Some Observations,a Suggestion,and Some Comments on the Conway-Roberts Article

This article provides new tools for the evaluation of dynamic stochastic general equilibrium (DSGE) models and applies them to a large-scale new Keynesian model. We approximate the DSGE model by a vector autoregression, and then systematically relax the implied cross-equation restrictions and document how the model fit changes. We also compare the DSGE model's impulse responses to structural shocks with those obtained after relaxing its restrictions. We find that the degree of misspecification in this large-scale DSGE model is no longer so large as to prevent its use in day-to-day policy analysis, yet is not small enough to be ignored.     

On Using Linear Regressions in Welfare Economics

This article consists of two parts. The first part shows that the ordinary least squares regression coefficient is a weighted average of slopes between adjacent sample points. When applied to a linear regression, with income as the independent variable, the regression coefficient depends heavily on the slopes of high-income groups. The weight of the highest income decile may well exceed that of the other nine deciles. This may be undesirable, especially if the regression is used for welfare analysis, because the marginal propensities to consume attributed to the commodities are determined by the high-income groups. The second part of the article proposes alternative estimators, the extended Gini estimators, that enable investigators to control the weighting scheme and to incorporate their social views into the weighting scheme of the estimators     

Asymptotic Inference on Cointegrating Rank in Partial Systems

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.     

Concentration Ellipsoids,Their Planes of Support,and the Linear Regression Model

The relationship between the concentration ellipsoid of a random vector and its planes of support is exploited to provide a geometric derivation and interpretation of existing results for a general form of the linear regression model. In particular, the planes of support whose points of tangency to the ellipsoid are contained in the range (or column space) of the design matrix are the source of all linear unbiased minimum variance estimators. The connection between this idea and estimators based on projections is explored, as is also its use in obtaining and interpreting some existing relative efficiency results.     

Computational and statistical efficiency of semiparametric gls estimators

In this note, we report a dramatic improvement in the computational efficiency of semiparametric generalized least squares(SGLS) estimation. Computation of SGLS estimates no longer presents serious problems with data sets of moderate size. We also correct a numerical error in the standard errors of the SGLS estimates reported in our recent paper in this journal (Horowitz and Neumann, 1987). The corrected standard errors of SGLS are comparable to those we reported for quantile estimates.     

MODELING THE LIFETIME OF LONGITUDINAL ELEMENTS

In the study of the stochastic behaviour of the lifetime of an element as a function of its length, it is often observed that the failure time (or lifetime) decreases as the length increases. In probabilistic terms, such an idea can be expressed as follows. Let T be the lifetime of a specimen of length x, so the survival function, which denotes the probability that an element of length x survives till time t, will be given by S_T (t, x) = P(T > t/α(x), where α(x) is a monotonically decreasing function. In particular, it is often assumed that T has a Weibull distribution. In this paper, we propose a generalization of this Weibull model by assuming that the distribution of T is Generalized gamma (GG). Since the GG model contains the Weibull, Gamma and Lognormal models as special and limiting cases, a GG regression model is an appropriate tool for describing the size effect on the lifetime and for selecting among the embedded models. Maximum likelihood estimates are obtained for the GG regression model with α(x) = cx^b . As a special case this provide an alternative to the usual approach to estimation for the GG distribution which involves reparametrization. Related parametric inference issues are addressed and illustrated using two experimental data sets. Some discussion of censored data is also provided.     

