Results 1  10
of
17
Some Impossibility Theorems In Econometrics With Applications To Instrumental Variables, Dynamic Models And Cointegration
 Econometrica
, 1995
"... General characterizations of valid confidence sets and tests in problems which involve locally almost unidentified (LAU) parameters are provided and applied to several econometric models. Two types of inference problems are studied: (1) inference about parameters which are not identifiable on certai ..."
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Cited by 124 (16 self)
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General characterizations of valid confidence sets and tests in problems which involve locally almost unidentified (LAU) parameters are provided and applied to several econometric models. Two types of inference problems are studied: (1) inference about parameters which are not identifiable on certain subsets of the parameter space, and (2) inference about parameter transformations with singularities (discontinuities). When a LAU parameter or parametric function has an unbounded range, it is shown under general regularity conditions that any valid confidence set with level 1 \Gamma ff for this parameter should be unbounded with probability close to 1 \Gamma ff in the neighborhood of nonidentification subsets and should as well have a nonzero probability of being unbounded under any distribution compatible with the model: no valid confidence set which is bounded with probability one does exist. These properties hold even if "identifying restrictions" are imposed. Similar results also ob...
GMM with many moment conditions
 Econometrica
, 2006
"... This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variabl ..."
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Cited by 14 (1 self)
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This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported.
Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys Prior
 Journal of Econometrics
, 1998
"... Posterior distributions in limited information analysis of the simultaneous equations model using the ..."
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Cited by 12 (2 self)
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Posterior distributions in limited information analysis of the simultaneous equations model using the
Finite Sample Analysis of TwoPass CrossSectional Regressions
"... We investigate the finite sample properties of the twopass crosssectional regression (CSR) methodology, which is popular for estimating risk premia and testing beta pricing models. We find that the finite sample distributions of the estimated risk premia differ significantly from their asymptoti ..."
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Cited by 5 (2 self)
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We investigate the finite sample properties of the twopass crosssectional regression (CSR) methodology, which is popular for estimating risk premia and testing beta pricing models. We find that the finite sample distributions of the estimated risk premia differ significantly from their asymptotic distributions. In particular, the risk premia estimates obtained from the secondpass CSR of average returns on estimated betas can be seriously biased even when the number of time series observations is reasonably large. In addition, the standard error of the estimated risk premia based on the asymptotic distribution overstates the actual standard error. We show that popular adjusted estimators in the literature have no finite integral moments and therefore cannot be used to correct the bias. We propose a new bias adjustment of the estimated zerobeta rate and risk premia and we show that the adjusted version has a smaller bias than the unadjusted version. In the empirical asset pricing literature, the popular twopass crosssectional regression (CSR) methodology developed by Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) is often used for estimating of risk premia and testing beta asset pricing models. Although there are many variations on this twopass methodology, its basis setup always involves two steps. In the first
Computationally Efficient Recursions for TopOrder Invariant Polynomials with Applications ∗
"... evaluation of toporder invariant polynomials and moments of ratio of quadratic forms in normal random variables. ” Hillier first became involved as a referee of that earlier paper. His contribution has been confined mainly to suggesting the generating function approach, simplifying some of the proo ..."
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Cited by 1 (0 self)
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evaluation of toporder invariant polynomials and moments of ratio of quadratic forms in normal random variables. ” Hillier first became involved as a referee of that earlier paper. His contribution has been confined mainly to suggesting the generating function approach, simplifying some of the proofs, and contributing a few additional results. We are grateful to Plamen Koev, Peter Phillips, Serge Provost, Marko Riedel and two anonymous referees for helpful comments and suggestions. Kan gratefully acknowledges financial support from the National Bank Financial of Canada.
TWO NEW ZEALAND PIONEER ECONOMETRICIANS By
, 2010
"... Two distinguished New Zealanders pioneered some of the foundations of modern econometrics. Alec Aitken, one of the most famous and welldocumented mental arithmeticians of all time, contributed the matrix formulation and projection geometry of linear regression, generalized least squares (GLS) estim ..."
