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We study the asymptotic behavior of instrumental variable estimators in the static panel model under many-instruments asymptotics. We provide new estimators and standard errors based on concentrated instruments as alternatives to an estimator based on maximum likelihood. We prove that the latter estimator is consistent under many-instruments asymptotics only if the starting value in an iterative procedure is root-N consistent. A similar approach for continuous updating GMM shows the derivation is nontrivial. For the standard cross-sectional case (T = 1), the simple formulation of standard errors offer an alternative to earlier formulations.

Empirical evidence suggests that many macroeconometric and financial models are subject to both instability and identification problems. We address both issues under the unified framework of time-varying information, which includes changes in instrument strength, in second moment of instruments, and in the variance of moment conditions. Our new estimation method exploits these changes for increased efficiency of the estimates of the (stable) structural parameters. We also propose a multivariate estimator for common changes in a system of linear equations. We obtain more precise estimates of the price indexation and output gap parameters than standard methods in a NKPC model.

In this paper, I investigate the estimation of linear regression models with strictly exogenous instruments under minimal identifying assumptions. I introduce a uniformly (in the data¿generating process) consistent estimator under nearly minimal identifying assumptions. The proposed estimator, called the integrated instrumental variables (IIV) estimator, is a simple weighted least¿squares estimator. It does not require the choice of a bandwidth or tuning parameter, or the selection of a finite set of instruments. Thus, the estimator is extremely simple to implement. Monte Carlo evidence supports the theoretical claims and suggests that the IIV estimator is a robust complement to optimal instrumental variables in finite samples. In an application with quarterly UK data, the IIV estimator estimates a positive and significant elasticity of intertemporal substitution and an equally sensible estimate for its reciprocal, in sharp contrast to instrumental variables methods that fail to identify these parameters.

We study subvector inference in the linear instrumental variables model assuming homoskedasticity but allowing for weak instruments. The subvector Anderson and Rubin (1949) test that uses chi square critical values with degrees of freedom reduced by the number of parameters not under test, proposed by Guggenberger, Kleibergen, Mavroeidis, and Chen (2012), controls size but is generally conservative. We propose a conditional subvector Anderson and Rubin test that uses data‐dependent critical values that adapt to the strength of identification of the parameters not under test. This test has correct size and strictly higher power than the subvector Anderson and Rubin test by Guggenberger et al. (2012). We provide tables with conditional critical values so that the new test is quick and easy to use. Application of our method to a model of risk preferences in development economics shows that it can strengthen empirical conclusions in practice. Asymptotic size linear IV regression subvector inference weak instruments C12 C26

We compare the finite sample performance of a number of Bayesian and classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider Bayesian approaches developed by Chao and Phillips, Geweke, Kleibergen and van Dijk, and Zellner. Amongst the sampling theory methods, OLS, 2SLS, LIML, Fuller&rsquo, s modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist et al. and Blomquist and Dahlberg are also considered. Since the posterior densities and their conditionals in Chao and Phillips and Kleibergen and van Dijk are nonstandard, we use a novel &ldquo, Gibbs within Metropolis&ndash, Hastings&rdquo, algorithm, which only requires the availability of the conditional densities from the candidate generating density. Our results show that with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner&rsquo, s MELO does the best. When the endogeneity is not weak and &rho, &omega, 12&gt, 0, where &rho, is the correlation coefficient between the structural and reduced form errors, and &omega, 12 is the covariance between the unrestricted reduced form errors, the Bayesian method of moments (BMOM) outperforms all other estimators by a wide margin. When the endogeneity is not weak and &beta, &rho, &lt, 0 (&beta, being the structural parameter), the Kleibergen and van Dijk approach seems to work very well. Surprisingly, the performance of JIVE was disappointing in all our experiments.

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 eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k ≥ p, where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification.

A standard test for weak instruments compares the first-stage F-statistic to a table of critical values obtained by Stock and Yogo (2005) using simulations. We derive a closed-form solution for the expectation from which these critical values are derived, as well as present some second-order asymptotic approximations that may be of value in the presence of multiple endogenous regressors. Inspection of this new result provides insights not available from simulation, and will allow software implementations to be generalised and improved. Finally, we explore the calculation of p-values for the first-stage F-statistic weak instruments test.

