients on the basis of the neoclassical multi-sectoral produc-tion function. The adopted production function is of the two-level CES type, which is quite effective for avoiding the multi-collinearity problem. As a result, the estimates obtained are quite stable, satisfying the quasi-concavity conditions of the production function for all the sectors. Comparative statics based on the Jacobian of the excess supply function for each commodity market reveal that, owing to the factor substitution the effect of an increase in the final demand on the level of the production is significantly smaller than that which occurs in the open Leontief model with fixed input coefficients.     

Calculating Cumulants of a Taylor Expansion of a Multivariate Function

A method, which we believe is simpler and more transparent than the one due to McCullagh (1984) , is described for obtaining the cumulants of a scalar multivariate stochastic Taylor expansion. Its generalisation is also suggested. An important feature, previously not reported, is that the expansion of every cumulant of order ≥ 2 is made up of separate subseries.
In order to handle certain frequently occurring sums over permutations of members of compound index sets, we introduce a new notation  [ m ]_*,  where   m   is a positive integer.     

Minimum distance estimation of the errors-in-variables model using linear cumulant equations

We consider a multiple mismeasured regressor errors-in-variables model. We develop closed-form minimum distance estimators from any number of estimating equations, which are linear in the third and higher cumulants of the observable variables. Using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions. The estimators perform well in Monte Carlos calibrated to resemble the data from our applications. Although the cumulant estimators are asymptotically equivalent to the moment estimators from Erickson and Whited (2002), the finite-sample performance of the cumulant estimators exceeds that of the moment estimators.     

Bias reduction when data are rounded

Analytical bias reduction methods are developed for univariate rounded data for the first time. Extensions are given to rounding of multivariate data, and to smooth functionals of several distributions. As a by‐product, we give for the first time the relation between rounded and unrounded multivariate cumulants. Estimators obtained by analytical bias reduction are compared with bootstrap and jackknife estimators by simulation.     

Can Findings of Qualitative Research in Education be Generalized?

Most qualitative researchers do not recommend generalization from qualitative studies, as this research is not based on random samples and statistical controls. The objective of this study is to explore the degree to which in-service teachers understand the controversial aspects of generalization in both qualitative and quantitative educational research and as to how this can facilitate problems faced by the teachers in the classroom. The study is based on 83 participants who had registered for a 10-week course on ‘Methodology of Investigation in Education’ as part of their Master’s degree program. The course is based on 11 readings drawing on a philosophy of science perspective (positivism, constructivism, Popper, Kuhn, Lakatos). Course activities included written reports, class room discussions based on participants’ presentations, and written exams. Based on the results obtained it is concluded: (1) almost 91% of the teachers agreed that external generalization in a different social context is feasible; (2) almost 63% of the participants used a fairly inconsistent approach, that is in a theoretical context agreed that qualitative research cannot be generalized and still when asked with respect to the experience of two particular teachers, agreed that generalization was possible; (3) almost 28% of the participants used a consistent approach. Some of the reasons provided by the participants as to why generalization was feasible are discussed. An analogy is drawn with respect to Piaget’s methodology, viz., it was not based on random samples or statistical treatments and still his oeuvre has been generalized (criticisms not withstanding) in both the psychology and educational literature.     

Designs for estimating an extremal point of quadratic regression models in a hyperball

This paper is devoted to studying optimal designs for estimating an extremal point of a multivariate quadratic regression model in the unit hyperball. The problem of estimating an extremal point is reduced to that of estimating certain parameters of a corresponding nonlinear (in parameters) regression model. For this reduced problem truncated locally D-optimal designs are found in an explicit form. The result is a generalization of the results of Fedorov and Müller (1997) for onedimensional quadratic regression function in the unit segment. Received February 2002     

A note on the equivalence of specification tests in the two-factor multivariate variance components model

This note offers a generalization of Hausman and Taylor's equivalence of specification tests in the single-equation variance (error) components model to the two-factor multivariate variance components case. The relationship between the specification tests and the hypothesis test in the model proposed by Mundlak is also discussed.     

Mixture of MLP-experts for trend forecasting of time series: A case study of the Tehran stock exchange

A new method for forecasting the trend of time series, based on mixture of MLP experts, is presented. In this paper, three neural network combining methods and an Adaptive Network-Based Fuzzy Inference System (ANFIS) are applied to trend forecasting in the Tehran stock exchange. There are two experiments in this study. In experiment I, the time series data are the Kharg petrochemical company’s daily closing prices on the Tehran stock exchange. In this case study, which considers different schemes for forecasting the trend of the time series, the recognition rates are 75.97%, 77.13% and 81.64% for stacked generalization, modified stacked generalization and ANFIS, respectively. Using the mixture of MLP experts (ME) scheme, the recognition rate is strongly increased to 86.35%. A gain and loss analysis is also used, showing the relative forecasting success of the ME method with and without rejection criteria, compared to a simple buy and hold approach. In experiment II, the time series data are the daily closing prices of 37 companies on the Tehran stock exchange. This experiment is conducted to verify the results of experiment I and to show the efficiency of the ME method compared to stacked generalization, modified stacked generalization and ANFIS.     