ESTIMATION OF PARAMETERS IN ARFIMA PROCESSES: A SIMULATION STUDY

It is known that, in the presence of short memory components, the estimation of the fractional parameter d in an Autoregressive Fractionally Integrated Moving Average, ARFIMA(p, d, q), process has some difficulties (see [1] Smith, J., Taylor, N. and Yadav, S. 1997. Comparing the bias and misspecification in ARFIMA models. Journal of Time Series Analysis, 18(5): 507–527. [Crossref] , [Google Scholar]). In this paper, we continue the efforts made by Smith et al. [1] Smith, J., Taylor, N. and Yadav, S. 1997. Comparing the bias and misspecification in ARFIMA models. Journal of Time Series Analysis, 18(5): 507–527. [Crossref] , [Google Scholar] and Beveridge and Oickle [2] Beveridge, S. and Oickle, C. 1993. Estimating fractionally integrated time series models. Economics Letters, 43: 137–142.  [Google Scholar] by conducting a simulation study to evaluate the convergence properties of the iterative estimation procedure suggested by Hosking [3] Hosking, J. 1981. Fractional differencing. Biometrika, 68(1): 165–176. [Crossref], [Web of Science ®] , [Google Scholar]. In this context we consider some semiparametric approaches and a parametric method proposed by Fox-Taqqu[4] Fox, R. and Taqqu, M. S. 1986. Large-sample properties of parameter estimates for strongly dependent stationary gaussian time series. The Annals of Statistics, 14(2): 517–532. [Crossref], [Web of Science ®] , [Google Scholar]. We also investigate the method proposed by Robinson [5] Robinson, P. M. 1995a. Log-periodogram regression of time series with long range dependence. The Annals of Statistics, 23(3): 1048–1072. [Crossref], [Web of Science ®] , [Google Scholar] and a modification using the smoothed periodogram function.     

AN IMPROVED COMPOUND ESTIMATOR FOR ROBUST REGRESSION

ABSTRACT

Advances in statistical computing software have led to a substantial increase in the use of ordinary least squares (OLS) regression models in the engineering and applied statistics communities. Empirical evidence suggests that data sets can routinely have 10% or more outliers in many processes. Unfortunately, these outliers typically will render the OLS parameter estimates useless. The OLS diagnostic quantities and graphical plots can reliably identify a few outliers; however, they significantly lose power with increasing dimension and number of outliers. Although there have been recent advances in the methods that detect multiple outliers, improvements are needed in regression estimators that can fit well in the presence of outliers. We introduce a robust regression estimator that performs well regardless of outlier quantity and configuration. Our studies show that the best available estimators are vulnerable when the outliers are extreme in the regressor space (high leverage). Our proposed compound estimator modifies recently published methods with an improved initial estimate and measure of leverage. Extensive performance evaluations indicate that the proposed estimator performs the best and consistently fits the bulk of the data when outliers are present. The estimator, implemented in standard software, provides researchers and practitioners a tool for the model-building process to protect against the severe impact from multiple outliers.     

Performance of Confidence Intervals in Regression Models with Unbalanced One-Fold Nested Error Structures

Abstract

In this article we consider the problem of constructing confidence intervals for a linear regression model with unbalanced nested error structure. A popular approach is the likelihood-based method employed by PROC MIXED of SAS. In this article, we examine the ability of MIXED to produce confidence intervals that maintain the stated confidence coefficient. Our results suggest that intervals for the regression coefficients work well, but intervals for the variance component associated with the primary level cannot be recommended. Accordingly, we propose alternative methods for constructing confidence intervals on the primary level variance component. Computer simulation is used to compare the proposed methods. A numerical example and SAS code are provided to demonstrate the methods.     

BARTLETT CORRECTED LIKELIHOOD RATIO TESTS IN LOCATION-SCALE NONLINEAR MODELS

The paper derives Bartlett corrections for improving the chisquare approximation to the likelihood ratio statistics in a class of location-scale family of distributions, which encompasses the elliptical family of distributions and also asymmetric distributions such as the extreme value distributions. We present, in matrix notation, a Bartlett corrected likelihood ratio statistic for testing that a subset of the nonlinear regression coefficients in this class of models equals a given vector of constants. The formulae derived are simple enough to be used analytically to obtain several Bartlett corrections in a variety of important models. We show that these formulae generalize a number of previously published results. We also present simulation results comparing the sizes and powers of the usual likelihood ratio tests and their Bartlett corrected versions when the scale parameter is considered known and when this parameter is uncorrectly specified.