|
on Econometrics |
| By: | Candelon, Bertrand; Metiu, Norbert |
| Abstract: | Determining whether a data set contains one or more outliers is a challenge commonly faced in applied statistics. This paper introduces a distribution-free test for multiple outliers in data drawn from an unknown data generating process. Besides, a sequential algorithm is proposed in order to identify the outlying observations in the sample. Our methodology relies on a two-stage nonparametric bootstrap procedure. Monte Carlo experiments show that the proposed test has good asymptotic properties, even for relatively small samples and heavy tailed distributions. The new outlier detection test could be instrumental in a wide range of statistical applications. The empirical performance of the test is illustrated by means of two examples in the fields of aeronautics and macroeconomics. -- |
| Keywords: | bootstrap,mode testing,nonparametric statistics,outlier detection |
| JEL: | C14 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:022013&r=ecm |
| By: | Kunpeng Li; Degui Li; Zhongwen Lian; Cheng Hsiao |
| Abstract: | We study a partially linear varying coefficient model where the regressors are generated by the multivariate unit root I(1) processes. The influence of the explanatory vectors on the response variable satisfies the semiparametric partially linear structure with the nonlinear component being functional coefficients. The profile likelihood estimation methodology with the first-stage local polynomial smoothing is applied to estimate both the constant coefficients in the linear component and the functional coefficients in the nonlinear component. The asymptotic distribution theory for the proposed semiparametric estimators is established under some mild conditions, from which both the parametric and nonparametric estimators are shown to enjoy the well-known super-consistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the developed methodology and results. |
| Keywords: | Functional coefficients, local polynomial fitting, profile likelihood, semiparametric estimation, unit root process. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-2&r=ecm |
| By: | Gunnar Bårdsen (Department of Economics, Norwegian University of Science and Technology); Luca Fanelli |
| Abstract: | This paper proposes a new evaluation approach of the class of small-scale `hybrid' New Keynesian Dynamic Stochastic General Equilibrium (NK-DSGE) models typically used in monetary policy and business cycle analysis. The novelty of our method is that the empirical assessment of the NK-DSGE model is based on a conditional sequence of likelihood-based tests conducted in a Vector Autoregressive (VAR) system in which both the low and high frequency implications of the model are addressed in a coherent framework. The idea is that if the low frequency behaviour of the original time series of the model can be approximated by unit roots, stationarity must be imposed by removing the stochastic trends. This means that with respect to the original variables, the solution of the NK-DSGE model is a VAR that embodies a set of recoverable unit roots/cointegration restrictions, in addition to the cross-equation restrictions implied by the rational expectations hypothesis. The procedure is based on the sequence `LR1->LR2->LR3', where LR1 is the cointegration rank test, LR2 the cointegration matrix test and LR3 the cross-equation restrictions test: LR2 is computed conditional on LR1 and LR3 is computed conditional on LR2. The type-I errors of the three tests are set consistently with a pre-fixed overall nominal significance level and the NK-DSGE model is not rejected if no rejection occurs. We investigate the empirical size properties of the proposed testing strategy by a Monte Carlo experiment and illustrate the usefulness of our approach by estimating a monetary business cycle NK-DSGE model using U.S. quarterly data. |
| Keywords: | DSGE models, LR test, Maximum Likelihood, New-Keynesian model, VAR |
| JEL: | C5 E4 E5 |
| Date: | 2013–01–30 |
| URL: | http://d.repec.org/n?u=RePEc:nst:samfok:14113&r=ecm |
| By: | Manabu Asai (Faculty of Economics Soka University, Japan and Wharton School University of Pennsylvania); Michael McAleer (Econometric Institute Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute, The Netherlands and Institute of Economic Research Kyoto University, Japan and Department of Quantitative Economics Complutense University of Madrid, Spain) |
| Abstract: | There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. We conduct a two-step procedure, namely estimating the parameter of fractional integration via log-periodgram regression in the rst step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure shows reasonable performances in nite samples. The empirical results for the bivariate data of the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV processes rather than one-factor and two-factor models of Wishart autoregressive processes for the covariance structure. |
| Keywords: | Diusion process; Multivariate stochastic volatility; Long memory; Fractional Brownian motion; Generalized Method of Moments. |
| JEL: | C32 C51 G13 |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:848&r=ecm |
| By: | Fan, Jianqing; Liao, Yuan; Shi, Xiaofeng |
