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on Econometrics |
| By: | Yang Yan; Dajing Shang; Oliver Linton (Institute for Fiscal Studies and Cambridge University) |
| Abstract: | This paper proposes efficient estimators of risk measures in a semiparametric GARCH model defined through moment constraints. Moment constraints are often used to identify and estimate the mean and variance parameters and are however discarded when estimating error quantiles. In order to prevent this efficiency loss in quantile estimation we propose a quantile estimator based on inverting an empirical likelihood weighted distribution estimator. It is found that the new quantile estimator is uniformly more efficient than the simple empirical quantile and a quantile estimator based on normalized residuals. At the same time, the efficiency gain in error quantile estimation hingeson the efficiency of estimators of the variance parameters. We show that the same conclusion applies to the estimation of conditional Expected Shortfall. Our comparison also leads to interesting implications of residual bootstrap for dynamic models. We find that these proposed estimators for conditional Value-at-Risk and expected shortfall are asymptotically mixed normal. This asymptotic theory can be used to construct confidence bands for these estimators by taking account of parameter uncertainty. Simulation evidence as well as empirical results are provided. |
| Keywords: | Empirical Likelihood; Empirical process; GARCH; Quantile; Value-at-Risk; Expected Shortfall. |
| JEL: | C14 C22 G22 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:25/12&r=ecm |
| By: | Martin Huber; Blaise Melly |
| Abstract: | Identi?cation in most sample selection models depends on the independence of the regressors and the error terms conditional on the selection probability. All quantile and mean functions are parallel in these models; this implies that quantile estimators cannot reveal any? per assumption non-existing? heterogeneity. Quantile estimators are nevertheless useful for testing the conditional independence assumption because they are consistent under the null hypothesis. We propose tests of the Kolmogorov-Smirnov type based on the conditional quantile regression process. Monte Carlo simulations show that their size is satisfactory and their power su¢ cient to detect deviations under realistic data generating processes. We apply our procedures to female wage data from the 2011 Current Population Survey and show that homogeneity is clearly rejected. |
| Keywords: | sample selection, quantile regression, independence, test |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2012-11&r=ecm |
| By: | Bai, Jushan; Liao, Yuan |
| Abstract: | We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the factor loadings or common factors because it essentially treats the idiosyncratic error to be homoskedastic and cross sectionally uncorrelated. For the efficient estimation, it is essential to estimate a large error covariance matrix. We assume the model to be conditionally sparse, and propose two approaches to estimating the common factors and factor loadings; both are based on maximizing a Gaussian quasi-likelihood and involve regularizing a large covariance sparse matrix. In the first approach the factor loadings and the error covariance are estimated separately while in the second approach they are estimated jointly. Extensive asymptotic analysis has been carried out. In particular, we develop the inferential theory for the two-step estimation. Because the proposed approaches take into account the large error covariance matrix, they produce more efficient estimators than the classical PCA methods or methods based on a strict factor model. |
| Keywords: | High dimensionality; unknown factors; principal components; sparse matrix; conditional sparse; thresholding; cross-sectional correlation; penalized maximum likelihood; adaptive lasso; heteroskedasticity |
| JEL: | C31 C33 C01 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41558&r=ecm |
| By: | Christian Gouriéroux (Crest et Université de Toronto); Jean-Michel Zakoian (Canada et University Lille 3) |
| Abstract: | Standard risk measures, such as the Value-at-Risk (VaR), or the Expected Shortfall, have to be estimated and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the Profit and Loss variable, induces an asymptotic bias of order 1/n in the coverage probabilities. This paper shows how to correct for this bias by introducing a new estimator of the VaR, called Estimation adjusted VaR (EVaR). This adjustment allows for a joint treatment of theoretical and estimation risks, taking into account for their possible dependence. The estimator is derived for a general parametric dynamic model and is particularized to stochastic drift and volatility models. The finite sample properties of the EVaR estimator are studied by simulation and an empirical study of the S&P Index is proposed |
| Keywords: | Value-at-Risk,Estimation Risk,Bias Correction, ARCH Model |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2012-16&r=ecm |
| By: | Xiaohong Chen (Institute for Fiscal Studies and Yale University); David T. Jacho-Chavez; Oliver Linton (Institute for Fiscal Studies and Cambridge University) |
| Abstract: | We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of v n- consistent estimators whose cardinality increases with sample size. A special case of our framework corresponds to the conditional moment restriction and the implied estimator in that case is shown to achieve the semiparametric efficiency bound. The proofs do not rely on smoothness of underlying criterion functions. |
| Keywords: | Instrumental Variables; Minimum Distance; Semiparametric Efficiency; Two-Stage Least Squares |
| JEL: | C12 C13 C14 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:26/12&r=ecm |
| By: | Arnak Dalalyan (Crest); Yuri Ingster (St Petersburg State Electotechnical University); Alexandre B. Tsybakov (Crest) |
| Abstract: | We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant covariates. The compound model is characterized by three main parameters : the structure parameter describing the macroscopic form of the compound function, the microscopic sparsity parameter indicating the maximal number of relevant covariates in each component and the usual smoothness parameter corresponding to the complexity of the members of the compound. We find non-asymptotic minimax rate of convergence of estimators in such a model as a function of these three parameters. We also show that this rate can be attained in an adaptive way |
| Keywords: | Compound functional model, Minimax estimation, Sparse additive stucture, Dimension reduction, Structure adaptation |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2012-20&r=ecm |
| By: | Leeb, Hannes; Pötscher, Benedikt M. |
| Abstract: | We point out that the ideas underlying some test procedures recently proposed for testing post-model-selection (and for some other test problems) in the econometrics literature have been around for quite some time in the statistics literature. We also sharpen some of these results in the statistics literature and show that some of the proposals in the econometrics literature lead to tests that do not have the claimed size properties. |
