The standardized effect of a compound of dummy variables or polynomial terms

A method is proposed to obtain standardized regression coefficients for composite variables made up of dummy variables or polynomial terms. The method to be described enables the researcher to compare the effect of the composite variable with the effects of other predictor variables. Forming a composite variable is particularly useful in polynomial regression where individual regression coefficients are hard to interpret. A second application is assessing the impact of a compound of dummy variables. An empirical example dealing with the curvilinear relationship between church involvement and prejudice is used to illustrate the approach.     

A comparative study of finite sample properties of band spectrum regression estimators

Monte Carlo methods are used to compared the small sample properties of several approaches to seasonal adjustment when the objective is to estimate regression coefficients. The methods compared are band spectrum regression, the dummy variable method and the moving average method. The results seem to indicate that band spectrum regression will have superior small sample properties compared with the dummy variable method, which again seemto be preferable to ordinary least squares and to the moving average method.     

Use of minimum risk approach in the estimation of regression models with missing observations

This article considers a linear regression model with some missing observations on the response variable and presents two estimators of regression coefficients employing the approach of minimum risk estimation. Small disturbance asymptotic properties of these estimators along with the traditional unbiased estimator are analyzed and conditions, that are easy to check in practice, for the superiority of one estimator over the other are derived. Received May 2001     

Accounting for Macroeconomic Influences on the Firm

Accounting based measures of exposure to macroeconomic shocks in exchange rates, interest rates and inflation do not capture the economic effects on the corporation of such shocks. We suggest measures that conceptually are coefficients in a multiple regression. The coefficients capture the sensitivity of a firm's real value or cash flows to unanticipated changes in each variable holding other variables constant. Information about such sensitivity coefficients would enable external stakeholders to distinguish between risk caused by firm-specific factors on the one hand and macroeconomic factors on the other. Scenario analysis is discussed as an alternative method for evaluating sensitivity coefficients. Information requirements for scenario and regression analysis are compared. Sensitivity coefficients can be used to identify a firm's functional currency or currency basket in which cash flows are independent of exchange rate changes. An example built on an actual case in Appendix demonstrates how insights can be gained from estimates of the suggested exposure measures.     

Endogenous selection or treatment model estimation

In a sample selection or treatment effects model, common unobservables may affect both the outcome and the probability of selection in unknown ways. This paper shows that the distribution function of potential outcomes, conditional on covariates, can be identified given an observed variable V$V$ that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes. Selection model estimators based on this identification are provided, which take the form of simple weighted averages, GMM, or two stage least squares. These estimators permit endogenous and mismeasured regressors. Empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model.     

Local structural quantile effects in a model with a nonseparable control variable

I consider a semiparametric version of the nonseparable triangular model of Chesher [Chesher, A., 2003. Identification in nonseparable models. Econometrica 71, 1405–1441]. The proposed model is linear in coefficients, where the coefficients are unknown functions of unobserved latent variables. Using a control variable idea and quantile regression methods, I propose a simple two-step estimator for the coefficients evaluated at particular values of the latent variables. Under the condition that the instruments are locally relevant (i.e. they affect a particular conditional quantile of interest of the endogenous variable) I establish consistency and asymptotic normality. Simulation experiments confirm the theoretical results.     

A fully Bayesian tracking algorithm for mitigating disparate prediction misclassification

We develop a fully Bayesian tracking algorithm with the purpose of providing classification prediction results that are unbiased when applied uniformly to individuals with differing sensitive variable values, e.g., of different races, sexes, etc. Here, we consider bias in the form of group-level differences in false prediction rates between the different sensitive variable groups. Given that the method is fully Bayesian, it is well suited for situations where group parameters or regression coefficients are dynamic quantities. We illustrate our method, in comparison to others, on simulated datasets and two real-world datasets.     

Estimating regression coefficients from survey data by asymptotic design-cum-model based approach

Postulating a linear regression of a variable of interest on an auxiliary variable with values of the latter known for all units of a survey population, we consider appropriate ways of choosing a sample and estimating the regression parameters. Recalling Thomsen’s (1978) results on non-existence of ‘design-cum-model’ based minimum variance unbiased estimators of regression coefficients we apply Brewer’s (1979) ‘asymptotic’ analysis to derive ‘asymptotic-design-cummodel’ based optimal estimators assuming large population and sample sizes. A variance estimation procedure is also proposed.     

Substituut-variabelen in correlatieberekingen

The recently repeated assertion that in correlation analysis it makes little difference whether one variable (x₂) is used instead of another one (x₃), provided the coefficient of correlation (r₂₃) between x₂ and x₃ is high, is scrutinized.
To that purpose the ranges of coefficients of correlation with respect to the substitute variable are expressed in formula 3. Moreover, by way of example, extreme values of coefficients of simple correlation (r₁₃ and r₃₄), of multiple correlation (R_1.34 and R_3.14) and of regression (α₁₃ and α₁₄, α₃₁ and α₃₄) relating to the substitute variable, are calculated on the basis of empirical values of coefficients of simple correlation relating to the substituted and the remaining variables.
The outcome of those calculations are summarized in the tables 1 and 3, and in the graph.
Table 1 presents ranges of r₁₃ for given values of r₁₂ and r₂₃, table 3 shows extreme values of coefficients of single and multiple correlation and regression in case an additional variable x₄ is introduced and r₁₂, r₁₄, r₂₄ and r₂₃ are given. The graph shows an ellipse as the boundary of the inner closed domain of compatible values of r₁₃ and r₃₄.
Those results clearly indicate the need for caution in substituting one variable by another.     