| Abstract: | Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely unknown, and a simple inequality in the previous literature gives an infeasible upper bound for the estimation error. In addition, numerical studies illustrate that this upper bound is very crude. In this paper, we propose factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the accuracy of the risk estimation. The H-CLUB is constructed based on three different estimates of the volatility matrix: sample covariance, approximate factor model with known factors, and unknown factors (POET, Fan, Liao and Mincheva, 2013). For the first time in the literature, we derive the limiting distribution of the estimated risks in high dimensionality. Our numerical results demonstrate that the proposed upper bounds significantly outperform the traditional crude bounds, and provide insightful assessment of the estimation of the portfolio risks. In addition, our simulated results quantify the relative error in the risk estimation, which is usually negligible using 3-month daily data. Finally, the proposed methods are applied to an empirical study. |
| Keywords: | High dimensionality; approximate factor model; unknown factors; principal components; sparse matrix; thresholding; risk management; volatility |
| JEL: | G11 C38 G32 C58 |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:44206&r=ecm |
| By: | Nils Herger (Study Center Gerzensee) |
| Abstract: | Within the context of the firm location choice problem, Guimarães et al. (2003) have shown that a Poisson count regression and a conditional logit model yield identical coeffcient estimates. Yet, the corresponding interpretation differs since these discrete choice models reflect polar cases as regards the degree with which the different locations are similar. Schmidheiny and Brülhart (2011) have shown that these cases can be reconciled by adding a fixed outside option to the choice set and transforming the conditional logit into a nested logit framework. This gives rise to a dissimilarity parameter that equals 1 for the Poisson count regression (where locations are completely dissimilar) and 0 for the conditional logit model (where locations are completely similar). Though intermediate values are possible, the nested logit framework does not permit the dissimilarity parameter to be pinned down. We show that, with panel data and adopting a choice consistent normalisation, the fixed outside option can also be introduced into the Poisson count framework, from which the estimation of the dissimilarity parameter is relatively straightforward. The different location choice models are illustrated with an empirical application using cross-border acquisitions data. |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:szg:worpap:1302&r=ecm |
| By: | Michał Brzeziński (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | We analyse statistical inference for top income shares in finite samples. The asymptotic inference performs poorly even in large samples. The standard bootstrap tests give some improvement, but can be unreliable. Semi-parametric bootstrap approach is accurate in moderate and larger samples. |
| Keywords: | top income shares, income distribution, inference, bootstrap, semi-parametric bootstrap |
| JEL: | C15 C14 I3 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2013-01&r=ecm |
| By: | Michał Brzeziński (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | Richness indices are distributional statistics used to measure the incomes, earnings, or wealth of the rich. This paper uses a linearization method to derive the sampling variances for recently introduced distributionally-sensitive richness measures when estimated from survey data. The results are derived for two cases: (1) when the richness line is known, and (2) when it has to be estimated from the sample. The proposed approach enables easy consideration of the effects of a complex sampling design. Monte Carlo results suggest that the proposed approach allows for reliable inference in case of “concave” richness indices, but that it is not satisfactory in case of “convex” richness measures. |
| Keywords: | richness, affluence, distributional indices, variance estimation, statistical inference |
| JEL: | C12 C46 D31 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2013-03&r=ecm |
| By: | Cheng-Der Fuh; Huei-Wen Teng; Ren-Her Wang |
| Abstract: | Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we propose a general account for finding the optimal tilting measure. To this end, when the moment generating function of the underlying distribution exists, we obtain a simple and explicit expression of the optimal alternative distribution. The proposed algorithm is quite general to cover many interesting examples, such as normal distribution, noncentral $\chi^2$ distribution, and compound Poisson processes. To illustrate the broad applicability of our method, we study value-at-risk (VaR) computation in financial risk management and bootstrap confidence regions in statistical inferences. |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1302.0583&r=ecm |
| By: | Yu-Chin Hsu (Institute of Economics, Academia Sinica, Taipei, Taiwan); Chung-Ming Kuan (Department of Finance, National Taiwan University); Meng-Feng Yen (Department of Accountancy, and Graduate Institute of Banking and Finance, National Cheng Kung University) |
