A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators

Richardson, David H.; Wu, De-Min

doi:10.2307/1909670

Cited by 41 publications

(15 citation statements)

References 7 publications

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“…Nagar (1959) derived a large N expansion of the bias in a fairly complicated fashion, while a simpler derivation was given in Hahn and Hausman (2002b). In fact, the same second order approximation 2 Note that these numerical results are consistent with earlier analytical work by Richardson and Wu (1971) and Chao and Swanson (2007). In particular, see Proposition 3.1 of Chao and Swanson (2007).…”

Section: Finite Sample Behavior Of K-class Estimatorssupporting

confidence: 75%

Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

Harding

Hausman

Palmer

2016

Advances in Econometrics

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This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite sample unbiased k-class estimator, we introduce a double k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperforms Fuller (1977) estimators in terms of mean bias and MSE.JEL: C31, C13, C15

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Section: Finite Sample Behavior Of K-class Estimatorssupporting

confidence: 75%

Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

Harding

Hausman

Palmer

2016

Advances in Econometrics

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“…In particular, we focus on the IV estimator, and derive explicit analytical formulae for the asymptotic bias (ABIAS) and asymptotic mean-squared error (AMSE) of this estimator under the local-to-zero/weakinstrument framework pioneered by Staiger and Stock (1997). The formulae that we derive correspond to the exact bias and MSE functions of the 2SLS estimator, as derived by Richardson and Wu (1971), under the assumption of a simultaneous equations model with fixed instruments and Gaussian error distribution; and in this sense our results can be viewed as generalizing theirs to the more general setting with possibly nonnormal errors and stochastic instruments.…”

Section: Introductionmentioning

confidence: 99%

Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction

Chao

Swanson

2007

Journal of Econometrics

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We provide analytical formulae for the asymptotic bias (ABIAS) and mean-squared error (AMSE) of the IV estimator, and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage F-statistic to converge to a finite (possibly small) positive limit as the number of instruments approaches infinity. Our analytical formulae can be viewed as generalizing the bias and MSE results of [Richardson and Wu 1971. A note on the comparison of ordinary and two-stage least squares estimators. Econometrica 39, 973-982] to the case with nonnormal errors and stochastic instruments. Our approximations are shown to compare favorably with approximations due to [Morimune 1983. Approximate distributions of k-class estimators when the degree of overidentifiability is large compared with the sample size. Econometrica 51, 821-841] and [Donald and Newey 2001. Choosing the number of instruments. Econometrica 69, 1161-1191], particularly when the instruments are weak. We also construct consistent estimators for the ABIAS and AMSE, and we use these to further construct a number of bias corrected OLS and IV estimators, the properties of which are examined both analytically and via a series of Monte Carlo experiments. r 2006 Elsevier B.V. All rights reserved. JEL classifications: C13; C31

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“…On the other hand, the weighted regression model which is comparatively computed here to treat all the observation with an equal treatment, shows a p-value of 0.000 < 0.05 for the IV which is also significant to explain the WPI being the dependent variable. Both of the regressions exhibit significance of IV (Exchange rate) to explain the DV (WPI) but no reliance is yet based on this end and we further our analysis to check for the existence of any serial correlation within the series (see, Keirs, 1997;Richardson & Wu, 1971). Note.…”

Section: Resultsmentioning

confidence: 99%

Assessing the Exchange Rate Volatility as an External Shock to Chinese Economy

Azimi¹

2016

IJEF

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Theoretically, the rate of exchange is one of the major drivers of inflation that influences the wholesale price index (WPI) in countries where significant emphasis is put over import and export like China. In this paper, the exchange rate's clustering volatility and its impulsiveness as an external shock to WPI is investigated on a set of time series data which represents 4,067 daily observation of Chinese Economy from August 12, 2004-September 30, 2015. The ordinary least square and weighted regression analysis reveal significant p-values of 0.000 for exchange rate that explain the WPI throughout the stated period. The autoregressive conditional heteroskedasticity and generalized autoregressive conditional heteroskedasticity model exhibit significant probability value of 0.000 and 0.044 respectively for WPI and the exchange rate. It is found that the previous days' volatility of WPI influences the future volatility of WPI as an internal shock in addition to the previous days' impulsiveness of the exchange rate which influences the future volatility of the WPI as an external shock. The testing models are thoroughly applied and their stability and validity are evidenced thereto.

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A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators

Cited by 41 publications

References 7 publications

Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments

Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction

Assessing the Exchange Rate Volatility as an External Shock to Chinese Economy

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