Efficient estimation of limited dependent variable models with endogenous explanatory variables

This paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables. General results on asymptotic efficiency of two-stage and Amemiya GLS estimators are derived and used to obtain a simple, asymptotically efficient estimator of the structural coefficients. This estimator can be calculated by applying GLS to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables. It is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi-square method.     

Polynomial approximations in cross-sectional models

The time-series distributed lag techniques of econometrics can be usefully applied to cross-sectional, spatial and cross-section time-series situations. The application is perfectly natural in cross-section, time-series models when regression coefficients evolve systematically as the cross-section grouping variable changes. The evolution of such coefficients lends itself to polynomial approximation or more general smoothing restrictions. These ideas are not new, Gersovitz and McKinnon (1978) and Trivedi and Lee (1981) providing two of the earliest applications of cross-equation smoothing techniques. However, their applications were in the context of coefficient variation due to seasonal changes and this may account for the non-diffusion of these techniques. The approach here is illustrated in the context of age-specific household formation equations based on census data, using Almon polynomials when the regression coefficients vary systematically by age group. A second application is provided, using spatial data, explaining the incidence of crime, by region; using polynomial and geometric smoothing to model distance declining regional effects.     

The use of dummy variables to compute predictions,prediction errors,and confidence intervals

This paper presents a method for computing predictions, prediction error variances, and confidence intervals, which can be implemented with any regression program. It demonstrates that a regression estimated for an augmented data set, obtained by (1) combining n sample points with r forecast points, and (2) including r dummy variables (each equalling one only for the corresponding forecast point), will yield r dummy variable coefficients and variances which equal the corresponding prediction errors and prediction error variances. Since most programs lack special routines to calculate these magnitudes, while manual computation is cumbersome, the proposed method is of considerable practical value.     

Censored regression quantiles with endogenous regressors

This paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous (and continuously distributed) and instrumental variables are available for them. A “distributional exclusion” restriction is imposed on the unobservable errors, whose conditional distribution is assumed to depend on the regressors and instruments only through a lower-dimensional “control variable,” here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments. This assumption, which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable, is used to motivate a two-stage estimator of the censored regression coefficients. In the first stage, the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated, as are the first-stage reduced-form residuals to be used as control variables. The second-stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors, using only pairs of observations for which both estimated quantiles are positive (i.e., in the uncensored region) and the corresponding difference in estimated control variables is small. The paper gives the form of the asymptotic distribution for the proposed estimator, and discusses how it compares to similar estimators for alternative models.     

Control variate method for stationary processes

The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE.     

Zur Bewertung von Schätzungen bei der gewöhnlichen Regressionsanalyse

Summary In this paper the multiple regression analysis is considered. The regression coefficients obtained by this method are examined with respect to their numerical stability. With simple stability considerations a criteria is given which can be used if an estimator is to evaluate.     

Reparameterized inverse gamma regression models with varying precision

In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model.     

On direction of dependence

Under the assumption of the existence of linear relationship between two random variables, new formulas are introduced to express the coefficient of correlation. One of these formulas, the fourth power of the correlation coefficient is used to determine the direction of dependency between two random variables. Also an interpretation of the correlation coefficient as an asymmetric function of kurtosis coefficient and skewness coefficient of dependent variable and independent variable is provided. In the absent of the intercept in linear regression, the correlation coefficient is also expressed as a ratio of coefficients of variation between independent and dependent variables.     

A Caution Regarding Rules of Thumb for Variance Inflation Factors

The Variance Inflation Factor (VIF) and tolerance are both widely used measures of the degree of multi-collinearity of the ith independent variable with the other independent variables in a regression model. Unfortunately, several rules of thumb – most commonly the rule of 10 – associated with VIF are regarded by many practitioners as a sign of severe or serious multi-collinearity (this rule appears in both scholarly articles and advanced statistical textbooks). When VIF reaches these threshold values researchers often attempt to reduce the collinearity by eliminating one or more variables from their analysis; using Ridge Regression to analyze their data; or combining two or more independent variables into a single index. These techniques for curing problems associated with multi-collinearity can create problems more serious than those they solve. Because of this, we examine these rules of thumb and find that threshold values of the VIF (and tolerance) need to be evaluated in the context of several other factors that influence the variance of regression coefficients. Values of the VIF of 10, 20, 40, or even higher do not, by themselves, discount the results of regression analyses, call for the elimination of one or more independent variables from the analysis, suggest the use of ridge regression, or require combining of independent variable into a single index.     

Total Labour Requirements and Value Added Productivity of Labour in the Process of Economic Development

When the inverse of the value added productivity of labour is regressed on total labour requirements (which is equivalent to labour values), a significant relationship is obtained. This indicates that the value added productivity of labour can be explained by total labour requirements (labour values). The mean value of the regression coefficients is about 1.7. The regression coefficients have a tendency to increase during the process of rapid economic development and to decrease afterwards. Such movements are explained by value added linkages. This study is based on input–output analysis, where total labour requirements per monetary unit of output and the value added productivity of labour are calculated for each of 24 industries in Japan, Korea and USA, every 5 years between 1960 to 1985.     

Bayesian estimation of the switching regression model with autocorrelated errors

In this paper, we make a Bayesian analysis of the switching (two-phase) regression model when the subset of the regression coefficients shifts and the error terms are generated by a first-order autoregressive process. The posterior distributions of the shift point and other parameters are derived, and some numerical studies are performed. From the numerical studies, we see that the shift point is accurately estimated when the shift of the regression coefficient is relatively large. Also, the conditional distributions of the autocorrelation and regression coefficients on the shift point are compared with the marginal ones.