| Abstract: | We propose a stepwise test, Step-SPA(k), for multiple inequalities testing. This test is analogous to the Step-SPA test of Hsu, Hsu, and Kuan (2010, Journal of Empirical Finance) but has asymptotic control of a generalized familywise error rate: the probability of at least k false rejections. This test is also an improvement of Step-RC(k) of Romano and Wolf (2007, Annals of Statistics) because it avoids the least favorable configuration used in Step-RC(k). We show that the proposed Step-SPA(k) is consistent, in that it can identify the violated null hypotheses with probability approaching one. It is also shown analytically and by simulations that Step-SPA(k) is more powerful than Step-RC(k) under any power notion defined in Romano and Wolf (2005, Econometrica). An empirical study on CTA fund performance is also provided to illustrate this test. |
| Keywords: | data snooping, familiywise error rate, least favorable conguration, multiple inequalities testing, Reality Check, SPA test, stepwise test |
| JEL: | C12 C52 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:sin:wpaper:13-a001&r=ecm |
| By: | Jianqing Fan; Yuan Liao; Xiaofeng Shi |
| Abstract: | Estimating and assessing the risk of a large portfolio is an important topic in financial econometrics and risk management. The risk is often estimated by a substitution of a good estimator of the volatility matrix. However, the accuracy of such a risk estimator for large portfolios is largely unknown, and a simple inequality in the previous literature gives an infeasible upper bound for the estimation error. In addition, numerical studies illustrate that this upper bound is very crude. In this paper, we propose factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the accuracy of the risk estimation. The H-CLUB is constructed based on three different estimates of the volatility matrix: sample covariance, approximate factor model with known factors, and unknown factors (POET, Fan, Liao and Mincheva, 2013). For the first time in the literature, we derive the limiting distribution of the estimated risks in high dimensionality. Our numerical results demonstrate that the proposed upper bounds significantly outperform the traditional crude bounds, and provide insightful assessment of the estimation of the portfolio risks. In addition, our simulated results quantify the relative error in the risk estimation, which is usually negligible using 3-month daily data. Finally, the proposed methods are applied to an empirical study. |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1302.0926&r=ecm |
| By: | Chaohua Dong; Jiti Gao |
| Abstract: | In this paper, expansions of functionals of Lévy processes are established under some Hilbert spaces and their orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Lévy processes are considered. Several expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Lévy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. Simulations and empirical study are provided to illustrate the theoretical results. |
| Keywords: | Asymptotic theory Expansion, Lévy Process, Nonstationary time series, Orthogonal Series, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-3&r=ecm |
| By: | Victor Aguirregabiria; Pedro Mira |
| Abstract: | This paper deals with the identification and estimation of discrete games of incomplete information with multiple equilibria when we allow for three types of unobservables for the researcher: (a) payoff-relevant variables that are players' private information; (b) payoff-relevant variables that are common knowledge to all the players; and (c) non-payoff-relevant or "sunspot" variables which are common knowledge to the players. The specification of the payoff function is nonparametric, and the probability distributions of the unobservables is also nonparametric but with finite support (i.e., finite mixture model). We show that if the number of players in the game is greater than two and the number of discrete choice alternatives is greater than the number of mixtures in the distribution of the unobservables, then the model is nonparametrically identified under the same type of exclusion restrictions that we need for identification without unobserved heterogeneity. In particular, it is possible to separately identify the relative contributions of payoff-relevant and "sunspot" type of unobserved heterogeneity to observed players' behavior. We also present results on the identification of counterfactual experiments using the estimated model. |
| Keywords: | Discrete games of incomplete information; Multiple equilibria in the data; Unobserved heterogeneity; Sunspots; Finite mixture models. |
| JEL: | C13 C35 |
| Date: | 2013–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-474&r=ecm |
| By: | Claudia Foroni (Norges Bank (Central Bank of Norway)); Massimiliano Marcellino (European University Institute, Bocconi University and CEPR) |
| Abstract: | The development of models for variables sampled at di¤erent frequencies has attracted substantial interest in the recent econometric literature. In this paper we provide an overview of the most common techniques, including bridge equations, MIxed DAta Sampling (MIDAS) models, mixed frequency VARs, and mixed frequency factor models. We also consider alternative techniques for handling the ragged edge of the data, due to asynchronous publication. Finally, we survey the main empirical applications based on alternative mixed frequency models |
| Keywords: | mixed-frequency data, mixed-frequency VAR, MIDAS, nowcasting, forecasting |
| JEL: | E37 C53 |
| Date: | 2013–02–06 |
| URL: | http://d.repec.org/n?u=RePEc:bno:worpap:2013_06&r=ecm |