Estimating process capability index C′′pmk for asymmetric tolerances: Distributional properties

Pearn et al. (1999) considered a capability index C ^′′ _pmk, a new generalization of C _pmk, for processes with asymmetric tolerances. In this paper, we provide a comparison between C ^′′ _pmk and other existing generalizations of C _pmk on the accuracy of measuring process performance for processes with asymmetric tolerances. We show that the new generalization C ^′′ _pmk is superior to other existing generalizations of C _pmk. Under the assumption of normality, we derive explicit forms of the cumulative distribution function and the probability density function of the estimated index . We show that the cumulative distribution function and the probability density function of the estimated index can be expressed in terms of a mixture of the chi-square distribution and the normal distribution. The explicit forms of the cumulative distribution function and the probability density function considerably simplify the complexity for analyzing the statistical properties of the estimated index . Received April 2000     

A dynamic generalization of the tobin model

The paper studies the stability and the non-neutrality of money issues of the neoclassical monetary growth theory when the liquidity preference function and the price dynamics equation are generalized in the Tobin model. Our generalization introduces Tobin's real purchasing power into the liquidity preference function, thereby allowing real balance flows to exert direct income effects. Such effects allow a number of separate cases in the price dynamics behavior, some of which lead to results that differ from the neoclassical propositions. Thus, these propositions are sensitive to the choice of a particular proxy measure of the transactions motives of the demand for money.     

A generalization of the logistic growth function and its estimation

Summary This paper presents a generalization of the logistic growth function based on a model for relative growth rates. The basic relative growth rate model is based on the Riccati differential equation, which has a solution that closely resembles the familiar S -shaped logistic curve. For estimation purposes, a statistical version of this model is developed in which linear, exponential, and modified exponential growth in addition to logistic growth arise as special cases under various statistical hypotheses. The growth of yeast cells, population growth of the Netherlands and an example from the telephone industry are provided as illustrations of the model.     

Skew probability curves with negative powers of time and related to random walks in series

Summary The well known probability distribution of first arrival times of a particle undergoing random walk or Brownian movement in one dimension is extended to allow for steps in series each in a different medium. Previously this led to considering a certain distribution defined by its cumulants, which form a simple series generalising that for the known distribution. This is illustrated by the particular case of two first passages in series. Approximations to the probability (density) curves are found, each of which consists of a sharp peak followed by a long tail where the ordinates are very nearly proportional to t-^W, W ≥ 3/2. A generalisation can yield smaller W down to ca. 0.1. It is concluded that this explains why negative powers of time are found in so many physiological clearance curves of all kinds. Numerical tables are based on distributions with very smal step times, and give ones built up from the sum of a varying number of steps. The parameters 01 the triangle formed by the inflection tangents are given in order to describe the peaks.     

On a bayesian criterion for choosing predictive sub-models in linear regression

Summary We treat the model selection problem in regression as a decision problem in which the decisions are the alternative predictive distributions based on the different sub-models and the parameter space is the set of possible future values of the regressand. The loss function balances out the conflicting needs for a predictive distribution with mean close to the true value ofy but without too great a variation. The treatment is Bayesian and the criterion derived is a Bayesian generalization of Mallows (1973)C _p , the Bivar criterion (Young 1982) and AIC (Akaike 1974). An application using a graphical sensitivity analysis is presented.     

Equilibrium in abstract economies without ordered preferences and with a measure space of agents

We report a generalization of Aumann's (1966) existence theorem to economies without ordered preferences and with externalities in consumption. Our work can alternatively be viewed as a generalization of the Shafer–Sonnenschein (1975) theorem to economies with a continuum of agents.     

Homogeneous semi-Markov reliability models for credit risk management*

Abstract The credit risk problem is one of the most important issues of modern financial mathematics. Fundamentally it consists in computing the default probability of a company going into debt. The problem can be studied by means of Markov transition models. The generalization of the transition models by means of homogeneous semi-Markov models is presented in this paper. The idea is to consider the credit risk problem as a reliability problem. In a semi-Markov environment it is possible to consider transition probabilities that change as a function of waiting time inside a state. The paper also shows how to apply semi-Markov reliability models in a credit risk environment. In the last section an example of the model is provided. Mathematics Subject Classification (2000): 60K15, 60K20, 90B25, 91B28 Journal of Economic Literature Classification: G21, G33     

Generalizing the standard product rule of probability theory and Bayes's Theorem

In this paper the usual product rule of probability theory is generalized by relaxing the assumption that elements of sets are equally likely to be drawn. The need for such a generalization has been noted by Jeffreys [1998. Theory of Probability, 3rd ed, reprinted in Oxford classics Series, Oxford University Press (1st ed.,1939), Oxford. pp. 24–25], among others, in his work on an axiom system for scientific learning from data utilizing Bayes's Theorem. It is shown that by allowing probabilities of elements to be drawn to be different, generalized forms of the product rule and Bayes's Theorem are obtained that reduce to the usual product rule and Bayes's Theorem under certain assumptions that may be satisfactory in many cases encountered in practice in which the principle of insufficient reason is inadequate. Also, in comparing alternative hypotheses, allowing the prior odds to be random rather than fixed provides a useful generalization of the standard posterior odds.