Little attention has been paid to the finite-sample properties of tests for overidentifying restrictions in linear regression models with a single endogenous regressor and weak instruments. We study several such tests in models estimated by instrumental variables (IV) and limited-information maximum likelihood (LIML). Under the assumption of Gaussian disturbances, we derive expressions for a variety of test statistics as functions of eight mutually independent random variables and two nuisance parameters. The distributions of the statistics are shown to have an ill-defined limit as the parameter that determines the strength of the instruments tends to zero and as the correlation between the disturbances of the structural and reduced-form equations tends to plus or minus one. Simulation experiments demonstrate that this makes it impossible to perform reliable inference near the point at which the limit is ill-defined. Several bootstrap procedures are proposed. They alleviate the problem and allow reliable inference when the instruments are not too weak. We also study the power properties of the bootstrap tests.

This study is part of an emerging literature that aims to shed light on China's development finance activities in Africa using quantitative estimation techniques. This paper empirically investigates whether African authoritarian regimes receive more Chinese development finance than democratic ones. I use four different measures of democracy/autocracy which allows me to check whether my results depend on the specific indicator chosen. The OLS results suggest that Chinese development finance does not systematically flow to more authoritarian countries, controlling for strategic, economic, political, institutional and geographic confounding factors. The results are not driven by the specific democracy indicator used in the analysis. The findings remain virtually unchanged if I reduce the sample to Sub-Saharan Africa only. Furthermore, the results stand up to several robustness checks, including FE, RE and instrumental variable estimation.

In a weak and many instruments setting, 2SLS can be severely biased towards OLS and the standard errors can be way too small. LIML is an attractive alternative, especially when the many-instruments robust (MIR) standard errors are used as proposed by Bekker (1994).In this note we present an alternative approach to LIML through concentrated instrumental variables (CIV). This is a class of instrumental variables indexed by a single parameter. When this parameter belongs to a certain set, 2SLS estimators using CIV instruments, are many-instruments consistent. We refer to them as CIV estimators. Moreover, the usual expression for the asymptotic variance of IV estimators is many instruments consistent. One particular choice of CIV parameter, within this set, yields LIML. We thus get an alternative to the many-instruments robust (MIR) standard errors of Bekker (1994) that is of the usual simple IV form.As a byproduct, we present a new estimator, which we call the CIVE. This is a two-step estimator where the CIV parameter is based on 2SLS in the first step. It avoids LIML but is equally good to a very high degree. This suggests a simple MIR estimation strategy in an weak and many instruments setting: do 2SLS to obtain the CIV parameter, and then obtain the CIVE by another 2SLS step. (C) 2016 Elsevier B.V. All rights reserved.

We describe exact inference based on group-invariance assumptions that specify various forms of symmetry in the distribution of a disturbance vector in a general nonlinear model. It is shown that such mild assumptions can be equivalently formulated in terms of exact confidence sets for the parameters of the functional form. When applied to the linear model, this exact inference provides a unified approach to a variety of parametric and distribution-free tests. In particular, we consider exact instrumental variable inference, based on symmetry assumptions. The unboundedness of exact confidence sets is related to the power to reject a hypothesis of underidentification. In a multivariate instrumental variables context, generalizations of Anderson-Rubin confidence sets are considered. (C) 2007 Elsevier B.V. All rights reserved.

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 Richardson and Wu (1971) is discussed. One consequence of the asymptotic framework adopted here is that consistent estimators for the ABIAS and AMSE can be obtained. As a result, we are able to construct a number of bias corrected OLS and IV estimators, which we show to be consistent under a sequential asymptotic scheme. These bias-corrected estimators are also robust, in the sense that they remain consistent in a conventional asymptotic setup, where the model is fully identified. A small Monte Carlo experiment documents the relative performance of our bias adjusted estimators versus standard IV, OLS, LIML estimators, and it is shown that our estimators have lower bias than LIML for various levels of endogeneity and instrument relevance.

