
on Econometrics 
By:  Giuseppe Cavaliere (University of Bologna); Morten Ã˜rregaard Nielsen (Queen's University and CREATES); A. M. Robert Taylor (University of Essex) 
Abstract:  In a recent paper Hualde and Robinson (2011) establish consistency and asymptotic normality for conditional sumofsquares estimators, which are equivalent to conditional quasimaximum likelihood estimators, in parametric fractional time series models driven by conditionally homoskedastic shocks. In contrast to earlier results in the literature, their results apply over an arbitrarily large set of admissible parameter values for the (unknown) memory parameter covering both stationary and nonstationary processes and invertible and noninvertible processes. In this paper we extend their results to the case where the shocks can display conditional and unconditional heteroskedasticity of a quite general and unknown form. We establish that the consistency result presented in Hualde and Robinson (2011) continues to hold under heteroskedasticity as does asymptotic normality. However, we demonstrate that the covariance matrix of the limiting distribution of the estimator now depends on nuisance parameters which derive both from the weak dependence in the process (as is also the case for the corresponding result in Hualde and Robinson, 2011) but additionally from the heteroskedasticity present in the shocks. Asymptotically pivotal inference can be performed on the parameters of the heteroskedastic model, provided a conventional "sandwich" estimator of the variance is employed. 
Keywords:  (un)conditional heteroskedasticity, conditional sumofsquares, fractional integration, quasimaximum likelihood estimation 
JEL:  C13 C22 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:qed:wpaper:1324&r=ecm 
By:  Chen, Min; Zhu, Ke 
Abstract:  This article proposes Cramervon Mises (CM) and KolmogroveSmirnov (KS) test statistics based on the signs of a time series to test the null hypothesis that the series is a martingale difference sequence (MDS) with conditional heteroscedasity. Both of test statistics allowing for heavytailedness, nonstationarity, and nonlinear serial dependence of unknown forms, are easytoimplement. Unlike the signbased varianceratio test in Wright (2000), our signbased CM and KS tests have no need to select the lag. Unlike other often used specification tests for MDS, our signbased CM and KS tests are robust and have exact distributions which can be simulated easily. Simulation studies and applications further demonstrate the importance of our signbased CM and KS tests. 
Keywords:  Conditional heteroscedasity; Cramervon Mises test; KolmogroveSmirnov test; Martingale difference; Robustness. 
JEL:  C1 C12 
Date:  2014–06–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:56347&r=ecm 
By:  Nakata, Taisuke (Board of Governors of the Federal Reserve System (U.S.)); Tonetti, Christopher (Stanford GSB) 
Abstract:  There exists an extensive literature estimating idiosyncratic labor income processes. While a wide variety of models are estimated, GMM estimators are almost always used. We examine the validity of using likelihood based estimation in this context by comparing the small sample properties of a Bayesian estimator to those of GMM. Our baseline studies estimators of a commonly used simple earnings process. We extend our analysis to more complex environments, allowing for real world phenomena such as time varying and heterogeneous parameters, missing data, unbalanced panels, and nonnormal errors. The Bayesian estimators are demonstrated to have favorable bias and efficiency properties. 
Keywords:  Labor income process; small sample properties; GMM; bayesian estimation; error component models 
Date:  2014–03–31 
URL:  http://d.repec.org/n?u=RePEc:fip:fedgfe:201425&r=ecm 
By:  Michael McAleer (University of Canterbury); Christian M. Hafner 
Abstract:  One of the most popular univariate asymmetric conditional volatility models is the exponential GARCH (or EGARCH) specification. In addition to asymmetry, which captures the different effects on conditional volatility of positive and negative effects of equal magnitude, EGARCH can also accommodate leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. However, there are as yet no statistical properties available for the (quasi) maximum likelihood estimator of the EGARCH parameters. It is often argued heuristically that the reason for the lack of statistical properties arises from the presence in the model of an absolute value of a function of the parameters, which does not permit analytical derivatives or the derivation of statistical properties. It is shown in this paper that: (i) the EGARCH model can be derived from a random coefficient complex nonlinear moving average (RCCNMA) process; and (ii) the reason for the lack of statistical properties of the estimators of EGARCH is that the stationarity and invertibility conditions for the RCCNMA process are not known. 
