Asymptotic expansions of the distributions of the structural variance estimators in a simultaneous equations system

Asymptotic expansions of three alternative classes of structural variance estimators associated with the k-class estimators of structural coefficients are derived for two parameter sequences: a sequence in which the non-centrality parameter increases while the sample size stays fixed (called large-μ or small-disturbance sequence), and that in which the number of observations increases. The accuracy of approximations to small-sample distributions are numerically examined with help of Monte Carlo studies. Properties of the sum of squared residuals of an estimated structural equation are also found from our study.     

Unit Root Analyses of the Causality Between Japanese Money and Income

Unit root techniques and cointegration analysis have develop ed considerably in the last ten years. At the same time, the nonstationary test for Granger causality has been developed. We shed some new light on Japanese money supply and income causality by using nonstationary techniques. We specify univariate ARMA models of money, income, GNP deflator and rate of interest, initially by using the Dickey and Fuller (DF) or the augmented DF (ADF) tests. Two diagnostic tests are applied to each selected ARMA regression. One is the residual DF test, and the other is the moving average (MA) unit root test of residuals . After selecting the ARMA model, some causality tests are applied to the error correction model (ECM) of a vector autoregression (VAR) one of which is ordinary least squares (OLS) and another is the maximum likelihood (ML) method. The former requires only the standard F -test on the deleted variables in the ECM. The latter requires the Johansen's ML method in estimating cointegration. Causality is found to go from income to money supply but not the other way. Appendices include a simple implementation of the MA unit root test, a pedagogical proof of the Granger causality tests developed by Toda and Phillips (1993) and an interpretation of the test proposed by Toda and Yamamoto (1995).
JEL Classification Numbers: C32, E50     

A Modified GARCH Model with Spells of Shocks

The GARCH model is modified to capture the effect on volatilities of the consecutive number of positive or negative shocks. The new model is tested against the Shanghai Shcomp and Nikkei225 indices and found particularly useful in analyzing the Shcomp index. Similarly, the EGARCH model is extended along the same line as the GARCH model and is applied to the same sets of data. Stationarity of the new GARCH (1, 1) model is proved, and also derived is the asymptotic distribution of the quasi-maximum likelihood estimator.     

Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system

In this paper asymptotic expansions are derived for the density functions of the TSLS and LIML estimates of coefficients in a simultaneous equation system when the sample size increases and the effect of the exogenous variables increases along the sample size. These approximations are used to compare the asymptotic moments of the TSLS and LIML estimates and the concentration of probability around the true value of the estimates.     

Decision rules for the choice of structural equations

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.     

The numerical values of some key parameters in econometric models

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.     

Potential for visual communications technology in business

The authors describe the methodology used in a survey conducted by NTT to assess the potential of visual communications technology in business and the conclusions drawn. Communications activities were investigated in detail at a selected manufacturing company, and several fundamental communication patterns suitable for the application of visual communications services were defined. It was concluded that the areas with the greatest potential for such services were ‘investigation/ inquiry’, ‘negotiation’, and ‘submitting information’. To confirm these needs, a questionnaire was mailed to major corporations throughout Japan. Finally, several services and systems were proposed.     

ESTIMATING THE RANK OF COINTEGRATION AFTER ESTIMATING THE ORDER OF A VECTOR AUTOREGRESSION*

Small sample properties are studied for the maximum likelihood test in determining the rank of cointegration. Firstly, some statistical methods are developed to determine the lag order of the vector auto-regressive (VAR) processes with unit roots. The asymptotic x² distribution of the likelihood ratio statistic is proved. Then the asymptotic standard normal distribution of the t-ratio is established for coefficients of differenced variables in the error correction representation. The t-ratio can be used to test the significance of individual coefficients in the highest order term of VAR processes without using any information on co-integration. The small sample properties of the likelihood ratio test, the t-test, AIC, and BIC are explored by simulations which are found indispensable in finding the order of VAR processes possibly with unit roots. Furthermore, and most importantly, our simulation shows that the trace test for finding the rank of co-integration does not depend much on the lag order selection criteria. Whichever procedure is used to find the lag order of a VAR process, the trace or the maximum eigen value test may on average give a similar rank of co-integration though this can be wrong.