Convergence of information,random variables and noise

Random variables such as state-dependent prices often convey information while entering directly into a decision environment. To understand the convergence properties of behavior based on such random variables, the function mapping any random variable to the information it generates is examined. With respect to convergence in probability of random variables, the information map is continuous with respect to pointwise convergence of information only at completely revealing random variables. Continuity holds when the information map is restricted to any subset of random variables to which the same smooth independent term has been added. Relationships between convergence in distribution of perturbed random variables and convergence in distribution of conditional expectations are also studied.     

Multivariate analysis of coffee images: A study in the simultaneous display of multivariate quantitative and qualitative variables for several assessors

The paper discusses a small image study in which seven assessors judge nine brands of coffee in terms of six quantitative variables and five categorical variables. Generalised Procrustes Analysis and Generalised Biplots are combined to display simultaneously information on the brands and on both quantitative and categorical variables. An outline is given of the methodology.     

Structural equation modeling with ordinal variables: a large sample case study

In the behavioral sciences, response variables are often non-continuous, ordinal variables. Conventional structural equation models (SEMs) have been generalized to accommodate ordinal responses. In this study, three different estimation methods on real data were performed with ordinal variables. Empirical results obtained from the different estimation methods on given real large sample educational data were investigated and compared to recent simulation results. As a result, even very large sample is available, model estimations and fits for ordinal data are affected from inconvenient estimation methods thus it is concluded that asymptotically distribution free estimation method specialized for ordinal variables is more convenient way to model ordinal variables.     

Macroeconomic forecasting using structural factor analysis

The use of a small number of underlying factors to summarize the information from a much larger set of information variables is one of the new frontiers in forecasting. In prior work, the estimated factors have not usually had a structural interpretation and the factors have not been chosen on a theoretical basis. In this paper we propose several variants of a general structural factor forecasting model, and use these to forecast certain key macroeconomic variables. We make the choice of factors more structurally meaningful by estimating factors from subsets of information variables, where these variables can be assigned to subsets on the basis of economic theory. We compare the forecasting performance of the structural factor forecasting model with that of a univariate AR model, a standard VAR model, and some non-structural factor forecasting models. The results suggest that our structural factor forecasting model performs significantly better in forecasting real activity variables, especially at short horizons.     

Influence of freight transport purchasing processes on logistical variables related to CO2 emissions: a case study in Sweden

Emissions from freight transport stem from logistical variables such as vehicle utilisation, fuel efficiency, and distance. The purpose is to determine how shippers’ freight transport purchasing processes influence logistical variables. A multiple case study of freight transport purchasing processes was conducted, based on interviews with transport purchasers and providers. Three causes of influence of shippers’ purchasing processes on logistical variables were found: specific requirements, network structure of transport providers, and scope of contract. Specifications by purchasers, especially time requirements, influence several logistical variables (‘mode used’, ‘length of haul’, ‘load factor’, ‘empty running’, and ‘fuel efficiency’). This paper clarifies the implications of transport purchasing on CO₂ emissions in terms of logistical variables, which are understood in transportation research and practice. It describes the effects of shippers’ requirements on transport providers’ execution of transport. The results provide a foundation for shippers to discuss their influence on logistical variables with transport providers.     

Bias of OLS Estimators due to Exclusion of Relevant Variables and Inclusion of Irrelevant Variables

In this paper, I discuss three issues related to bias of OLS estimators in a general multivariate setting. First, I discuss the bias that arises from omitting relevant variables. I offer a geometric interpretation of such bias and derive sufficient conditions in terms of sign restrictions that allows us to determine the direction of bias. Second, I show that inclusion of some omitted variables will not necessarily reduce the magnitude of bias as long as some others remain omitted. Third, I show that inclusion of irrelevant variables in a model with omitted variables can also have an impact on the bias of OLS estimators. I use a running example of a simple wage regression to illustrate my arguments.     

Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables

The aim of this paper is to convey to a wider audience of applied statisticians that nonparametric (matching) estimation methods can be a very convenient tool to overcome problems with endogenous control variables. In empirical research one is often interested in the causal effect of a variable X on some outcome variable Y . With observational data, i.e. in the absence of random assignment, the correlation between X and Y generally does not reflect the treatment effect but is confounded by differences in observed and unobserved characteristics. Econometricians often use two different approaches to overcome this problem of confounding by other characteristics. First, controlling for observed characteristics, often referred to as selection on observables, or instrumental variables regression, usually with additional control variables. Instrumental variables estimation is probably the most important estimator in applied work. In many applications, these control variables are themselves correlated with the error term, making ordinary least squares and two-stage least squares inconsistent. The usual solution is to search for additional instrumental variables for these endogenous control variables, which is often difficult. We argue that nonparametric methods help to reduce the number of instruments needed. In fact, we need only one instrument whereas with conventional approaches one may need two, three or even more instruments for consistency. Nonparametric matching estimators permit     consistent estimation without the need for (additional) instrumental variables and permit arbitrary functional forms and treatment effect heterogeneity.     