Keywords:  Leverage, asymmetry, existence, random coefficient models, complex nonlinear moving average process 
JEL:  C22 C52 C58 G32 
Date:  2014–06–16 
URL:  http://d.repec.org/n?u=RePEc:cbt:econwp:14/16&r=ecm 
By:  Rousseau, Judith 
Abstract:  Although there have been a lot of developpements in the recent years on estimation in Bayesian nonparametric models, from a theoretical point view as well as from a methodological point of view, little has been done on Bayesian testing in nonparametric frameworks. In this talk I will be interested on asymptotic properties of Bayesian tests when at least one of the hypotheses is nonparametric. I will first give some results on goodness of fit types of tests where one is interested in testing a parametric model against a nonparametric alternative embedding the parametric model. Then I will discuss the more delicate problem where both hypotheses are nonparametric. Such cases involve in particular tests for monotonicity, twosample tests and estimation of the number of components in nonparametric mixture models. It will be shown that the Bayes factor or equivalently the 01 loss function might not be appropriate in such cases and that modifications need to be considered. 
Keywords:  consistency; Bayes factors; tests; Bayesian nonparametrics; 
JEL:  C11 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:dau:papers:123456789/13438&r=ecm 
By:  Huber, Martin; Mellace, Giovanni; Lechner, Michael 
Abstract:  Using a comprehensive simulation study based on empirical data, this paper investigates the finite sample properties of different classes of parametric and semiparametric estimators of (natural or pure) direct and indirect causal effects used in mediation analysis under sequential conditional independence assumptions. The estimators are based on regression, inverse probability weighting, and combinations thereof. Our simulation design uses a large population of Swiss jobseekers and considers variations of several features of the data generating process and the implementation of the estimators that are of practical relevance. We find that no estimator performs uniformly best (in terms of root mean squared error) in all simulations. Overall, socalled ‘gcomputation’ dominates. However, differences between estimators are often (but not always) minor in the various setups and the relative performance of the methods often (but not always) varies with the features of the data generating process. 
Keywords:  Causal mechanisms, direct effects, indirect effects, simulation, empirical Monte Carlo Study, causal channels, mediation analysis, causal pathways 
JEL:  C21 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:usg:econwp:2014:15&r=ecm 
By:  Scricciolo, Catia; Rousseau, Judith; Rivoirard, Vincent; Donnet, Sophie 
Abstract:  Empirical Bayes procedures are commonly used based on the supposed asymptotic equivalence with fully Bayesian procedures, which, however, has not so far received full theoretical support in terms of uncertainty quantification. In this note, we provide some results on contraction rates of empirical Bayes posterior distributions which are illustrated in nonparametric curve estimation using Dirichlet process mixture models. 
Keywords:  empirical Bayes selection of prior hyperparameters; nonparametric curve estimation; Dirichlet process mixtures; 
JEL:  C11 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:dau:papers:123456789/13437&r=ecm 
By:  Varang Wiriyawit; Benjamin Wong 
Abstract:  We highlight how detrending within Structural Vector Autoregressions (SVAR) is directly linked to the shock identification. Consequences of trend misspecification are investigated using a prototypical Real Business Cycle model as the Data Generating Process. Decomposing the different sources of biases in the estimated impulse response functions, we find the biases arising directly from trend misspecification are not trivial when compared to other widely studied misspecifications. Our example also illustrates how misspecifying the trend can also distort impulse response functions of even the correctly detrended variable within the SVAR system. 
