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We introduce a routine, weakivtest, that implements the test for weak instruments by Montiel Olea and Pflueger (2013, Journal of Business and Economic Statistics 31: 358-369). weakivtest allows for errors that are not conditionally homoskedastic and serially uncorrelated. It extends the Stock and Yogo (2005, Testing for weak instruments in linear IV regression. In Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, ed. D. W. K. Andrews and J. J. Stock, 80-108. [Cambridge University Press]) weak-instrument tests available in ivreg2 and in the ivregress postestimation command estat firststage. weakivtest tests the null hypothesis that instruments are weak or that the estimator's Nagar (1959, Econometrica 27: 575-595) bias is large relative to a benchmark for both two-stage least-squares estimation and limited-information maximum likelihood with one endogenous regressor. The routine can accommodate Eicker-Huber-White heteroskedasticity robust estimates, Newey and West (1987, Econometrica 55: 703-708) heteroskedasticityand autocorrelation-consistent estimates, and clustered variance estimates. [ABSTRACT FROM AUTHOR]

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 eitherI(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 theNIcase. Instruments based on integrable functions of laggedNIregressors 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. [ABSTRACT FROM AUTHOR]

We study several methods of constructing confidence sets for the coefficient of the single right-hand-side endogenous variable in a linear equation with weak instruments. Two of these are based on conditional likelihood ratio (CLR) tests, and the others are based on invertingtstatistics or the bootstrapPvalues associated with them. We propose a new method for constructing bootstrap confidence sets based ontstatistics. In large samples, the procedures that generally work best are CLR confidence sets using asymptotic critical values and bootstrap confidence sets based on limited-information maximum likelihood (LIML) estimates. [ABSTRACT FROM AUTHOR]

A parameter in a statistical model is identified if its value can be uniquely determined from the distribution of the observable data. We consider the context of an instrumental variable analysis with a binary outcome for estimating a causal risk ratio. The semiparametric generalized method of moments and structural mean model frameworks use estimating equations for parameter estimation. In this paper, we demonstrate that lack of identification can occur in either of these frameworks, especially if the instrument is weak. In particular, the estimating equations may have no solution or multiple solutions. We investigate the relationship between the strength of the instrument and the proportion of simulated data sets for which there is a unique solution of the estimating equations. We see that this proportion does not appear to depend greatly on the sample size, particularly for weak instruments (p² ≤ 0.01). Poor identification was observed in a considerable proportion of simulated data sets for instruments explaining up to 10% of the variance in the exposure with sample sizes up to 1 million. In an applied example considering the causal effect of body mass index (weight (kg)/height (m)²) on the probability of early menarche, estimates and standard errors from an automated optimization routine were misleading. [ABSTRACT FROM AUTHOR]

The problem of weak identification has recently attracted attention in the analysis of structural macroeconomic models. Using robust methods can result in large confidence sets making precise inference difficult. We overcome this problem in the analysis of the hybrid New Keynesian Phillips Curve and a forward-looking Taylor rule by employing stronger instruments. We suggest exploiting information from a large macroeconomic data set by generating factors and using them as additional instruments. This approach results in stronger instrument sets and hence smaller weak-identification robust confidence sets. It allows us to conclude that there has been a shift toward more active monetary policy from the pre-Volcker regime to the Volcker-Greenspan tenure. [ABSTRACT FROM AUTHOR]

Economists are often interested in the coefficient of a single endogenous explanatory variable in a linear simultaneous-equations model. One way to obtain a confidence set for this coefficient is to invert the Anderson-Rubin (AR) test. The AR confidence sets that result have correct coverage under classical assumptions. However, AR confidence sets also have many undesirable properties. It is well known that they can be unbounded when the instruments are weak, as is true of any test with correct coverage. However, even when they are bounded, their length may be very misleading, and their coverage conditional on quantities that the investigator can observe (notably, the Sargan statistic for overidentifying restrictions) can be far from correct. A similar property manifests itself, for similar reasons, when a confidence set for a single parameter is based on inverting an F-test for two or more parameters. [ABSTRACT FROM AUTHOR]

We present methods for testing hypotheses and estimating confidence sets for structural parameters of economic models in the presence of instabilities and breaks of unknown form. These methods constructively explore information generated by changes in the data-generating process to improve the inference of parameters that remain stable over time. The proposed methods are suitable for models cast in the generalized method of moments framework, which makes their application wide. Moreover, they are robust to the presence of weak instruments. The genstest command in Stata implements these methods to conduct hypothesis tests and to estimate confidence sets. [ABSTRACT FROM AUTHOR]