| By: | Mark J. Holmes (Department of Economics, Waikato University, New Zealand); Jesús Otero (Facultad de Economía, Universidad del Rosario, Colombia); Theodore Panagiotidis (Department of Economics, University of Macedonia, Greece) |
| Abstract: | Long-run income convergence is investigated in the US context. We employ a novel pair-wise econometric procedure based on a probabilistic definition of convergence. The time-series properties of all the possible regional income pairs are examined by means of unit root and non-cointegration tests where inference is based on the fraction of rejections. We distinguish between the cases of strong convergence, where the implied cointegrating vector is [1,-1], and weak convergence, where long-run homogeneity is relaxed. To address cross-sectional dependence, we employ a bootstrap methodology to derive the empirical distribution of the fraction of rejections. We find supporting evidence of US states sharing a common stochastic trend consistent with a definition of convergence based on long-run forecasts of state incomes being proportional rather than equal. We find that the strength of convergence between states decreases with distance and initial income disparity. Using Metropolitan Statistical Areas data, evidence for convergence is stronger. |
| Keywords: | Panel data, cross-section dependence, pair-wise approach, income, convergence |
| JEL: | C2 C3 R1 R2 R3 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:10_13&r=ecm |
| By: | Christopher Reicher |
| Abstract: | DSGE models with generalized shock processes have been a major area of research in recent years. In this paper, I show that the structural parameters governing DSGE models are not identified when the driving process behind the model follows an unrestricted VAR. This finding implies that parameter estimates derived from recent attempts to estimate DSGE models with generalized driving processes should be treated with caution, and that there exists a tradeoff between identification and the risk of model misspecification |
| Keywords: | Identification, DSGE models, observational equivalence, maximum likelihood |
| JEL: | C13 C32 E00 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:kie:kieliw:1821&r=ecm |
| By: | Silvia Figini (Department of Economics and Management, University of Pavia); Paolo Giudici (Department of Economics and Management, University of Pavia) |
| Abstract: | In this paper we propose a novel approach to measure risks, when the data available are expressed in an ordinal scale. As a result we obtain a new index of risk bounded between 0 and 1, that leads to a risk ordering that is consistent with a stochastic dominance approach. The proposed measure, being non parametric, can be applied to a wide range of problems, where data are ordinal and where a point estimate of risk is needed. We also provide a method to calculate confidence intervals for the proposed risk measure, in a Bayesian non parametric framework. In order to evaluate the actual performance of what we propose, we analyse a database provided by a telecommunication company, with the final aim of measuring operational risks, starting from a self-assessment questionnaire. |
| Keywords: | Risk measurement, Ordinal variables, Operational risk |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:pav:demwpp:032&r=ecm |
| By: | Heather M. Anderson; Farshid Vahid |
| Abstract: | Decreases in stock market returns often lead to higher increases in volatility than increases in returns of the same magnitude, and it is common to incorporate these so-called leverage effects in GARCH and stochastic volatility models. Recent research has also found it useful to account for leverage in models of realized volatility, as well as in models of the continuous and jump components of realized volatility. This paper explores the use of smooth transition autoregressive (STAR) models for capturing leverage effects in multiple series of the continuous components of realized volatility. We find that the leverage effect is well captured by a common nonlinear factor driven by returns, even though the persistence in each country’s volatility is country specific. A three country model that incorporates both country specific persistence and a common leverage effect offers slight forecast improvements for mid-range horizons, relative to other models that do not allow for the common nonlinearity. |
| Keywords: | Realized Volatility, Bipower Variation, Common Factors, Fore-casting, Leverage, Smooth Transition Models. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2013-1&r=ecm |
| By: | Andini, Corrado (University of Madeira) |
| Abstract: | This paper provides an expression for the bias of the OLS estimator of the schooling coefficient in a simple static wage-schooling model where earnings persistence is not accounted for. It is argued that the OLS estimator of the schooling coefficient is biased upward, and the bias is increasing with potential labor-market experience and the degree of earnings persistence. In addition, NLSY data are used to show that the magnitude of the persistence bias is non-negligible, and the bias cannot be cured by increasing the control set. Further, it is shown that disregarding earnings persistence is still problematic for the estimation of the schooling coefficient even if individual unobserved heterogeneity and endogeneity are taken into account. Overall, the findings support the dynamic approach to the estimation of wage-schooling models recently suggested by Andini (2012; 2013). |
| Keywords: | schooling, wages, dynamic panel-data models |
