Predictive Regressions: A Reduced-Bias Estimation Method

In this chapter, we discuss large sample theory that can be applied under conditions that are quite likely to be met in large samples even when the Gauss–Markov conditions are broken. There are two reasons for using large sample theory. First, there may be some problems that corrupt our estimators in small samples but tends to diminish down as the sample gets bigger. Thus, if we cannot get a perfect small sample estimator, we will usually want to choose the one that will be best in large samples. Second, in some circumstances, the theory used to derive the properties of estimators in small samples just does not work, and working out the properties of the estimators can be impossible. This makes it very hard to choose between alternative estimators. In these circumstances we judge different estimators on their “large sample properties” because their “small (or finite) sample properties” are unknown.

This book provides a perspective on a number of approaches to financial modelling and risk management. It examines both theoretical and practical issues. Theoretically, financial risks models are models of a real and a financial “uncertainty”, based on both common and private information and economic theories defining the rules that financial markets comply to. Financial models are thus challenged by their definitions and by a changing financial system fueled by globalization, technology growth, complexity, regulation and the many factors that contribute to rendering financial processes to be continuously questioned and re-assessed. The underlying mathematical foundations of financial risks models provide future guidelines for risk modeling. The book’s chapters provide selective insights and developments that can contribute to better understand the complexity of financial modelling and its ability to bridge financial theories and their practice. Future Perspectives in Risk Models and Finance begins with an extensive outline by Alain Bensoussan et al. of GLM estimation techniques combined with proofs of fundamental results. Applications to static and dynamic models provide a unified approach to the estimation of nonlinear risk models. A second section is concerned with the definition of risks and their management. In particular, Guegan and Hassani review a number of risk models definition emphasizing the importance of bi-modal distributions for financial regulation. An additional chapter provides a review of stress testing and their implications. Nassim Taleb and Sandis provide an anti-fragility approach based on “skin in the game”. To conclude, Raphael Douady discusses the noncyclical CAR (Capital Adequacy Rule) and their effects of aversion of systemic risks. A third section emphasizes analytic financial modelling approaches and techniques. Tapiero and Vallois provide an overview of mathematical systems and their use in financial modeling. These systems span the fundamental Arrow-Debreu framework underlying financial models of complete markets and subsequently, mathematical systems departing from this framework but yet generalizing their approach to dynamic financial models. Explicitly, models based on fractional calculus, on persistence (short memory) and on entropy-based non-extensiveness. Applications of these models are used to define a modeling approach to incomplete financial models and their potential use as a “measure of incompleteness”. Subsequently Bianchi and Pianese provide an extensive overview of multi-fractional models and their important applications to Asset price modeling. Finally, Tapiero and Jinquyi consider the binomial pricing model by discussing the effects of memory on the pricing of asset prices.

factors. This makes it sound like the White’s matrix is the model. It is not: it is just a weighting applied to the variance-covariance matrix of the coefficients of the model, and it is derived from the regression residuals, not from the non-climatic subset of the explanatory variables as Benestad says. He then adds: Ordinary Least Squares (OLS) models may produce biased estimates, and the presence of heteroskedasticity in the residuals may be an indication of model misspecification such as incorrect functional form. The SHAZAM model therefore ought to give unbiased estimates of the coefficients describing the relationship between a number of factors and the temperature trend. Using OLS in the presence of heteroskedasticity does not cause biased parameter estimates, nor does using the White’s matrix adjustment change the functional form. Heteroskedasticity can produce inefficient estimates in small samples (i.e. the estimated variance can be too high). The correction applied has nothing to do with bias or functional form. These items are all discussed in the Kmenta book referenced in the paper itself.

Modeling of Social Economic Systems

Available methods for dealing with autocorrelated disturbanecs are unsatisfactory. They are computationally cumbersome and lead to estimators that have only weak asymptotic properties. Maximum likelihood estimation of all parameters is theoretically preferable, but has been unpopular due to the practical difficulties of numerical optimization in a multidimensional space. In this paper it is shown that the computational aspect of maximum likelihood estimation can be greatly simplified. The numerical search is confined to the interval (— 1, 1) of the autocorrelation parameter. The method is applicable to a single static equation as well as to autoregressive models with one or more equations. Some sampling experiments demonstrate the superiority of the maximum likelihood estimator over ordinary least squares, generalized least squares, and one other estimator in small samples.

