Econometrics, Volume 8, Issue 1 (March 2020) – 11 articles

This work describes a versatile and readily-deployable sensitivity analysis of an ordinary least squares (OLS) inference with respect to possible endogeneity in the explanatory variables of the usual k-variate linear multiple regression model. This sensitivity analysis is based on a derivation of the sampling distribution of the OLS parameter estimator, extended to the setting where some, or all, of the explanatory variables are endogenous. In exchange for restricting attention to possible endogeneity which is solely linear in nature—the most typical case—no additional model assumptions must be made, beyond the usual ones for a model with stochastic regressors. The sensitivity analysis quantifies the sensitivity of hypothesis test rejection p-values and/or estimated confidence intervals to such endogeneity, enabling an informed judgment as to whether any selected inference is “robust” versus “fragile.” The usefulness of this sensitivity analysis—as a “screen” for potential endogeneity issues—is illustrated with an example from the empirical growth literature. This example is extended to an extremely large sample, so as to illustrate how this sensitivity analysis can be applied to parameter confidence intervals in the context of massive datasets, as in “big data”. Full article

A factor model based covariance matrix is used to build a new form of Mahalanobis distance. The distribution and relative properties of the new Mahalanobis distances are derived. A new type of Mahalanobis distance based on the separated part of the factor model is defined. Contamination effects of outliers detected by the new defined Mahalanobis distances are also investigated. An empirical example indicates that the new proposed separated type of Mahalanobis distances predominate the original sample Mahalanobis distance. Full article

The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context. Full article

We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus–Miłoś family of inequality indices for ordered response data. We use Monte Carlo experiments to compare the empirical size and statistical power of asymptotic inference and the Studentized bootstrap test. In a broad variety of settings, both tests are found to have similar rejection probabilities of true null hypotheses, and similar power. Nonetheless, the asymptotic test remains correctly sized in the presence of certain types of severe class imbalances exhibiting very low or very high levels of inequality, whereas the bootstrap test becomes somewhat oversized in these extreme settings. Full article

Functional data is a common and important type in econometrics and has been easier and easier to collect in the big data era. To improve estimation accuracy and reduce forecast risks with functional data, in this paper, we propose a novel cross-validation model averaging method for generalized functional linear model where the scalar response variable is related to a random function predictor by a link function. We establish asymptotic theoretical result on the optimality of the weights selected by our method when the true model is not in the candidate model set. Our simulations show that the proposed method often performs better than the commonly used model selection and averaging methods. We also apply the proposed method to Beijing second-hand house price data. Full article

We provide a general overview of Bayesian model averaging (BMA) along with the concept of jointness. We then describe the relative merits and attractiveness of the newest BMA software package, BMS, available in the statistical language R to implement a BMA exercise. BMS provides the user a wide range of customizable priors for conducting a BMA exercise, provides ample graphs to visualize results, and offers several alternative model search mechanisms. We also provide an application of the BMS package to equity premia and describe a simple function that can easily ascertain jointness measures of covariates and integrates with the BMS package. Full article

Although a wide array of stochastic dominance tests exist for poverty measurement and identification, they assume the income distributions have independent poverty lines or a common absolute (fixed) poverty line. We propose a stochastic dominance test for comparing income distributions up to a common relative poverty line (i.e., some fraction of the pooled median). A Monte Carlo study demonstrates its superior performance over existing methods in terms of power. The test is then applied to some Canadian household survey data for illustration. Full article

Large-dimensional dynamic factor models and dynamic stochastic general equilibrium models, both widely used in empirical macroeconomics, deal with singular stochastic vectors, i.e., vectors of dimension r which are driven by a q-dimensional white noise, with $q<r$ . The present paper studies cointegration and error correction representations for an $I\left(1\right)$ singular stochastic vector ${\mathbf{y}}_t$ . It is easily seen that ${\mathbf{y}}_t$ is necessarily cointegrated with cointegrating rank $c\ge r-q$ . Our contributions are: (i) we generalize Johansen’s proof of the Granger representation theorem to $I\left(1\right)$ singular vectors under the assumption that ${\mathbf{y}}_t$ has rational spectral density; (ii) using recent results on singular vectors by Anderson and Deistler, we prove that for generic values of the parameters the autoregressive representation of ${\mathbf{y}}_t$ has a finite-degree polynomial. The relationship between the cointegration of the factors and the cointegration of the observable variables in a large-dimensional factor model is also discussed. Full article

The Japanese candlesticks’ technique is one of the well-known graphic methods of dynamic analysis of securities. If we apply Japanese candlesticks for the analysis of high-frequency financial data, then we need a numerical representation of any Japanese candlestick. Kacprzak et al. have proposed to represent Japanese candlesticks by ordered fuzzy numbers introduced by Kosiński and his cooperators. For some formal reasons, Kosiński’s theory of ordered fuzzy numbers has been revised. The main goal of our paper is to propose a universal method of representation of Japanese candlesticks by revised ordered fuzzy numbers. The discussion also justifies the need for such revision of a numerical model of the Japanese candlesticks. There are considered the following main kinds of Japanese candlestick: White Candle (White Spinning), Black Candle (Black Spinning), Doji Star, Dragonfly Doji, Gravestone Doji, and Four Price Doji. For example, we apply numerical model of Japanese candlesticks for financial portfolio analysis. Full article