In regressions involving integrable functions we examine the limit properties of instrumental variable (IV) estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (NI) processes. We show that this kind of nonlinearity in the regression function can significantly affect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the NI case. Instruments based on integrable functions of lagged NI regressors display long range dependence and so remain relevant even at long lags, continuing to contribute to variance reduction in IV estimation. However, simulations show that ordinary least square (OLS) is generally superior to IV estimation in terms of mean squared error (MSE), even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary. © 2014 Copyright Taylor and Francis Group, LLC. 33 676 712 676-712

Many papers which have estimated models with forward looking expectations have reported that the magnitude of the coefficients of the expectations term is very large when compared with the effects coming from past dynamics. This has sometimes been regarded as implausible and led to the feeling that the expectations coefficient is biased upwards. A relatively general argument that has been advanced is that the bias could be due to structural changes in the means of the variables entering the structural equation. An alternative explanation is that the bias comes from weak instruments. In this paper we investigate the issue of upward bias in the estimated coefficients of the expectations variable based on a model where we can see what causes the breaks and how to control for them. We conclude that weak instruments are the most likely cause of any bias and note that structural change can affect the quality of instruments. We also look at some empirical work in Castle et al. (2011) on the NK Phillips curve in the Euro Area and U.S, assessing whether the smaller coefficient on expectations that Castle et al. (2011) highlight is due to structural change. Our conclusion is that it is not. Instead it comes from their addition of variables to the NKPC. After allowing for the fact that there are weak instruments in the estimated re-specified model it would seem that the forward coefficient estimate is actually quite high rather than low.

This paper analyzes the problem of weak instruments on identification, estimation, and inference in a simple nonparametric model of a triangular system. The paper derives a necessary and sufficient rank condition for identification, based on which weak identification is established. Then nonparametric weak instruments are defined as a sequence of reduced‐form functions where the associated rank shrinks to zero. The problem of weak instruments is characterized as concurvity, which motivates the introduction of a regularization scheme. The paper proposes a penalized series estimation method to alleviate the effects of weak instruments and shows that it achieves desirable asymptotic properties. A data‐driven procedure is proposed for the choice of the penalization parameter. The findings of this paper provide useful implications for empirical work. To illustrate them, Monte Carlo results are presented and an empirical example is given in which the effect of class size on test scores is estimated nonparametrically.

Instrumental variable estimation is central to econometric analysis and has justiflably been receiving considerable and consistent attention in the literature in the past. Recent developments have focused on cases where instruments are either weak, in terms of correlations with the endogenous variables, or many or both. The present paper suggests a new way to deal with many, possibly weak, instruments. Our suggestion is to cross-sectionally average the instruments and use these averages as instruments. Intuition and interesting recent work by Hahn (2002) suggest that parsimonious devices used in the construction of the flnal instruments, may provide efiective estimation strategies. Our use of cross-sectional averaging promotes parsimony and therefore falls within the context of such arguments. We provide a theoretical analysis of this approach in terms of its consistency properties and also show, via a Monte Carlo study, that the approach can provide improved estimation compared to standard instrumental variables estimation.

In this paper, we use identification-robust methods to assess the empirical adequacy of a New Keynesian Phillips Curve (NKPC) equation. We focus on the Gali and Gertler’s (1999) specification, on both U.S. and Canadian data. Two variants of the model are studied: one based on a rational expectations assumption, and a modification to the latter which consists in using survey data on inflation expectations. The results based on these two specifications exhibit sharp differences concerning: (i) identification difficulties, (ii) backward-looking behavior, and (ii) the frequency of price adjustments. Overall, we find that there is some support for the hybrid NKPC for the U.S., whereas the model is not suited to Canada. Our findings underscore the need for employing identification robust inference methods in the estimation of expectations-based dynamic macroeconomic relations.

We propose a novel statistic for testing the structural parameters in Instrumental Variables Regression. The statistic is straightforward to compute and has a limiting distribution that is pivotal with a degrees of freedom parameter that is equal to the number of tested parameters. It therefore differs from the Anderson-Rubin statistic, whose limiting distribution is pivotal but has a degrees of freedom parameter that is equal to the number of instruments, and the Likelihood based, Wald, Likelihood Ratio and Lagrange Multiplier, statistics, whose limiting distributions are not pivotal. We analyze the relationship between the statistic and the concentrated likelihood of the structural parameters and show that its' limiting distribution is not affected by weak instruments. We discuss examples of the non-standard shapes of the asymptotically pivotal confidence sets that can be constructed using the statistic and investigate its power properties. To show its importance for practical purposes, we apply the statistic to the Angrist-Krueger (1991) data and find similar results as in Staiger and Stock (1997).This discussion paper has resulted in a publication in Econometrica, 2002, 70(5), 1781-1803.