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Cited by 1 (1 self)
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Two distinguished New Zealanders pioneered some of the foundations of modern econometrics. Alec Aitken, one of the most famous and welldocumented mental arithmeticians of all time, contributed the matrix formulation and projection geometry of linear regression, generalized least squares (GLS) estimation, algorithms for Hodrick Prescott (HP) style data smoothing (six decades before their use in economics), and statistical estimation theory leading to the Cramér Rao bound. Rex Bergstrom constructed and estimated by limited information maximum likelihood (LIML) the largest empirical structural model in the early 1950s, opened up the field of exact distribution theory, developed cyclical growth models in economic theory, and spent nearly 40 years of his life developing the theory of continuous time econometric modeling and its empirical application. We provide an overview of their lives, discuss some of their accomplishments, and develop some new econometric theory that connects with their foundational work.
EXACT DISTRIBUTION THEORY IN STRUCTURAL ESTIMATION WITH AN IDENTITY
, 2009
"... Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV, and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulas for ..."
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Cited by 1 (1 self)
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Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV, and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulas for a structural equation model without an identity are shown to apply also to models with an identity by specializing along a certain asymptotic parameter sequence. Some of the new exact results are obtained by means of a uniform asymptotic expansion. An interesting consequence of the new theory is that the uniform asymptotic approximation provides the exact distribution of the OLS estimator in the model considered by Bergstrom (1962). This example appears to be the first instance in the statistical literature of a uniform approximation delivering an exact expression for a probability density. DEDICATION In memory of Rex Bergstrom, whose pioneering paper in Econometrica (1962) opened up a new understanding of the comparative properties of simultaneous equations estimators by deriving their exact finite sample distributions.
Bias and MSE of The IV Estimator Under Weak Identification
, 2000
"... We provide results on properties of the IV estimator in the presence of weak instruments, beginning with the derivation of analytical formulae for the asymptotic bias (ABIAS) and mean squared error (AMSE), within the localtozero asymptotic framework of Staiger and Stock (1997). These results add t ..."
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We provide results on properties of the IV estimator in the presence of weak instruments, beginning with the derivation of analytical formulae for the asymptotic bias (ABIAS) and mean squared error (AMSE), within the localtozero asymptotic framework of Staiger and Stock (1997). These results add to the results of Staiger and Stock (1997), who have provided an approximate ABIAS measure for the twostage least squares (2SLS) estimator relative to that of the OLS estimator. In fact, with respect to ABIAS and AMSE, we are able to prove the conjecture put forth by Staiger and Stock (1997) that the limiting distribution of the 2SLS estimator under the localtozero assumption is the same as the exact distribution of this estimator under the more restrictive assumptions of xed instruments and Gaussian errors. We also obtain approximations for the ABIAS and AMSE formulae based on an asymptotic scheme; which, loosely speaking, requires the expectation of the first stage Fstatistic to converge ...
Explosive Roots 1
, 2010
"... 1This paper was inspired by reading Nielsen (2009). We thank two referees and the CoEditor for helpful comments on the original version. Magdalinos thanks the Cowles Foundation, Yale University, for hospitality in the Fall of 2009 when the paper was …rst ..."
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1This paper was inspired by reading Nielsen (2009). We thank two referees and the CoEditor for helpful comments on the original version. Magdalinos thanks the Cowles Foundation, Yale University, for hospitality in the Fall of 2009 when the paper was …rst
Estimation with an Identity ∗
, 2007
"... Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulae for ..."
Abstract
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Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulae for a structural equation model without an identity are shown to apply also to models with an identity by specializing along a certain asymptotic parameter sequence. Some of the new exact results are obtained by means of a uniform asymptotic expansion. An interesting consequence of the new theory is that the uniform asymptotic approximation provides the exact distribution of the OLS estimator in the model considered by Bergstrom (1962). This example appears to be the first instance in the statistical literature of a uniform approximation delivering an exact expression for a probability density.