Background An allele score is a single variable summarizing multiple genetic variants associated with a risk factor. It is calculated as the total number of risk factor-increasing alleles for an individual (unweighted score), or the sum of weights for each allele corresponding to estimated genetic effect sizes (weighted score). An allele score can be used in a Mendelian randomization analysis to estimate the causal effect of the risk factor on an outcome.Methods Data were simulated to investigate the use of allele scores in Mendelian randomization where conventional instrumental variable techniques using multiple genetic variants demonstrate ‘weak instrument’ bias. The robustness of estimates using the allele score to misspecification (for example non-linearity, effect modification) and to violations of the instrumental variable assumptions was assessed.Results Causal estimates using a correctly specified allele score were unbiased with appropriate coverage levels. The estimates were generally robust to misspecification of the allele score, but not to instrumental variable violations, even if the majority of variants in the allele score were valid instruments. Using a weighted rather than an unweighted allele score increased power, but the increase was small when genetic variants had similar effect sizes. Naive use of the data under analysis to choose which variants to include in an allele score, or for deriving weights, resulted in substantial biases.Conclusions Allele scores enable valid causal estimates with large numbers of genetic variants. The stringency of criteria for genetic variants in Mendelian randomization should be maintained for all variants in an allele score. [ABSTRACT FROM AUTHOR]

This article focuses on the empirical approach proposed by Hall and Jones (1999) to estimate the effect of what they call ‘social infrastructure’ on productivity across countries. We consider the issue of weak identification in their linear instrumental variables model. The evidence obtained from partially robust estimators, such as the k-class and jackknife estimators, is interpreted on the basis of Monte Carlo studies. Our findings suggest that using certain k-class estimators allows exclusive reliance on the linguistic variables to instrument for institutional quality despite their low correlation with the endogenous regressor in question. [ABSTRACT FROM PUBLISHER]

In simple static linear simultaneous equation models, the empirical distributions of IV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. We demonstrate that the limiting distribution of consistent IV is not affected by conditioning on exogenous regressors, whereas that of inconsistent OLS is. The OLS asymptotic and simulated actual variances are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of IV and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background, the consequences for the identification of parameters of interest are examined for a setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval assumptions on the correlation between endogenous regressor and disturbance. This yields OLS-based modified confidence intervals, which are usually conservative, as is established by simulation. Often they compare favourably with IV-based intervals and accentuate their frailty. The latter is demonstrated in an empirical illustration. [ABSTRACT FROM AUTHOR]

We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically. [ABSTRACT FROM AUTHOR]

This paper addresses the question of how to conduct inference on weakly identified coefficients in unstable econometric models. The weak correlations between the instruments and the relevant first-order condition are modelled as local to zero, and we focus on moderate parameter instabilities. We show that, in the presence of weak identification, asymptotic distributions on the estimators and tests remain robust to moderate instability. Therefore, inference on the subset of stable parameters remains robust to moderate instability of nuisance parameters. In addition, in an unstable model where some parameters are weakly identified, weak-instrument asymptotics in the literature can be used to make valid inference for the weakly identified coefficients after the strongly identified coefficients are concentrated out. [ABSTRACT FROM AUTHOR]

This article explores the link between the real business cycle and core bank earnings. Using bank-level data and an estimation technique which corrects for weak instruments, evidence confirms that pre-provision Net Interest Income (NII) is determined by the term structure of interest rates rather than output fluctuations. Output growth is only found to be significant when Loan-Loss Provisions (LLP) are taken into account. [ABSTRACT FROM PUBLISHER]

This article considers the estimation and testing of a within-group two-stage least squares (TSLS) estimator for instruments with varying degrees of weakness in a longitudinal (panel) data model. We show that adding the repeated cross-sectional information into a regression model can improve the estimation in weak instruments. Moreover, the consistency and limiting distribution of the TSLS estimator are established when both N and T tend to infinity. Some asymptotically pivotal tests are extended to a longitudinal data model and their asymptotic properties are examined. A Monte Carlo experiment is conducted to evaluate the finite sample performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Background Mendelian randomization is used to test and estimate the magnitude of a causal effect of a phenotype on an outcome by using genetic variants as instrumental variables (IVs). Estimates of association from IV analysis are biased in the direction of the confounded, observational association between phenotype and outcome. The magnitude of the bias depends on the F-statistic for the strength of relationship between IVs and phenotype. We seek to develop guidelines for the design and analysis of Mendelian randomization studies to minimize bias.Methods IV analysis was performed on simulated and real data to investigate the effect on bias of size of study, number and choice of instruments and method of analysis.Results Bias is shown to increase as the expected F-statistic decreases, and can be reduced by using parsimonious models of genetic association (i.e. not over-parameterized) and by adjusting for measured covariates. Using data from a single study, the causal estimate of a unit increase in log-transformed C-reactive protein on fibrinogen (μmol/l) is shown to increase from −0.005 (P = 0.99) to 0.792 (P = 0.00003) due to injudicious choice of instrument. Moreover, when the observed F-statistic is larger than expected in a particular study, the causal estimate is more biased towards the observational association and its standard error is smaller. This correlation between causal estimate and standard error introduces a second source of bias into meta-analysis of Mendelian randomization studies. Bias can be alleviated in meta-analyses by using individual level data and by pooling genetic effects across studies.Conclusions Weak instrument bias is of practical importance for the design and analysis of Mendelian randomization studies. Post hoc choice of instruments, genetic models or data based on measured F-statistics can exacerbate bias. In particular, the commonly cited rule of thumb that F > 10 avoids bias in IV analysis is misleading. [ABSTRACT FROM AUTHOR]