| Keywords: | Tests in presence of nuisance parameters; inference post model selection |
| JEL: | C52 C12 C01 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41459&r=ecm |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | A prominent use of local to unity limit theory in applied work is the construction of confidence intervals for autogressive roots through inversion of the ADF t statistic associated with a unit root test, as suggested in Stock (1991). Such confidence intervals are valid when the true model has an autoregressive root that is local to unity (rho = 1 + (c/n)) but are invalid at the limits of the domain of definition of the localizing coefficient c because of a failure in tightness and the escape of probability mass. Consideration of the boundary case shows that these confidence intervals are invalid for stationary autoregression where they manifest locational bias and width distortion. In particular, the coverage probability of these intervals tends to zero as c approaches -infinity, and the width of the intervals exceeds the width of intervals constructed in the usual way under stationarity. Some implications of these results for predictive regression tests are explored. It is shown that when the regressor has autoregressive coefficient |rho| < 1 and the sample size n approaches infinity, the Campbell and Yogo (2006) confidence intervals for the regression coefficient have zero coverage probability asymptotically and their predictive test statistic Q erroneously indicates predictability with probability approaching unity when the null of no predictability holds. These results have obvious implications for empirical practice. |
| Keywords: | Autoregressive root, Confidence belt, Confidence interval, Coverage probability, Local to unity, Localizing coefficient, Predictive regression, Tightness |
| JEL: | C22 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1879&r=ecm |
| By: | Andres, P.; Harvey, A. |
| Abstract: | In dynamic conditional score models, the innovation term of the dynamic specification is the score of the conditional distribution. These models are investigated for non-negative variables, using distributions from the generalized beta and generalized gamma families. The log-normal distribution is also considered. Applications to the daily range of stock market indices are reported and models are fitted to duration data. |
| Keywords: | Burr distribution; Durations; Range; Score; Un-observed components; Weibull distribution |
| JEL: | C22 G10 |
| Date: | 2012–09–26 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1240&r=ecm |
| By: | Oliver Linton (Institute for Fiscal Studies and Cambridge University); Yoon-Jae Whang (Institute for Fiscal Studies and Seoul National University) |
| Abstract: | We propose a new statistical test of the stochastic dominance efficiency of a given portfolio over a class of portfolios. We establish its null and alternative asymptotic properties, and define a method for consistently estimating critical values. We present some numerical evidence that our tests work well in moderate sized samples. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:27/12&r=ecm |
| By: | Henderson, Daniel J. (University of Alabama); Maasoumi, Esfandiar (Emory University) |
| Abstract: | This paper offers some new directions in the analysis of nonparamertric models with exogenous treatment assignment. The nonparametric approach opens the door to the examination of potentially different distributed outcomes. When combined with cross-validation, it also identifies potentially irrelevant variables and linear versus nonlinear effects. Examination of the distribution of effects requires distribution metrics, such as stochastic dominance tests for ranking based on a wide range of criterion functions, including dollar valuations. We can identify subgroups with different treatment outcomes. We offer an empirical demonstration based on the GAIN data. In the case of one covariate (English as the primary language), there is support for a statistical inference of uniform first order dominant treatment effects. We also find several others that indicate second and higher order dominance rankings to a statistical degree of confidence. |
| Keywords: | bootstrap, GAIN, nonparametric, rehabilitation, stochastic dominance, treatment effects |
| JEL: | C14 |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp6874&r=ecm |
| By: | Biørn, Erik; Wangen, Knut R. |
| Abstract: | We establish a `map' for describing a wide class of Limited Dependent Variables models much used in the econometric literature. The classification system, or language, is an extension of Amemiya's typology for tobit models and is intended to facilitate communication among researchers. The class is defined in relation to distributions of latent variables of an arbitrarily high dimension; the region of support can be divided into an arbitrary number of subsets, and the observation rules in each subset can be any combination of the observed, censored, and missing status. Consistent labeling is suggested at different levels of detail. |
| Keywords: | Limited dependent variables; Latent variables; Censoring; Truncation; Missing observations |
| JEL: | C24 C25 |
| Date: | 2012–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41461&r=ecm |
| By: | Luc Behaghel (Paris School of Economics); Bruno Crépon (CREST); Marc Gurgand (J-PAL); Thomas Le barbanchon |
| Abstract: | We propose a novel selectivity correction procedure to deal with survey attrition, at the crossroads of the “Heckit" and of the bounding approach of Lee (2009). As a substitute for the instrument needed in sample selectivity correction models, we use information on the number of attempts that were made to obtain response to the survey from each individual who responded. We obtain set identification, but if the number of attempts to reach each individuals is high enough, we can come closer to point identification. We apply our sample selection correction in the context of a job-search experiment with low and unbalanced response rates |
| Keywords: | Survey non response ,sample selectivity , treatment effect models, randomized controlled trial |
| JEL: | C31 C93 J6 |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2012-15&r=ecm |
| By: | Sebastien Valeyre; Denis Grebenkov; Sofiane Aboura; Qian Liu |
| Abstract: | We present a new volatility model, simple to implement, that combines various attractive features such as an exponential moving average of the price and a leverage effect. This model is able to capture the so-called "panic effect", which occurs whenever systematic risk becomes the dominant factor. consequently, in contrast to other models, this new model is as reactive as the implied volatility indices. We also test the reactivity of our model using extreme events taken from the 470 most liquid European stocks over the last decade. We show that the reactive volatility model is more robust to extreme events, and it allows for the identification of precursors and replicas of extreme events. |
| Date: | 2012–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1209.5190&r=ecm |