Measurement error is a continuing concern for sociologists. A particularly nagging problem has been estimating regression coefficients of multiplicative effects when the component variables contain measurement error. Recently, Heise (1986) presented a corrected estimator for multiplicative terms containing measurement error. The research presented here extends Heise's work, and examines the use of an alternate corrected/constrained estimator proposed by Fuller (1980, 1987). The results of a Monte Carlo simulating give some support for Heise's findings, while providing further explanation for the behavior of estimators. The simulation focuses on small samples (n = 60 and n = 90), and examines the impact of different levels of measurement reliability on error correction procedures. Estimators are compared on the basis of bias, variance, root mean squared error, and singlesample inference accuracy. OLS is included as a benchmark. Results indicated only modest improvements over OLS in estimation using the corrected/constrained estimator, and some hazards in using the simpler corrected estimator in small samples. OLS is judged to be fairly robust and predictable in its inaccuracy.

For a commonly occurring pattern of missing data, estimators of regression coefficients are derived by a non-likelihood method. The small-sample properties are investigated for the case of normality assumptions. The estimators are shown to be unbiased, exact small-sample variance formulae are derived, comparisons are made with ordinary least-squares estimators and it is demonstrated that the estimators can be more efficient than maximum-likelihood estimators in small samples.

A DCC-type approach for realized covariance modeling with score-driven dynamics

The aim of this paper is to demonstrate the impact of high leverage observations on the performances of prominent and popular Heteroskedasticity-Consistent Covariance Matrix Estimators (HCCMEs) with the help of computer simulation. Firstly, we figure out high leverage observations, then remove them and recalculate the HCCMEs without these observations in order to compare the HCCME performances with and without high leverage points. We identify high leverage observations with the Minimum Covariance Determinant (MCD). We select from among different covariates and disturbance term variances from the related literature in simulation runs in order to compare the percentage difference between the expected value of the HCCME and true covariance matrix as well as the symmetric loss function. Our results revealed that the elimination of high leverage (high MCD distance) observations had improved the HCCME performances considerably and under some settings substantially, depending on the degree of leverage. We hope our theoretical findings will be benefited for practical purposes in applications.

Time-Series Estimation of Structural Import Demand Equations: A Cross-Country Analysis

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honor¨¦ estimator, Hansen¡¯s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honor¨¦ estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honor¨¦ estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.

Econometric modelling in finance and risk management: An overview

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

Neurite orientation dispersion and density imaging (NODDI) estimates microstructural properties of brain tissue relating to the organisation and processing capacity of neurites, which are essential elements for neuronal communication. Descriptive statistics of NODDI tissue metrics are commonly analyzed in regions-of-interest (ROI) to identify brain-phenotype associations. Here, the conventional method to calculate the ROI mean weights all voxels equally. However, this produces biased estimates in the presence of CSF partial volume. This study introduces the tissue-weighted mean, which calculates the mean NODDI metric across the tissue within an ROI, utilising the tissue fraction estimate from NODDI to reduce estimation bias. We demonstrate the proposed mean in a study of white matter abnormalities in young onset Alzheimer's disease (YOAD). Results show the conventional mean induces significant bias that correlates with CSF partial volume, primarily affecting periventricular regions and more so in YOAD subjects than in healthy controls. Due to the differential extent of bias between healthy controls and YOAD subjects, the conventional mean under- or over-estimated the effect size for group differences in many ROIs. This demonstrates the importance of using the correct estimation procedure when inferring group differences in studies where the extent of CSF partial volume differs between groups. These findings are robust across different acquisition and processing conditions. Bias persists in ROIs at higher image resolution, as demonstrated using data obtained from the third phase of the Alzheimer's disease neuroimaging initiative (ADNI); and when performing ROI analysis in template space. This suggests that conventional ROI means of NODDI metrics are biased estimates under most contemporary experimental conditions, the correction of which requires the proposed tissue-weighted mean. The tissue-weighted mean produces accurate estimates of ROI means and group differences when ROIs contain voxels with CSF partial volume. In addition to NODDI, the technique can be applied to other multi-compartment models that account for CSF partial volume, such as the free water elimination method. We expect the technique to help generate new insights into normal and abnormal variation in tissue microstructure of regions typically confounded by CSF partial volume, such as those in individuals with larger ventricles due to atrophy associated with neurodegenerative disease.

