Template-type: ReDIF-Article 1.0 Author-Name: Forchini, Giovanni Author-Name: Hillier, Grant Title: CONDITIONAL INFERENCE FOR POSSIBLY UNIDENTIFIED STRUCTURAL EQUATIONS Journal: Econometric Theory Pages: 707-743 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: The possibility that a structural equation may not be identified casts doubt on measures of estimator precision that are usually used. Using the Fieller–Creasy problem for illustration, we argue that an observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence we argue that inference in such models should be conditioned on the observed value of that statistic (or statistics).We examine in detail the effects of such conditioning on the properties of the ordinary least squares (OLS) and two-stage least squares (TSLS) estimators for the coefficients of the endogenous variables in a single structural equation. We show that (a) conditioning has very little impact on the properties of the OLS estimator but a substantial impact on those of the TSLS estimator; (b) the conditional variance of the TSLS estimator can be very much larger than its unconditional variance (when the identifiability statistic is small) or very much smaller (when the identifiability statistic is large); and (c) conditional mean-square-error comparisons of the two estimators favor the OLS estimator when the sample evidence only weakly supports the identifiability hypothesis but favor TSLS when that evidence moderately supports identifiability.Finally, we note that another consequence of our argument is that the statistic upon which Anderson–Rubin confidence sets are based is in fact nonpivotal.We are grateful for the constructive comments offered by Peter Phillips and three anonymous referees that greatly improved the paper. Giovanni Forchini acknowledges support from ESRC grant NR00429424115. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195011/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:707-743_19 Template-type: ReDIF-Article 1.0 Author-Name: Bekker, Paul Author-Name: Kleibergen, Frank Title: FINITE-SAMPLE INSTRUMENTAL VARIABLES INFERENCE USING AN ASYMPTOTICALLY PIVOTAL STATISTIC Journal: Econometric Theory Pages: 744-753 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: We consider the K-statistic, Kleibergen's (2002, Econometrica 70, 1781–1803) adaptation of the Anderson–Rubin (AR) statistic in instrumental variables regression. Whereas Kleibergen (2002) especially analyzes the asymptotic behavior of the statistic, we focus on finite-sample properties in a Gaussian framework. The AR statistic then has an F-distribution. The finite-sample distribution of the K-statistic is, however, affected by nuisance parameters. We consider two extreme cases for the nuisance parameters, which provide tight bounds for the exact distribution. The first case amounts to perfect identification—which is similar to the asymptotic case—where the statistic has an F-distribution. In the other extreme case there is total underidentification. For the latter case we show how to compute the exact distribution. We thus provide tight bounds for exact confidence sets based on the K-statistic. Asymptotically the two bounds converge, except when there is a large number of redundant instruments.The authors' research documented in this paper has been funded by the NWO Vernieuwingsimpuls research grant “Empirical Comparison of Economic Models.” File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195023/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:744-753_19 Template-type: ReDIF-Article 1.0 Author-Name: Nicolau, João Title: BIAS REDUCTION IN NONPARAMETRIC DIFFUSION COEFFICIENT ESTIMATION Journal: Econometric Theory Pages: 754-777 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: In this paper, we quantify the asymptotic bias of the Florens-Zmirou (1993, Journal of Applied Probability 30, 790–804) and Jiang and Knight (1997, Econometric Theory 13, 615–645) estimator for the diffusion coefficient when the step of discretization is fixed, and then we propose a bias adjustment that partially compensates for the distortion. Also, we show that our estimators have all the asymptotic properties of the Florens-Zmirou and Jiang and Knight estimator when the step of discretization goes to zero. We provide some examples.I thank the editor Peter C.B. Phillips and the two referees for comments and suggestions that led to considerable improvement of the paper. I am also grateful to Carlos Braumann and Tom Kundert for helpful comments. This research was supported by the Fundação para a Ciência e a Tecnologia (FCT) and by POCTI. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195035/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:754-777_19 Template-type: ReDIF-Article 1.0 Author-Name: Abadir, Karim M. Author-Name: Rockinger, Michael Title: DENSITY FUNCTIONALS, WITH AN OPTION-PRICING APPLICATION Journal: Econometric Theory Pages: 778-811 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: We present a method of estimating density-related functionals, without prior knowledge of the density's functional form. The approach revolves around the specification of an explicit formula for a new class of distributions that encompasses many of the known cases in statistics, including the normal, gamma, inverse gamma, and mixtures thereof. The functionals are based on a couple of hypergeometric functions. Their parameters can be estimated, and the estimates then reveal both the functional form of the density and the parameters that determine centering, scaling, etc. The function to be estimated always leads to a valid density, by design, namely, one that is nonnegative everywhere and integrates to 1. Unlike fully nonparametric methods, our approach can be applied to small datasets. To illustrate our methodology, we apply it to finding risk-neutral densities associated with different types of financial options. We show how our approach fits the data uniformly very well. We also find that our estimated densities' functional forms vary over the dataset, so that existing parametric methods will not do uniformly well.We thank Hans-Jürg Büttler, Aleš Černý, Tony Culyer, Les Godfrey, David Hendry, Sam Kotz, Steve Lawford, Peter Phillips, Bas Werker, and three anonymous referees for their comments. We also thank for their feedback the participants at the seminars and conferences where this paper has been invited, in particular the 1998 CEPR Finance Network Workshop, the 1998 METU conference, the 1998 FORC (Warwick) conference “Options: Recent Advances,” Money Macro & Finance Group, the Swiss National Bank, Imperial College, Tilburg University, Université Libre de Bruxelles, the University of Oxford, Southampton University, and UMIST. The first author acknowledges support from the ESRC (UK) grant R000239538. The second author acknowledges help from the HEC Foundation and the European Community TMR grant “Financial Market Efficiency and Economic Efficiency.” This paper was written when the second author was affiliated with HEC-Paris. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195047/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:778-811_19 Template-type: ReDIF-Article 1.0 Author-Name: Al-Falou, A.A. Author-Name: Trummer, D. Title: IDENTIFIABILITY OF RECURRENT NEURAL NETWORKS Journal: Econometric Theory Pages: 812-828 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: We examine the identifiability of a nonlinear state space system under general assumptions. The discrete time evolution of the state is generated by a recurrent Elman network. For a large set of Elman networks we determine the class of observationally equivalent minimal systems, i.e., minimal systems that exhibit the same input-output behavior.The authors are grateful for discussions with M. Deistler and D. Bauer. A.A. Al-Falou was funded by the ERNSI network within the European Union program Training and Mobility of Researchers (TMR). D. Trummer was funded by the FWF (Austrian Science Fund). We thank an anonymous referee for helpful comments and suggestions. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195059/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:812-828_19 Template-type: ReDIF-Article 1.0 Author-Name: Harris, David Author-Name: McCabe, Brendan Author-Name: Leybourne, Stephen Title: SOME LIMIT THEORY FOR AUTOCOVARIANCES WHOSE ORDER DEPENDS ON SAMPLE SIZE Journal: Econometric Theory Pages: 829-864 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: In this paper we provide some weak convergence results for sample statistics of the product of a variable with its kth-order lag. We assume the variable is a stationary vector that can be represented by linear process, and the lag length k is allowed to be a function of the sample size. Employing the Beveridge–Nelson decomposition, we derive a new functional central limit theorem for this situation and establish related stochastic integral convergence results. We then consider the behavior of associated long-run variance estimators and also extend our analysis to the case where the sample statistics are based on regression residuals. We illustrate the potential range of application of these techniques in the context of (i) testing for I(0) versus I(1) behavior and (ii) estimation and testing in a heteroskedastically cointegrated regression model.We thank the co-editor and the referees for helpful comments on earlier drafts. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195060/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:829-864_19 Template-type: ReDIF-Article 1.0 Author-Name: Davies, P.L. Author-Name: Krämer, W. Title: THE DICKEY–FULLER TEST FOR EXPONENTIAL RANDOM WALKS Journal: Econometric Theory Pages: 865-877 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: A common test in econometrics is the Dickey–Fuller test, which is based on the test statistic . We investigate the behavior of the test statistic if the data yt are given by an exponential random walk exp(Zt) where Zt = Zt−1 + σεt and the εt are independent and identically distributed random variables. The test statistic DF(T) is a nonlinear transformation of the partial sums of εt process. Under certain moment conditions on the εt we show that tends to one as λ → 0. For the particular case that the εt define a simple random walk it is shown that plimT→∞ DF(T)/T exists and the limit is evaluated. The theoretical results are illustrated by some simulation experiments.We gratefully acknowledge the help of an anonymous referee whose comments on the first two versions of this paper enabled us to reduce the number of mistakes and to increase the clarity of presentation. The authors' research was supported in part by Sonderforschungsbereich 475, University of Dortmund. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195072/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:865-877_19 Template-type: ReDIF-Article 1.0 Author-Name: Baltagi, Badi H. Title: 03.5.1. A Concise Derivation of the Wallace and Hussain Fixed Effects Transformation Journal: Econometric Theory Pages: 879-879 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: A concise derivation of the Wallace and Hussain fixed effects transformation. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603215085/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:879-879_21 Template-type: ReDIF-Article 1.0 Author-Name: Kristensen, Dennis Author-Name: Linton, Oliver Title: 03.5.2. Consistent Standard Errors for Target Variance Approach to GARCH Estimation Journal: Econometric Theory Pages: 879-880 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: Consistent standard errors for target variance approach to GARCH estimation. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603225081/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:879-880_22 Template-type: ReDIF-Article 1.0 Author-Name: de Jong, Robert M. Title: 02.5.1. A Mixingale Inequality Using an Exponential Moment Journal: Econometric Theory Pages: 880-881 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: A Mixingale inequality using an exponential moment. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603235088/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:880-881_23 Template-type: ReDIF-Article 1.0 Author-Name: , Title: PROBLEMS AND SOLUTIONS Journal: Econometric Theory Pages: 879-883 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: File-URL: https://www.cambridge.org/core/product/identifier/S0266466603195084/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:5:p:879-883_11 Template-type: ReDIF-Article 1.0 Author-Name: Anatolyev, Stanislav Title: 02.5.2. Durbin–Watson Statistic and Random Individual Effects Journal: Econometric Theory Pages: 882-883 Issue: 5 Volume: 19 Year: 2003 Month: October Abstract: Durbin–Watson statistic and random individual Effects. File-URL: https://www.cambridge.org/core/product/identifier/S0266466603245084/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:882-883_24