
on Econometrics 
By:  Liu, Xiaochun 
Abstract:  This paper considers the locationscale quantile autoregression in which the location and scale parameters are subject to regime shifts. The regime changes are determined by the outcome of a latent, discretestate Markov process. The new method provides direct inference and estimate for different parts of a nonstationary time series distribution. Bayesian inference for switching regimes within a quantile,via a threeparameter asymmetricLaplace distribution, is adapted and designed for parameter estimation. The simulation study shows reasonable accuracy and precision in model estimation. From a distribution point of view, rather than from a mean point of view, the potential of this new approach is illustrated in the empirical applications to reveal the countercyclical risk pattern of stock markets and the asymmetric persistence of real GDP growth rates and real tradeweighted exchange rates. 
Keywords:  AsymmetricLaplace Distribution, MetropolisHastings, BlockataTime, Asymmetric Dynamics, Transition Probability 
JEL:  C51 C58 E0 E3 E32 G1 
Date:  2013–10–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:55800&r=ecm 
By:  Dai, Deliang (Linnaeus university); Holgersson, Thomas (Linnaeus university, Jönköping university, & Centre of Excellence for Science and Innovation Studies (CESIS)); Karlsson, Peter (Linnaeus university & Jönköping university,) 
Abstract:  This paper treats the problem of estimating individual Mahalanobis distances (MD) in cases when the dimension of the variable p is proportional to the sample size n. Asymptotic expected values are derived under the assumption p/n>c, 0 
Keywords:  Increasing dimension data; Mahalanobis distance; Inverse covariance matrix; Smoothing 
JEL:  C38 C46 C50 
Date:  2014–05–06 
URL:  http://d.repec.org/n?u=RePEc:hhs:cesisp:0362&r=ecm 
By:  Isabelle Charlier; Davy Paindaveine 
Abstract:  In this paper, we use quantization to construct a nonparametric estimator of conditionalquantiles of a scalar response Y given a ddimensional vector of covariates X. First we focuson the population level and show how optimal quantization of X, which consists in discretizingX by projecting it on an appropriate grid of N points, allows to approximate conditionalquantiles of Y given X. We show that this is approximation is arbitrarily good as N goesto infinity and provide a rate of convergence for the approximation error. Then we turnto the sample case and define an estimator of conditional quantiles based on quantizationideas. We prove that this estimator is consistent for its fixedN population counterpart. Theresults are illustrated on a numerical example. Dominance of our estimators over local constant/linear ones and nearest neighbor ones is demonstrated through extensive simulationsin the companion paper Charlier et al. (2014). 
Date:  2014–05 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/161134&r=ecm 
By:  Albis, Manuel Leonard F.; Mapa, Dennis S. 
Abstract:  The estimated Vector AutoRegressive (VAR) model is sensitive to model misspecifications, such as omitted variables, incorrect laglength, and excluded moving average terms, which results in biased and inconsistent parameter estimates. Furthermore, the symmetric VAR model is more likely misspecified due to the assumption that variables in the VAR have the same level of endogeneity. This paper extends the Bayesian Averaging of Classical Estimates, a robustness procedure in crosssection data, to a vector timeseries that is estimated using a large number of Asymmetric VAR models, in order to achieve robust results. The combination of the two procedures is deemed to minimize the effects of misspecification errors by extracting and utilizing more information on the interaction of the variables, and cancelling out the effects of omitted variables and omitted MA terms through averaging. The proposed procedure is applied to simulated data from various forms of model misspecifications. The forecasting accuracy of the proposed procedure was compared to an automatically selected equal laglength VAR. The results of the simulation suggest that, under misspecification problems, particularly if an important variable and MA terms are omitted, the proposed procedure is better in forecasting than the automatically selected equal laglength VAR model. 
Keywords:  BACE, AVAR, Robustness Procedures 
JEL:  C5 C52 C58 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:55902&r=ecm 
By:  Brännäs, Kurt (Department of Economics, Umeå School of Business and Economics) 
Abstract:  The paper suggests and studies count data models corresponding to previously studied spatial econometric models for continuous variables. A novel way of incorporating spatial weights is considered for both time and space dynamic models with or without simultaneity. The paper also contains a brief discussion about estimation issues. 
Keywords:  Integervalued; Space; Time; Regional; Thinning; Estimation 
JEL:  C31 C32 C51 R12 R15 R23 
Date:  2014–05–06 
URL:  http://d.repec.org/n?u=RePEc:hhs:umnees:0883&r=ecm 
By:  António Alberto Santos (Faculty of Economics, University of Coimbra and GEMF, Portugal); João Andrade (Instituto de Telecomunicações, Dept. Electrical and Comp. Eng., University of Coimbra, Portugal) 
Abstract:  In this paper, we show how to estimate the parameters of stochastic volatility models using Bayesian estimation and Markov chain Monte Carlo (MCMC) simulations through the approximation of the aposteriori distribution of parameters. Simulated independent draws are made possible by using Graphics Processing Units (GPUs) to compute several Markov chains in parallel. We show that the higher computational power of GPUs can be harnessed and put to good use by addressing two challenges. Bayesian estimation using MCMC simulations benefit from powerful processors since it is a complex numerical problem. Moreover, sequential approaches are characterized for drawing highly correlated samples which reduces the Effective Sample Size (ESS) associated with the simulated values obtained from the posterior distribution under a Bayesian analysis. However, under the proposed parallel expression of the algorithm, we show that a faster convergence rate is possible by running independent Markov chains, drawing lower correlations and therefore increase the ESS. The results obtained with this approach are presented for the Stochastic Volatility (SV) model, basic and with leverage. 