| JEL: | C23 I21 J31 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp7186&r=ecm |
| By: | Winzer, Christian |
| Abstract: | Continuity of energy supplies is a central aspect of concerns about energy security. Although the continuity of supplies can be influenced by a large number of risks, most models only analyse a small subset of risk sources and often neglect interdependencies between them. In this paper we introduce a probabilistic time-series model that quantifies the impact of inter-dependent natural, technical and human risk sources on energy supply continuity. Based on a case study of Italian gas and electricity markets we conclude that typical simplifications in time-series models and alternative approaches lead to a bias, which justifies the usage of detailed time-series models of interdependent risks such as the framework suggested in this paper, even though more detailed versions of this and other frameworks may quickly become very resource intensive. |
| Keywords: | Energy security, security of supply, reliability, Monte-Carlo simulation, measurement. |
| Date: | 2013–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1305&r=ecm |
| By: | André Kurmann; Elmar Mertens |
| Abstract: | Beaudry and Portier (American Economoc Review, 2006) propose an identification scheme to study the effects of news shocks about future productivity in Vector Error Correction Models (VECM). This comment shows that their methodology does not have a unique solution, when applied to their VECMs with more than two variables. The problem arises from the interplay of cointegration assumptions and long-run restrictions imposed by Beaudry and Portier (2006). |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2013-08&r=ecm |
| By: | Victor Aguirregabiria; Junichi Suzuki |
| Abstract: | This paper addresses a fundamental identification problem in the structural estimation of dynamic oligopoly models of market entry and exit. Using the standard datasets in existing empirical applications, three components of a firm's profit function are not separately identified: the fixed cost of an incumbent firm, the entry cost of a new entrant, and the scrap value of an exiting firm. We study the implications of this result on the power of this class of models to identify the effects of different comparative static exercises and counterfactual public policies. First, we derive a closed-form relationship between the three unknown structural functions and the two functions that are identified from the data. We use this relationship to provide the correct interpretation of the estimated objects that are obtained under the `normalization assumptions' considered in most applications. Second, we characterize a class of counterfactual experiments that are identified using the estimated model, despite the non-separate identification of the three primitives. Third, we show that there is a general class of counterfactual experiments of economic relevance that are not identified. We present a numerical example that illustrates how ignoring the non-identification of these counterfactuals (i.e., making a `normalization assumption' on some of the three primitives) generates sizable biases that can modify even the sign of the estimated effects. Finally, we discuss possible solutions to address these identification problems. |
| Keywords: | Dynamic structural models; Market entry and exit; Identification; Fixed cost; Entry cost; Exit value; Counterfactual experiment; Land price. |
| JEL: | L10 C01 C51 C54 C73 |
| Date: | 2013–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-475&r=ecm |
| By: | Michał Brzeziński (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | The coefficient of relative risk aversion (CRRA) is notoriously difficult to estimate. Recently, Barro and Jin (On the size distribution of macroeconomic disasters, Econometrica 2011; 79(3): 434–455) have come up with a new estimation approach that fits a power-law model to the tail of distribution of macroeconomic disasters. We show that their results can be successfully replicated using a more refined power-law fitting methodology and a more comprehensive data set. |
| Keywords: | coefficient of relative risk aversion, power-law modelling, macroeconomic disasters, replication, robust statistics |
| JEL: | D81 E32 C46 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2013-04&r=ecm |
| By: | Keiler, Sebastian; Eder, Armin |
| Abstract: | This study applies a novel way of measuring, quantifying and modelling the systemic risk within the financial system. The magnitude of risk spill over effects is gauged by introducing a specific weighting scheme. This approach originally stems from spatial econometrics. The methodology allows for a decomposition of the credit spread into a systemic, systematic and idiosyncratic risk premium. We identify considerable risk spill overs due to the interconnectedness of the financial institutes in the sample. In stress tests, up to one fifth of the CDS spread changes are owing to financial contagion. These results also give an alternative explanation for the nonlinear relationship between a debtor's theoretical probability of default and the observed credit spreads - known as the credit spread puzzle. -- |
| Keywords: | systemic risk,financial contagion,spatial econometrics,CDS spreads,government policy and regulation |
| JEL: | C21 G12 G18 G21 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:012013&r=ecm |