Configurational demographic predictors of work–nonwork satisfaction

Contemporary work–life balance research tends to treat demographic variables as moderators, grouping variables, or control variables influencing work and nonwork satisfaction. Yet earlier theories were premised on the assumption that they are, in fact, predictors of work and nonwork satisfaction even though those assumptions have not yet been tested empirically. Drawing on an Australian study comprising 798 white‐collar employees and using a fuzzy‐set qualitative comparative analysis technique, we investigate demographic variables as potential configurational predictors affecting work–nonwork satisfaction, defined as a combination of work satisfaction and nonwork satisfaction. The analysis revealed different scenarios and specific patterns between configurational solution terms leading to work–nonwork satisfaction. Employment status and age of children (specifically age differences between children) were the most important demographic variables influencing employees' work–nonwork satisfaction.     

A Better Understanding of Granger Causality Analysis: A Big Data Environment

This paper aims to provide a better understanding of the causal structure in a multivariate time series by introducing several statistical procedures for testing indirect and spurious causal effects. In practice, detecting these effects is a complicated task, since the auxiliary variables that transmit/induce indirect/spurious causality are very often unknown. The availability of hundreds of economic variables makes this task even more difficult since it is generally infeasible to find the appropriate auxiliary variables among all the available ones. In addition, including hundreds of variables and their lags in a regression equation is technically difficult. The paper proposes several statistical procedures to test for the presence of indirect/spurious causality based on big data analysis. Furthermore, it suggests an identification procedure to find the variables that transmit/induce the indirect/spurious causality. Finally, it provides an empirical application where 135 economic variables were used to study a possible indirect causality from money/credit to income.     

On variable ordination of modified Cholesky decomposition for estimating time-varying covariance matrices

Estimating time-varying covariance matrices of the vector of interest is challenging both computationally and statistically due to a large number of constrained parameters. In this work, we consider an order-averaged Cholesky-log-GARCH (OA-CLGARCH) model for estimating time-varying covariance matrices through the orthogonal transformations of the vector based on the modified Cholesky decomposition. The proposed method is to transform the vector at each time as a linear transformation of uncorrelated latent variables and then to use simple univariate GARCH models to model them separately. But the modified Cholesky decomposition relies on a given order of variables, which is often not available, to sequentially orthogonalize the variables. The proposed method develops an order-averaged strategy for the Cholesky-GARCH method to alleviate the effect of order of variables. The merits of the proposed method are illustrated through simulations and real-data studies.     

Identification with latent variables

This is an essay on a unified approach to the identifiability problem in static models with and without hidden endogenous variables. As is well known, when some of these variables are unobserved, the prior information requirements for models when all endogenous variables are observed, are still there. In addition, extra prior information that takes the place of the means and covariances of the missing variables will have to be supplied directly or indirectly by the statistical researcher. In the paper we characterize the quality and quantity of the required information for the general linear static model and apply it when the model is i) an econometric demand and supply model with missing observations on the quantity transacted, ii) a factor analysis model with observed characteristics of the test takers and iii) a LISREL Model without fixed exogenous variables. With unknown true parameters, the exact rank conditions are seldom verifiable but we do recommend an implementable check-list that is adequate for almost all parameters.     

Remarks on the strong law of large numbers for a triangular array of associated random variables

A strong law of large numbers for a triangular array of strictly stationary associated random variables is proved. It is used to derive the pointwise strong consistency of kernel type density estimator of the one-dimensional marginal density function of a strictly stationary sequence of associated random variables, and to obtain an improved version of a result by Van Ryzin (1969) on the strong consistency of density estimator for a sequence of independent and identically distributed random variables.     

Dynamics between patent latent variables and patent price

This paper focuses on studying the relationship between patent latent variables and patent price. From the existing literature, seven patent latent variables, namely age, generality, originality, foreign filings, technology field, forward citations, and backward citations were identified as having an influence on patent value. We used Ocean Tomo's patent auction price data in this study. We transformed the price and the predictor variables (excluding the dummy variables) to its logarithmic value. The OLS estimates revealed that forward citations and foreign filings were positively correlated to price. Both the variables jointly explained 14.79% of the variance in patent pricing. We did not find sufficient evidence to come up with any definite conclusions on the relationship between price and the variables such as age, technology field, generality, backward citations and originality. The Heckman two-stage sample selection model was used to test for selection bias.     