Keywords:  Bayesian Estimation; Graphics Processing Unit; Parallel Computing; Simulation; StateSpace Models; Stochastic Volatility. 
JEL:  C11 C13 C15 C53 C63 C87 
Date:  2014–04 
URL:  http://d.repec.org/n?u=RePEc:gmf:wpaper:201410.&r=ecm 
By:  Holgersson, Thomas (Linnaeus university, Jönköping university, & Centre of Excellence for Science and Innovation Studies (CESIS)); Dai, Deliang (Linnaeus university) 
Abstract:  In this paper we derive central limit theorems for two different types of Mahalanobis distances in situations where the dimension of the parent variable increases proportionally with the sample size. It is shown that although the two estimators are closely related and behave similarly in nite dimensions, they have different convergence rates and are also centred at two different points in highdimensional settings. The limiting distributions are shown to be valid under some general moment conditions and hence available in a wide range of applications. 
Keywords:  Mahalanobis distance; increasing dimension; weak convergence; MarcenkoPastur distribution; outliers; Pearson family 
JEL:  C38 C46 C50 
Date:  2014–05–06 
URL:  http://d.repec.org/n?u=RePEc:hhs:cesisp:0361&r=ecm 
By:  Christopher Bruffaerts; Bram De Rock; Catherine Dehon 
Keywords:  nonparametric frontier models; directional distance; orderalpha frontiers; outlier detection; robust efficiency estimation 
Date:  2014–02 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/156905&r=ecm 
By:  Guanglei Hong (University of Chicago); Jonah Deutsch (Mathematica Policy Research); Heather D. Hill (University of Chicago) 
Abstract:  Conventional methods for mediation analysis generate biased results when the mediatoroutcome relationship depends on the treatment condition. This article introduces a new technique, ratioofmediatorprobability weighting (RMPW), for decomposing total effects into direct and indirect effects in the presence of treatmentbymediator interactions. The indirect effect can be further decomposed into a pure indirect effect and a natural treatmentbymediator interaction effect. The latter captures the treatment effect transmitted through a change in the mediational process. We illustrate how to apply the technique to identifying whether employment mediated the relationship between an experimental welfare program and maternal depression. In comparison with other techniques for mediation analysis, RMPW requires relatively few assumptions about the distribution of the outcome, the distribution of the mediator, and the functional form of the outcome model, and is easy to implement using standard statistical software. Simulation results reveal satisfactory performance of the parametric and nonparametric RMPW procedures under the identification assumptions and show a relatively higher level of robustness of the nonparametric procedure. We provide a tutorial and Stata code for implementing this technique. 
Keywords:  Causal inference; direct effect; indirect effect; mediation mechanism; potential outcome; propensity score 
JEL:  C10 C14 C54 I38 
Date:  2013–09 
URL:  http://d.repec.org/n?u=RePEc:hka:wpaper:2013009&r=ecm 
By:  Fernandes, Marcelo; Preumont, PierreYves 
Abstract:  This paper uses a multivariate response surface methodology to analyze the size distortion of the BDS test when applied to standardized residuals of rstorder GARCH processes.The results show that the asymptotic standard normal distribution is an unreliable approximation, even in large samples. On the other hand, a simple logtransformation of the squared standardized residuals seems to correct most of the size problems. Nonetheless, the estimated response surfaces can provide not only a measure of the size distortion, but also more adequate critical values for the BDS test in small samples. 
Date:  2014–05–05 
URL:  http://d.repec.org/n?u=RePEc:fgv:eesptd:361&r=ecm 
By:  Sarah Brown (Economics Department, University of Sheffield); William Greene (Economics Department, Stern Business School, New York University); Mark N. Harris (School of Economics and Finance, Curtin University) 
Abstract:  Latent class, or finite mixture, modelling has proved a very popular, and relatively easy, way of introducing muchneeded heterogeneity into empirical models right across the social sciences. The technique involves (probabilistically) splitting the population into a finite number of (relatively homogeneous) classes, or types. Within each of these, typically, the same statistical model applies, although these are characterised by differing parameters of that distribution. In this way, the same explanatory variables can have differing effects across the classes, for example. A priori, nothing is known about the behaviours within each class; but ex post, researchers invariably label the classes according to expected values, however defined, within each class. Here we propose a simple, yet effective, way of parameterising both the class probabilities and the statistical representation of behaviours within each class, that simultaneously preserves the ranking of such according to classspecific expected values and which yields a parsimonious representation of the class probabilities. 
Keywords:  latent class models; finite mixture models; ordered probability models; expected values; body mass index 
JEL:  C3 D1 I1 
Date:  2014–04 
URL:  http://d.repec.org/n?u=RePEc:shf:wpaper:2014006&r=ecm 