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Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, the unbiased estimator is unique. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS …
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive mean-unbiased estimators for the structural parameter in instrumental variables models where the sign of one or more first stage coefficients is known. In the case with a single instrument, the unbiased estimator is unique. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong while retaining unbiasedness in finite samples. We show numerically that unbiasedness does not come at a cost of increased dispersion: in the single instrument case, the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample …
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, the unbiased estimator is unique. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS …
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this …
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, the unbiased estimator is unique. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS …
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Unbiased Instrumental Variables Estimation Under Known First-Stage Sign, Isaiah Andrews, Timothy B. Armstrong
Cowles Foundation Discussion Papers
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this …
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0: No conditions are placed on the expected Jacobian of the moment functions, …
Asymptotic Size Of Kleibergen's Lm And Conditional Lr Tests For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Asymptotic Size Of Kleibergen's Lm And Conditional Lr Tests For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
An influential paper by Kleibergen (2005) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures has not been determined in the literature. This paper does so. This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p …
Generic Results For Establishing The Asymptotic Size Of Confidence Sets And Tests, Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger
Generic Results For Establishing The Asymptotic Size Of Confidence Sets And Tests, Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic has a discontinuity in its limit distribution. The results are illustrated in three examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic …
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) tests and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For two of the three tests, all that is required is that the moment functions and their derivatives have 2 + γ bounded moments for some γ > 0 in i.i.d. scenarios. In stationary strong mixing time series cases, the same condition suffices, but the magnitude of …
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2+γ bounded moments for some γ>0. No conditions are placed on the expected Jacobian of the moment functions, on the …
Gmm Estimation For Dynamic Panels With Fixed Effects And Strong Instruments At Unity, Chirok Han, Peter C.B. Phillips
Gmm Estimation For Dynamic Panels With Fixed Effects And Strong Instruments At Unity, Chirok Han, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops new estimation and inference procedures for dynamic panel data models with fixed effects and incidental trends. A simple consistent GMM estimation method is proposed that avoids the weak moment condition problem that is known to affect conventional GMM estimation when the autoregressive coefficient (rho) is near unity. In both panel and time series cases, the estimator has standard Gaussian asymptotics for all values of rho in (-1, 1] irrespective of how the composite cross section and time series sample sizes pass to infinity. Simulations reveal that the estimator has little bias even in very small samples. The …
Rank Tests For Instrumental Variables Regression With Weak Instruments, Donald W.K. Andrews, Gustavo Soares
Rank Tests For Instrumental Variables Regression With Weak Instruments, Donald W.K. Andrews, Gustavo Soares
Cowles Foundation Discussion Papers
This paper considers tests in an instrumental variables (IVs) regression model with IVs that may be weak. Tests that have near-optimal asymptotic power properties with Gaussian errors for weak and strong IVs have been determined in Andrews, Moreira, and Stock (2006a). In this paper, we seek tests that have near-optimal asymptotic power with Gaussian errors and improved power with non-Gaussian errors relative to existing tests. Tests with such properties are obtained by introducing rank tests that are analogous to the conditional likelihood ratio test of Moreira (2003). We also introduce a rank test that is analogous to the Lagrange multiplier …
Inference With Weak Instruments, Donald W.K. Andrews, James H. Stock
Inference With Weak Instruments, Donald W.K. Andrews, James H. Stock
Cowles Foundation Discussion Papers
This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests (and confidence intervals derived from tests) than estimators. The paper also presents new testing results under “many weak IV asymptotics,” which are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. Asymptotic power envelopes for invariant tests are established. Power comparisons of the conditional likelihood ratio (CLR), Anderson-Rubin, and Lagrange multiplier tests are made. Numerical results show that the CLR test is on the asymptotic power envelope. This holds …
Exactly Distribution-Free Inference In Instrumental Variables Regression With Possibly Weak Instruments, Donald W.K. Andrews, Vadim Marmer
Exactly Distribution-Free Inference In Instrumental Variables Regression With Possibly Weak Instruments, Donald W.K. Andrews, Vadim Marmer
Cowles Foundation Discussion Papers
This paper introduces a rank-based test for the instrumental variables regression model that dominates the Anderson-Rubin test in terms of finite sample size and asymptotic power in certain circumstances. The test has correct size for any distribution of the errors with weak or strong instruments. The test has noticeably higher power than the Anderson-Rubin test when the error distribution has thick tails and comparable power otherwise. Like the Anderson-Rubin test, the rank tests considered here perform best, relative to other available tests, in exactly-identified models.
Optimal Invariant Similar Tests For Instrumental Variables Regression, Donald W.K. Andrews, Marcelo J. Moreira, James H. Stock
Optimal Invariant Similar Tests For Instrumental Variables Regression, Donald W.K. Andrews, Marcelo J. Moreira, James H. Stock
Cowles Foundation Discussion Papers
This paper considers tests of the parameter on endogenous variables in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine tests that maximize weighted average power (WAP) for arbitrary weight functions among invariant similar tests. Such tests include point optimal (PO) invariant similar tests. The results yield the power envelope for invariant similar tests. This allows one to assess and compare the …
Alternative Approximations Of The Bias And Mse Of The Iv Estimator Under Weak Identification With An Application To Bias Correction, John C. Chao, Norman R. Swanson
Alternative Approximations Of The Bias And Mse Of The Iv Estimator Under Weak Identification With An Application To Bias Correction, John C. Chao, Norman R. Swanson
Cowles Foundation Discussion Papers
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. The approximations so obtained are shown, via regression analysis, to yield good approximations for ABIAS and AMSE functions, and the AMSE approximation is shown to perform well relative to the approximation of Donald and Newey (2001). Additionally, the manner in which our framework generalizes that of …
Consistent Estimation With A Large Number Of Weak Instruments, John C. Chao, Norman R. Swanson
Consistent Estimation With A Large Number Of Weak Instruments, John C. Chao, Norman R. Swanson
Cowles Foundation Discussion Papers
This paper conducts a general analysis of the conditions under which consistent estimation can be achieved in instrumental variables regression when the available instruments are weak in the local-to-zero sense. More precisely, the approach adopted in this paper combines key features of the local-to-zero framework of Staiger and Stock (1997) and the many-instrument framework of Morimune (1983) and Bekker (1994) and generalizes both of these frameworks in the following ways. First, we consider a general local-to-zero framework which allows for an arbitrary degree of instrument weakness by modeling the first-stage coefficients as shrinking toward zero at an unspecified rate, say …