Consistent estimation in the bilinear multivariate errors-in-variables model

A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A∈ℝ^m×n, B∈ℝ^p×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.  An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study. Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01, G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors.     

Inferential Causal Models: Integrating Quality & Quantity

In-depth data analysis plus statistical modeling can produce inferentialcausal models. Their creation thus combines aspects of analysis by close inspection,that is, reason analysis and cross-tabular analysis, with statistical analysis procedures,especially those that are special cases of the generalized linear model (McCullaghand Nelder, 1989; Agresti, 1996; Lindsey, 1997). This paper explores some of the roots of this combined method and suggests some new directions. An exercise clarifies some limitations of classic reason analysis by showing how the cross tabulation of variables with controls for test factors may produce better inferences. Then, given the cross tabulation of several variables, by explicating Coleman effect parameters, logistic regressions, and Poisson log-linear models, it shows how generalized linear models provide appropriate measures of effects and tests of statistical significance. Finally, to address a weakness of reason analysis, a case-control design is proposed and an example is developed.     

COMPUTABLE GENERAL EQUILIBRIUM MODELS FOR DEVELOPMENT POLICY ANALYSIS IN LDCs

Abstract. The use of CGE models has gained much popularity among policy analysts in LDCs and there is a fast growing body of literature on this area of economics. In this survey, the advantages of general equilibrium approach over partial equilibrium approach in analysing a wide range of policy issues are highlighted. The evolution of CGE modelling is discussed and more than 60 CGE applications related to different policy issues in LDCs are surveyed. This comprehensive survey shows that the CGE models have become quite popular analytical tools among policy analysts in LDCs over the last decade or so. The debate in the economic profession regarding the value and appropriateness of using CGE models for policy analysis is examined in the final section of this paper. Some of the criticisms levelled at CGE models are discussed and it is argued that despite this criticism such models are capable of providing insight into important policy problems.     

A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

Pricing of Mutual Fund Services in Retirement Plans: Evidence from Open-End Equity Funds

Management fees of mutual funds are more costly to investors than is often realized. Moreover, research indicates that in many cases, the fees are not related to performance, contrary to what might be expected from an efficient market. This study uses sample data to illustrate the consequences of inefficiency to an individual investor. It then turns to an empirical examination of the determinants of the ratio of management fees to total assets (MER), investigating market concentration, fund performance, and non-performance characteristics as explanatory variables. All of these classes of variables contributed to the variation of MERs . JEL Classification G23     

Bayesian MCMC Mapping of Quantitative Trait Loci in a Half-sib Design: a Graphical Model Perspective

Graphical models provide a powerful and flexible approach to the analysis of complex problems in genetics. While task-specific software may be extremely efficient for any particular analysis, it is often difficult to adapt to new computational challenges. By viewing these genetic applications in a more general framework, many problems can be handled by essentially the same software. This is advantageous in an area where fast methodological development is essential. Once a method has been fully developed and tested, problem-specific software may then be required. The aim of this paper is to illustrate the potential use of a graphical model approach to genetic analyses by taking a very simple and well-understood problem by way of example.     

IntraLATA long-distance demand: carrier choice, usage demand and price elasticities

Competition in the long-distance market in the US continues to intensify; the 1996 Telecommunications Act has led to increased competition in long-distance telephony especially as the Regional Bell Operating Companies have begun to gain entry to long-haul, long-distance markets. In order to better understand the implications of having increased service offerings, models of how customers choose between carriers (and the impact of this choice on subsequent usage) will be useful. We develop the first publicly available models that simultaneously estimate choice and usage for intraLATA long-distance in the US. Utilizing a generalized Tobit model, the price responsiveness of usage and carrier choice are estimated. The results are generally consistent with expectations both in terms of theory and of practical experience in the industry.     

Environmental protection versus economic growth

This paper presents and analyses the differences in the eco-models implemented worldwide （such as whether and how carbon taxes being ＂recycled＂）, or in their efficiency parameters （inconsistent parameter values that account for different results）. This is the assumption that a real tradeoff exists between the production of environmental goods. The present article empirically proves that something must be given up in order to gain something else, and once equations are specified to trace out the path of the economy over time, the natural economic formulation of such equations will embody the notion of economic and bio-tradeoffs.     

The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors

We consider the normalized least squares estimator of the parameter in a nearly integrated first-order autoregressive model with dependent errors. In a first step we consider its asymptotic distribution as well as asymptotic expansion up to order O_p(T⁻¹). We derive a limiting moment generating function which enables us to calculate various distributional quantities by numerical integration. A simulation study is performed to assess the adequacy of the asymptotic distribution when the errors are correlated. We focus our attention on two leading cases: MA(1) errors and AR(1) errors. The asymptotic approximations are shown to be inadequate as the MA root gets close to −1 and as the AR root approaches either −1 or 1. Our theoretical analysis helps to explain and understand the simulation results of Schwert (1989) and DeJong, Nankervis, Savin, and Whiteman (1992) concerning the size and power of Phillips and Perron's (1988) unit root test. A companion paper, Nabeya and Perron (1994), presents alternative asymptotic frameworks in the cases where the usual asymptotic distribution fails to provide an adequate approximation to the finite-sample distribution.