Keywords:  Structural VAR, Identification, Detrending, Bias 
JEL:  C15 C32 C51 E37 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:een:camaaa:201446&r=ecm 
By:  Anton Skrobotov (Gaidar Institute for Economic Policy) 
Abstract:  Recent approaches in unit root testing that take into account the influences of the initial condition, trend, and breaks in the data using pretesting and performing the union of rejection testing strategies based on the information obtained. This allows for the use of more powerful tests, if there is uncertainty about some of the parameters in the model. This paper proposes the extension of the Harvey et al. (2012b) approach to the case of uncertainty over the initial condition. It has been shown that the procedures of Harvey et al. (2012b) have low power under a large initial condition because they include GLSbased tests. Therefore, the efficiency of some ADFtype unit root tests with breaks under various magnitudes of initial condition will be investigated, and the decision rule based on pretesting for a magnitude of the initial condition and simultaneous use of tests based on both GLS and OLS detrending is proposed. Additionally, the modification of the proposed algorithm using pretesting for the trend coefficient will be analyzed. Analysis of a situation with the possible presence of multiple structural breaks in trend will also be conducted in the paper. Two algorithms are proposed: the first involves only pretesting the initial condition, while the second involves pretesting the number of breaks based on the Kejriwal and Perron (2010) test. The asymptotic behavior of all tests is analyzed under both a localtounity representation of the autoregressive root and a localto zero representation of trend and breaks magnitudes. The proposed modifications save the high power for small initial conditions/trend/breaks and at the same time lead to the power close to one of the effective tests for large initial condition/trend/breaks. 
Keywords:  unit root test, infimum DickeyFuller tests, local trend, local trend break, asymptotic local power, union of rejection, pretesting, multiple breaks in trend. 
JEL:  C12 C22 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:gai:wpaper:0097&r=ecm 
By:  Monfort, A.; Renne, J.P.; Roussellet, G. 
Abstract:  We propose a new filtering and smoothing technique for nonlinear statespace models. Observed variables are quadratic functions of latent factors following a Gaussian VAR. Stacking the vector of factors with its vectorized outerproduct, we form an augmented state vector whose first two conditional moments are known in closedform. We also provide analytical formulae for the unconditional moments of this augmented vector. Our new quadratic Kalman filter (Qkf) exploits these properties to formulate fast and simple filtering and smoothing algorithms. A first simulation study emphasizes that the Qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70% RMSEs improvement of filtered values. Second, we provide evidence that Qkfbased maximumlikelihood estimates of model parameters always possess lower bias or lower RMSEs that the alternative estimators. 
Keywords:  nonlinear filtering, nonlinear smoothing, quadratic model, Kalman filter, pseudomaximum likelihood. 
JEL:  C32 C46 C53 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:bfr:banfra:486&r=ecm 
By:  Rousseau, Judith; Mengersen, Kerrie; Arbel, Julyan 
Abstract:  We present a dependent Bayesian nonparametric model for the proba bilistic modelling of speciesbysite data, i.e. population data where observations at different sites are classified into distinct species. We use a dependent version of the GriffithsEngenMcCloskey distribution, the distribution of the weights of the Dirichlet process, in the same lines as the Dependent Dirichlet process is defined. The prior is thus defined via the stickbreaking construction. Some distributional properties of this model are presented. 
Keywords:  Stickbreaking representation; GriffithsEngen McCloskey distribution; Covariatedependent mode; Bayesian nonparametrics; 
JEL:  C11 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:dau:papers:123456789/13439&r=ecm 
By:  Robert, Christian P.; Grazian, Clara 
Abstract:  Mixture models may be a useful and flexible tool to describe data with a complicated structure, for instance characterized by multimodality or asymmetry. In a Bayesian setting, it is a well established fact that one need to be careful in using improper prior distributions, since the posterior distribution may not be proper. This feature leads to problems in carry out an objective Bayesian approach. In this work an analysis of Jeffreys priors in the setting of finite mixture models will be presented. 
Keywords:  Objective Bayes; Mixture models; Jeffreys prior; 
JEL:  C11 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:dau:papers:123456789/13436&r=ecm 
By:  Michael Greenacre; H. Öztaç Ayhan 
Abstract:  The problem of outliers is wellknown in statistics: an outlier is a value that is far from the general distribution of the other observed values, and can often perturb the results of a statistical analysis. Various procedures exist for identifying outliers, in case they need to receive special treatment, which in some cases can be exclusion from consideration. An inlier, by contrast, is an observation lying within the general distribution of other observed values, generally does not perturb the results but is nevertheless nonconforming and unusual. For single variables, an inlier is practically impossible to identify, but in the multivariate case, thanks to interrelationships between variables, values can be identified that are observed to be more central in a distribution but would be expected, based on the other information in the data matrix, to be more outlying. We propose an approach to identify inliers in a data matrix, based on the singular value decomposition. An application is presented using a table of economic indicators for the 27 member countries of the European Union in 2011, where inlying values are identified for some countries such as Estonia and Luxembourg. 