Sequential estimate for linear regression models with uncertain number of effective variables

As a result of novel data collection technologies, it is now common to encounter data in which the number of explanatory variables collected is large, while the number of variables that actually contribute to the model remains small. Thus, a method that can identify those variables with impact on the model without inferring other noneffective ones will make analysis much more efficient. Many methods are proposed to resolve the model selection problems under such circumstances, however, it is still unknown how large a sample size is sufficient to identify those “effective” variables. In this paper, we apply sequential sampling method so that the effective variables can be identified efficiently, and the sampling is stopped as soon as the “effective” variables are identified and their corresponding regression coefficients are estimated with satisfactory accuracy, which is new to sequential estimation. Both fixed and adaptive designs are considered. The asymptotic properties of estimates of the number of effective variables and their coefficients are established, and the proposed sequential estimation procedure is shown to be asymptotically optimal. Simulation studies are conducted to illustrate the performance of the proposed estimation method, and a diabetes data set is used as an example.     

Which covariates should be controlled in propensity score matching? Evidence from a simulation study

Propensity score matching is a widely‐used method to measure the effect of a treatment in social as well as medicine sciences. An important issue in propensity score matching is how to select conditioning variables in estimation of the propensity scores. It is commonly mentioned that variables which affect both program participation and outcomes are selected. Using Monte Carlo simulation, this paper shows that efficiency in estimation of the Average Treatment Effect on the Treated can be gained if all the available observed variables in the outcome equation are included in the estimation of propensity scores. This result still holds in the presence of non‐sampling errors in the observed control variables.     

Modeling Criminal Activity in an Area in Economic Decline: Local Economic Conditions Are a Major Factor in Local Property Crimes

A bstract . A multi-factor model includes economic, apprehension, seasonal a n d plant closing variables as the explanatory regressors and crimes against property as the dependent variable. Different lag structures were used on the explanatory variables such as an Almon distributed lag of a second degree polynominal nature and the lagging of the dependent variable by one quarter so that the model would more closely approximate the environment being considered. The results suggest a definite seasonal pattern in crimes against property, and the economic variables measuring local, not national, conditions, appear to be more significant regressors than any other explanatory variables.     

The Ordinal Controversy Revisited

We present a discussion of the different dimensions of the ongoing controversy about the analysis of ordinal variables. The source of this controversy is traced to the earliest possible stage, measurement theory. Three major approaches in analyzing ordinal variables, called the non-parametric, the parametric, and the underlying variable approach, are identified and the merits and drawbacks of each of these approaches are pointed out. We show that the controversy on the exact definition of an ordinal variable causes problems with regard to defining ordinal association, and therefore to the interpretation of many recently designed models for ordinal variables, e.g., structure equation models using polychoric correlations, latent class models and ordinal response models. We conclude that the discussion with regard to ordinal variable modeling can only be fruitful if one makes a distinction between different types of ordinal variables. Five types of ordinal variables were identified. The problems concerning the analysis of these five types of ordinal variables are solved in some cases and remain a problem for others.     

Consistent estimation of correlations between observed interval variables with skewed distributions

Departures from multinormality due to skewness in observed distributions may result in inconsistent estimates of product-moment correlations between interval variables. Therefore, the robustness of the product-moment correlation estimator against skewness in the distributions of sample data on interval variables has been investigated. This estimator is robust against skewness of maximally about 1 in absolute value. If the observed distributions have larger skewnesses, the sample data on interval variables may be redistributed over normally distributed discrete variables with 10 categories each. The estimated polychoric correlations between these discrete variables represent consistent estimates of the product-moment correlations between the original interval variables in the population.     

Target arson: Update 1991 a study of selected old and new variables

The purpose of this study is to replicate and extend earlier studies on the impact of economic and sociological variables upon the incidence of arson fires and losses. The data used in this study covered the period from 1960 to 1988. Initially, a total of 180 variables classified generally as either economic or sociological were chosen for inclusion in the study. These variables were selected based upon their inclusion in other studies in which arson is investigated or upon literature suggesting that a variable is related to arson. Fourteen variables were found to have a significant relationship with the incidence of arson fires and losses. Implications for various individuals and government agencies are discussed.