Takamitsu Sawa

The exact moments of the least squares estimator for the autoregressive model

Abstract Exact mean and variance of the least squares estimate of the stationary first-order autoregressive coefficient, i.e., β in y t = α + βx t + u t are evaluated algebraically as well as numerically. It turns out that the least squares estimate is seriously biased for the sample of two-digits sizes typically dealt with in econometrics if the mean of the process is unknown, i.e., if the equation has a non-zero intercept (α≠0). Kendalls approximation to the mean and Barletts approximation to the variance are shown to be fairly good. Also, our numerical results confirm Orcutt and Winokurs ( Econometrica , Vol. 37) based on Monte Carlo experiments.

Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator

The distributions of the Limited Information Maximum Likelihood estimator for the coefficient of one endogenous variable are evaluated numerically. Tables are given for enough values of the parameters to cover all cases of interests. Comparisons are made with the Two-Stage Least Squares estimator.

The Exact Sampling Distribution of Ordinary Least Squares and Two-Stage Least Squares Estimators

Abstract This paper presents the exact sampling distributions of the ordinary and the two-stage least squares estimators of a structural parameter in a structural equation with two endogenous variables in a complete system of stochastic equations. The results show that the distributions of the two estimators are essentially similar to each other. It can also be seen that both distributions depend crucially upon the deviation of a regression coefficient of disturbance terms of two endogenous variables from a structural parameter, and that the first estimator possesses moments up to the order N-2, while the second possesses them up to the order K-1, where N is the sample size and K is the number of exogenous variables excluded from the equation to be estimated. The small sample properties of the estimators are investigated by numerical evaluations of the density functions.

The Exact Finite-Sample Distribution of the Limited-Information Maximum Likelihood Estimator in the Case of Two Included Endogenous Variables

Abstract This article is concerned with the exact finite-sample distribution of the limited-information maximum likelihood estimator when the structural equation being estimated contains two endogenous variables and is identifiable in a complete system of linear stochastic equations. The density function derived, which is represented as a doubly infinite series of a complicated form, reveals the important fact that for arbitrary values of the parameters in the model, the LIML estimator does not possess moments of order greater than or equal to one

The numerical values of some key parameters in econometric models

Abstract In the case of two endogenous variables, exogenous predetermined variables, and normally distributed disturbances, the distributions of the Two-Stage Least Squares (TSLS) and Limited Information Maximum Likelihood (LIML) estimators can be compared on the basis of three key parameters: the non-centrality parameter, a standardization of the structural coefficient, and the number of excluded exogenous variables. In this paper the values of these parameters are estimated in eleven structural equations from various actual econometric models. The distribution functions of the normalized TSLS and LIML estimators are given for the first two key parameters set at approximately their trimmed means, and the third at its median.

Carbon tax for subsidizing photovoltaic power generation systems and its effect on carbon dioxide emissions

This paper proposes a new framework for evaluating quantitatively the effect of carbon taxation. In this study, the tax revenues are supposed to be used only as a subsidy for installing Photovoltaic Power Generation (PV) Systems on houses. The evaluation model developed in this study comprises three sequential modules. The first module is for estimating the demand for the PV system under the subsidy and the carbon taxation policy, the second is the module for life-cycle inventory analysis based on the modified Input-Output table, and the third is the module for calculating the amount of carbon-dioxide emissions from the final-demand vector of the Input-Output table. Major findings of this study are as follows: (1) The amount of CO2-emission reduction increases by advertising the PV system with subsidy policy even under the same tax-rate. (2) The CO2-payback time of the PV system reduces by half if the GDP is assumed not to change after the introduction of carbon taxation.

Decision rules for the choice of structural equations

Abstract In practical econometric analysis we are faced with the problem of how to specify structural equations. The conventional t -test of coefficients is apparently inappropriate. The smallest root, say λ, of a certain determinantal equation provides us with basis for the test of overidentifying restrictions. The preliminary test, based on λ, may give us a possible decision rule for choosing a structural equation from nested alternatives. However, ambiguity remains in specifying the significance level. We propose a decision method called the unbiased decision rule; unbiased in the sense that we attain a correct decision with probability of more than a half. The critical points are found as the medians of non-central F -distributions. The degrees of freedom and the non-centrality parameter of non-central F -distributions are determined by the properties of contending models. We also discuss the implications of the unbiased decision rule in the context of the conventional pre-test.

Two-Stage Least Squares: In Which Direction Should the Residuals Be Minimized?

Abstract A structural equation in a complete system may be written with the coefficient of one endogenous variable as unity and the coefficients of the other endogenous variables as parameters. To estimate these parameters two-stage least squares is usually applied by minimizing residuals in the direction of the first variable. In this paper, when there is one such parameter, that procedure is compared with adapting two-stage least squares to minimize residuals in the direction of the second endogenous variable. Estimation of the slope of a linear functional relationship by using least squares to minimize residuals in alternative directions is also treated.

Commercial Viability of Space Solar Power System as a CDM Project

Publisher Summary This chapter examines the commercial viability of the Space Solar Power System (SSPS). The SSPS generates electric power during Earths orbit, and sends the power to the earth by a microwave beam. The cost of the SSPS was compared with that of photovoltaic power plant on the ground. The power-generation cost of the SSPS is estimated, based on a detailed model. It also showed that the cost of the SSPS is in the range of that of photovoltaic power generation systems, with electric power storage. The feasibility of the SSPS as a CDM project has been evaluated. The clean development mechanism (CDM), which is one of the flexible measures referred to as the Kyoto Mechanism, allows for the international transfer of CO2 emission permits. If an antenna for receiving the microwave beam, a rectenna, is set up in a country neighboring Japan, the SSPS can export the electric power to the country. The framework of CDM is considered applicable to this case. The application of CDM to the SSPS project means that Japan can use carbon credits by erecting the rectenna in China. The effect of CDM on the generation cost has been examined, assuming that the SSPS substitutes the coal-fired power plants in China. As a result, the SSPS can be commercially viable under the very restricted, but possible, conditions.

Economic Analysis of Plastic Recycling System Based on the Wastes Distribution.

Recycling of plastics has been attracting much attention in Japan and also in foreign countries. Recycling system is not easily introduced mainly due to its expensive cost. Economic evaluation of recycling, however, has not been fully investigated in Japan. In this study, fractionation, collection and processing of plastic waste in the residential and commercial sectors are taken into account. Especially the plasticswaste collection has been modeled quantitatively by using the regional mesh statistics and the reports on office survey provided by the Japanese government. Various kinds of plastics-recycling processes are evaluated from the viewpoint of both of life-cycle energy and economics. The evaluation results can be summarized as follows:The PET reclamation has good performance of energy saving. However, it takes a lot of cost for collection, and this technology is not economically acceptable even if the recycled resin has the same value as the virgin one. Some simulations show that cost reduction is possible by decreasing the labor hour for plastics collection. Furthermore, some measures for voluntary collection of PET containers are most effective if the government thinks the plastics recycling is preferable from the viewpoint of the local and global environment.