Keywords:  imputation, inlier, outlier, singular value decomposition 
JEL:  C19 C88 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:upf:upfgen:1423&r=ecm 
By:  Alex Haberis (Bank of England; Centre for Macroeconomics (CFM)); Andrej Sokol (Bank of England) 
Abstract:  In this paper we describe a procedure for implementing zero restrictions within the context of a sign restrictions identification scheme for VARs. The procedure introduces an additional step into the algorithm outlined in Fry and Pagan (2011) and RubioRamirez et al. (2006) for implementing sign restrictions. This extra step involves rotating a candidate identification matrix using Givens rotation matrices to introduce zero restrictions. We then check whether the elements of the candidate matrix satisfy the sign restrictions as usual. We illustrate how our procedure works by generating artificial data from the theoretical model of An and Schorfheide (2007), which implies certain restrictions on the impact of its structural shocks on the model's endogenous variables. We exploit our knowledge of that pattern to identify structural shocks from the reducedform errors of a VAR estimated on the simulated data. 
JEL:  C32 C51 E12 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:cfm:wpaper:1410&r=ecm 
By:  Helmut Lütkepohl; Aleksei Netsunajev; ; 
Abstract:  In structural vector autoregressive analysis identifying the shocks of interest via heteroskedasticity has become a standard tool. Unfortunately, the approaches currently used for modelling heteroskedasticity all have drawbacks. For instance, assuming known dates for variance changes is often unrealistic while more exible models based on GARCH or Markov switching residuals are dicult to handle from a statistical and computational point of view. Therefore we propose a model based on a smooth change in variance that is exible as well as relatively easy to estimate. The model is applied to a fivedimensional system of U.S. variables to explore the interaction between monetary policy and the stock market. It is found that previously used conventional identification schemes in this context are rejected by the data if heteroskedasticity is allowed for. Shocks identified via heteroskedasticity have a different economic interpretation than the shocks identified using conventional methods. 
Keywords:  Structural vector autoregressions, heteroskedasticity, smooth transition VAR models, identification via heteroskedasticity 
JEL:  C32 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014031&r=ecm 
By:  Jaya Krishnakumar; Florian Wendelspiess ChÃ¡vez JuÃ¡rez 
Abstract:  Measuring capabilities is a major challenge for the operationalization of the capability approach. Structural equation models (SEM) are being increasingly used as one possible methodology for estimating capabilities, but a certain skepticism remains about their appropriateness. In this paper, we perform a unique simulation experiment for testing the validity of such estimators. Using an agentbased modeling tool, we simulate a 'real' life scenario with individuals of heterogeneous characteristics and behaviors, having different capability sets, and making different decisions. We then run a SEM (MIMIC) model on the data generated in this simulated world to estimate the individual capabilities. Our results support the idea that SEM can coherently estimate the true capabilities. We find that using the linear predictor from the structural part of the SEM provides better results than using the 'classical' factor scores based on the full model. 
Keywords:  latent variable model, MIMIC, SEM, simulation, capability approach 
JEL:  C10 C15 D63 I00 I20 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:gen:geneem:14061&r=ecm 
By:  Herrera Gómez, Marcos; Ruiz Marín, Manuel; Mur Lacambra, Jesús 
Abstract:  The paper shows a new nonparametric test, based on symbolic entropy, which permits detect spatial causality in crosssection data. The test is robust to the functional form of the relation and has a good behaviour in samples of medium to large size. We illustrate the use of test with the case of relationship between migration and unemployment, using data on 3,108 U.S. counties for the period 20032008. 