This research consists of an introduction and four independent papers (though related) on the growth determinants of Ethiopian air transport in general and efficiency analysis of Ethiopian airports’ in particular. This introduction also highlights the concept of the research and provides an overview of the aviation sector’s performance including the rationale for the study and the contribution that the four papers make to existing literature on air transport. These four distinct studies use different model specifications, estimations and ranking of the performance of the airlines and airports. The differences in the airports’ performance are attributed to the objectives of the airports, data availability, the structure and the model’s underlying assumptions. To begin with, the first paper uses a cost minimization or input oriented approach for analyzing the cost efficiency of Ethiopian airports using the panel data stochastic frontier approach. It uses the time-invariant fixed effects, time-variant true fixed effects, specifying and estimating the time variant and time invariant approaches in (Kumbhakar et al., A practitioner's guide to stochastic frontier analysis using Stata (No, Cambridge University Press, BOOK), 2015) and (Battese and Coelli, Empirical Economics 20:325–332, 1995) models. The empirical findings elaborated international airports having higher passenger volumes attributing to lower cost efficiency compared to domestic airports. In other words, maximum cost efficiency was found at airports with low levels of services and facilities as compared to airports with better services and advanced facilities. The findings also show that airports having better infrastructure and airport specific facilities and services will continue to be inefficient compared to those having lower levels of facilities and services. Ethiopian airports should therefore introduce cost saving approaches based on reliable traffic forecasts. The second paper uses an output maximization or output oriented approach for analyzing the production efficiency of domestic and international Ethiopian airports using the stochastic frontier panel data approach for the period 2002–17. This study examines the technical efficiency of Ethiopian airports over time. It specifies (Kumbhakar et al., J Prod Anal 41:321–337, 2014) maximum likelihood method for separating persistent time-invariant inefficiency and transitory time-varying inefficiency from an unobservable individual effects. It also applies the fixed effects model and distance technical inefficiency using (Battese and Coelli, Empirical Economics 20:325–332, 1995) approach for a comparison. The findings indicate that most Ethiopian airports have relatively low technical efficiency which is required for developing competitive strategies that can attract more air traffic volumes and generate higher revenues. Classic customer handling, policy, and incentive schemes should therefore be introduced to increase passenger demand. Private and low-cost carriers should be encouraged to operate using the airports’ services. The third paper uses a factor demand approach and focuses on Ethiopian airports’ labor use efficiency by analyzing the panel data stochastic frontier input requirement function. It also specifies the (Kumbhakar and Heshmati, Am J Agr Econ 77:660–674, 1995) model and maximum likelihood estimation techniques of separating persistent time-invariant inefficiency and transitory time-varying inefficiency for estimating labor use efficiency of Ethiopian airports. The findings show that domestic airports are relatively better performing as compared to international airports. Similarly, most airports experience high persistent inefficiencies compared to transitory inefficiencies. This implies a need for taking lessons in the deployment of labor resources and introducing minimum labor requirement standards at all airports. The final paper examines the growth determinants of the Ethiopian air transport sector by testing the variables’ significance and the causality of the three separate but interdependent activity equations covering the period 1988–2018. Ethiopian Airlines’ passenger growth determinants, other airlines’ passenger growth determinants, and the determinants of air freight cargo growth. In this research, ordinary least squares, a seemingly unrelated regression estimation, and autoregressive distributed lag modelling approaches are applied to investigate the short-run and long-run causal relationships between air transport growth and some selected macroeconomic variables. The major findings show that most variables are statistically significant both in the short-run and long-run. Similarly, their respective error correction models are also significant and negative as expected implying strong and significant causal relationships between the short-run and long-run models. The econometric results of some specific variables vary which is attributed to high dependency on imported goods and services, absence of alternative passenger air transport systems, and steadily growing aggregate demand for air transport. The government should therefore pay due attention to stable macroeconomic growth and airlines also should have long-run strategic planning for reducing the effects of any internal and external shocks to the economy.KeywordsEthiopian airlinesAviation industryAir transportAirportsEfficiencyGrowthLabor useEthiopiaJEL ClassificationL93J01O4D24