We propose a Generalized Method of Moments (GMM) Lagrange multiplier statistic, i.e. the K-statistic, that uses the Jacobian at the evaluated parameter value instead of the expected Jacobian. To obtain its limit behavior, we use a novel assumption that brings GMM closer to maximum likelihood and which is easily satisfied. The usual asymptotic x2 distribution of the K-statistic then holds under a wider set of circumstances, like weak and many instrument asymptotics and combinations thereof, than the standard full rank case for the Jacobian. The behavior of the K-statistic can be spurious around inflexion points and the maximum of the objective function since the moment conditions are then not satisfied. Combinations of the K-statistic with statistics that test the validity of the moment equations overcome the spurious behavior. We conduct a power comparison to test for the risk aversion parameter in a stochastic discount factor model and construct its confidence set for observed consumption growth and asset return series.

The paper considers the K-statistic, Kleibergen’s (2000) adaptation ofthe Anderson-Rubin (AR) statistic in instrumental variables regression.Compared to the AR-statistic this K-statistic shows improvedasymptotic efficiency in terms of degrees of freedom in overidentifiedmodels and yet it shares, asymptotically, the pivotal property of theAR statistic. That is, asymptotically it has a chi-square distributionwhether or not the model is identified. This pivotal property is veryrelevant for size distortions in finite-sample tests. Whereas Kleibergen(2000) focuses especially on the asymptotic behavior of the statistic,the present paper concentrates on finite-sample properties in a Gaussianframework. In that case the AR statistic has an F-distribution.However, the K-statistic is not exactly pivotal. Its finite-sample distributionis affected by nuisance parameters. Here we consider the twoextreme cases, which provide tight bounds for the exact distribution.The first case amounts to perfect identification—which is similar tothe asymptotic case—where the statistic has an F-distribution. Inthe other extreme case there is total underidentification. For the lattercase we show how to compute the exact distribution. Thus weprovide tight bounds for exact confidence sets based on the efficientK-statistic. Asymptotically the two bounds converge, except whenthere is a large number of redundant instruments.This paper has resulted in a publication in Econometric Theory, 2003, 19, 744-53.

We consider testing for weak instruments in a model with multiple endogenous variables. Unlike Stock and Yogo (2005), who considered a weak instruments problem where the rank of the matrix of reduced form parameters is near zero, here we consider a weak instruments problem of a near rank reduction of one in the matrix of reduced form parameters. For example, in a two-variable model, we consider weak instrument asymptotics of the form [Formula: see text] where [Formula: see text] and [Formula: see text] are the parameters in the two reduced-form equations, [Formula: see text] is a vector of constants and [Formula: see text] is the sample size. We investigate the use of a conditional first-stage [Formula: see text]-statistic along the lines of the proposal by Angrist and Pischke (2009) and show that, unless [Formula: see text], the variance in the denominator of their [Formula: see text]-statistic needs to be adjusted in order to get a correct asymptotic distribution when testing the hypothesis [Formula: see text]. We show that a corrected conditional [Formula: see text]-statistic is equivalent to the Cragg and Donald (1993) minimum eigenvalue rank test statistic, and is informative about the maximum total relative bias of the 2SLS estimator and the Wald tests size distortions. When [Formula: see text] in the two-variable model, or when there are more than two endogenous variables, further information over and above the Cragg-Donald statistic can be obtained about the nature of the weak instrument problem by computing the conditional first-stage [Formula: see text]-statistics.

Large shareholders may play an important role for firm policies and performance, but identifying an effect empirically presents a challenge due to the endogeneity of ownership structures. However, unlike other blockholders, individuals tend to hold blocks in corporations that are located close to where they live. Using this fact, we create an instrument – the density of wealthy individuals near a firm’s headquarters – for the presence of a large, non-managerial individual shareholder in a public firm. We show that these shareholders have a large impact on firms. Consistent with theories of large shareholders as monitors, we find that they increase firm profitability, increase dividends, reduce corporate cash holdings, and reduce executive compensation. Consistent with the view that there exist conflicts between large and small owners in public firms, we uncover evidence of substitution toward less tax-efficient forms of distribution (dividends over repurchases). In addition, our analysis shows that large shareholders reduce the liquidity of the firm’s stock.