Keywords:  Spatial Econometrics, Causality, Nonparametric method 
JEL:  C01 C21 C46 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:56678&r=ecm 
By:  Zura Kakushadze 
Abstract:  We propose a framework for constructing factor models for alpha streams. Our motivation is threefold. 1) When the number of alphas is large, the sample covariance matrix is singular. 2) Its outofsample stability is challenging. 3) Optimization of investment allocation into alpha streams can be tractable for a factor model alpha covariance matrix. We discuss various risk factors for alphas such as: style risk factors; cluster risk factors based on alpha taxonomy; principal components; and also using the underlying tradables (stocks) as alpha risk factors, for which computing the factor loadings and factor covariance matrices does not involve any correlations with alphas, and their number is much larger than that of the relevant principal components. We draw insight from stock factor models, but also point out substantial differences. 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1406.3396&r=ecm 
By:  Sofiene El Aoud (FiQuant  Chaire de finance quantitative  Ecole Centrale Paris, MAS  Mathématiques Appliquées aux Systèmes  EA 4037  Ecole Centrale Paris); Frédéric Abergel (FiQuant  Chaire de finance quantitative  Ecole Centrale Paris, MAS  Mathématiques Appliquées aux Systèmes  EA 4037  Ecole Centrale Paris) 
Abstract:  We present in our work a continuous time Capital Asset Pricing Model where the volatilities of the market index and the stock are both stochastic. Using a singular perturbation technique, we provide approximations for the prices of european options on both the stock and the index. These approximations are functions of the model parameters. We show then that existing estimators of the parameter beta, proposed in the recent literature, are biased in our setting because they are all based on the assumption that the idiosyncratic volatility of the stock is constant. We provide then an unbiased estimator of the parameter beta using only implied volatility data. This estimator is a forward measure of the parameter beta in the sense that it represents the information contained in derivatives prices concerning the forward realization of this parameter, we test then its capacity of prediction of forward beta and we draw a conclusion concerning its predictive power. 
Date:  2014–02–28 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01006405&r=ecm 
By:  Varang Wiriyawit 
Abstract:  Extracting a trend component from nonstationary data is one of the first challenges in estimating a DSGE model. The misspecification of the component can distort structural parameter estimates and translate into a bias in policyrelevant statistic estimates. This paper investigates how important this bias is to estimated policy implications within a DSGE framework. The quantitative results suggest the bias in parameter estimates due to trend misspecification can result in significant inaccuracies in estimating statistics of interest. This then misleads policy conclusions. Particularly, a misspecified model is estimated using a deterministictrend specification when the true process is a randomwalk with drift. 
JEL:  C51 C52 E37 
Date:  2014–04 
URL:  http://d.repec.org/n?u=RePEc:acb:cbeeco:2014615&r=ecm 
By:  Takashi Kato; Jun Sekine; Hiromitsu Yamamoto 
Abstract:  A onefactor asset pricing model with an OrnsteinUhlenbeck process as its state variable is studied under partial information: the meanreverting level and the meanreverting speed parameters are modeled as hidden/unobservable stochastic variables. Noarbitrage pricing formulas for derivative securities written on a liquid asset and exponential utility indifference pricing formulas for derivative securities written on an illiquid asset are presented. Moreover, a conditionally linear filtering result is introduced to compute the pricing/hedging formulas and the Bayesian estimators of the hidden variables. 
Date:  2014–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1406.4275&r=ecm 
By:  Roberto Casarin (Department of Economics, University of Venice Cà Foscari); Monica Billio (Department of Economics, University of Venice, Cà Foscari); Anthony Osuntuyi (Department of Mathematics, Obafemi Awolowo University) 
Abstract:  A new Bayesian multichain Markov Switching GARCH model for dynamic hedging in energy futures markets is developed by constructing a system of simultaneous equations for the return dynamics on the hedged portfolio and futures. More specifically, both the mean and variance of the hedged portfolio are assumed to be governed by two unobserved discrete state processes, while the futures dynamics is driven by a univariate hidden state process. The noise in both processes are characterized by a MSGARCH model. This formulation has two main practical and conceptual advantages. First, the different states of the discrete processes can be identified as different volatility regimes. Secondly, the parameters can be easily interpreted as different hedging components. Our formulation also provides an avenue to analyze the contribution of the volatility dynamics and state probabilities to the optimal hedge ratio at each point in time. Moreover, the combination of the expected utility framework with regimeswitching models allows the definition of a robust minimum variance hedging strategy to also account for parameter uncertainty. Evidence of changes in the optimal hedging strategies before and after the financial crisis is found when the proposed robust hedging strategy is applied to crude oil spot and futures markets. 
Keywords:  Energy futures; GARCH; Hedge ratio; Markovswitching. 
JEL:  C1 C11 C15 C32 F31 G15 
Date:  2014 
URL:  http://d.repec.org/n?u=RePEc:ven:wpaper:2014:07&r=ecm 