The system GMM estimator for dynamic panel data models combines moment conditions for the model in first differences with moment conditions for the model in levels. It has been shown to improve on the GMM estimator in the first differenced model in terms of bias and root mean squared error. However, we show in this paper that in the covariance stationary panel data AR(1) model the expected values of the concentration parameters in the differenced and levels equations for the cross-section at time t are the same when the variances of the individual heterogeneity and idiosyncratic errors are the same. This indicates a weak instrument problem also for the equation in levels. We show that the 2SLS biases relative to that of the OLS biases are then similar for the equations in differences and levels, as are the size distortions of the Wald tests. These results are shown to extend to the panel data GMM estimators. [ABSTRACT FROM AUTHOR]

We propose a wild bootstrap procedure for linear regression models estimated by instrumental variables. Like other bootstrap procedures that we proposed elsewhere, it uses efficient estimates of the reduced-form equation(s). Unlike the earlier procedures, it takes account of possible heteroscedasticity of unknown form. We apply this procedure to t tests, including heteroscedasticity-robust t tests, and to the Anderson-Rubin test. We provide simulation evidence that it works far better than older methods, such as the pairs bootstrap. We also show how to obtain reliable confidence intervals by inverting bootstrap tests. An empirical example illustrates the utility of these procedures. [ABSTRACT FROM AUTHOR]

This paper provides the practitioner with a method of ascertaining when the concentration parameter in a simultaneous equations model is small. We provide some exact distribution theory for a proposed statistic and show that the statistic possesses the minimal desirable characteristics of a test statistic when used to test that the concentration parameter is zero. The discussion is then extended to consider how to test for weak instruments using this statistic as a basis for inference. We also discuss the statistic's relationship to various other procedures that have appeared in the literature. [ABSTRACT FROM AUTHOR]

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that writing all the test statistics—Student's t, Anderson–Rubin, the LM statistic of Kleibergen and Moreira ( K), and likelihood ratio (LR)—as functions of six random quantities leads to a number of interesting results about the properties of the tests under weak-instrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice. [ABSTRACT FROM AUTHOR]

Using many valid instrumental variables has the potential to improve efficiency but makes the usual inference procedures inaccurate. We give corrected standard errors, an extension of Bekker to nonnormal disturbances, that adjust for many instruments. We find that this adjustment is useful in empirical work, simulations, and in the asymptotic theory. Use of the corrected standard errors in t-ratios leads to an asymptotic approximation order that is the same when the number of instrumental variables grows as when the number of instruments is fixed. We also give a version of the Kleibergen weak instrument statistic that is robust to many instruments. [ABSTRACT FROM AUTHOR]

Abstract: Anderson and his collaborators have made seminal contributions to inference with instrumental variables and to dynamic panel data models. We review these contributions and the extensive economic and statistical literature that these contributions spawned. We describe our recent work in these two areas, presenting new approaches to (a) making valid inferences in the presence of weak instruments and (b) instrument and model selection for dynamic panel data models. Both approaches use empirical likelihood and resampling. For inference in the presence of weak instruments, our approach uses model averaging to achieve asymptotic efficiency with strong instruments but maintain valid inferences with weak instruments. For instrument and model selection, our approach aims at choosing valid instruments that are strong enough to be useful. [Copyright &y& Elsevier]

The instrumental variables (IV) method has recently become widely popular in applied econometrics. However, recent work in the literature has shown that if instruments do not hold the relevance and exogeneity conditions at least in a «strong» way, the estimation results could be quite different from the population parameters, and an interpretation of the results would be meaningless. This paper presents this problem and shows some recent tests to verify the validity of the instruments employed. Additionally, I apply those tests to the estimation of the effects of child labor and household work on school attainment, by using a sample of 913 children from the Peruvian Living Standard Measurement Survey (LSMS) of 1997 and 2000. In this estimation, the instruments selected passed all the tests of exogeneity and relevance, so we can trust the consistency of these results. They show that household work performed by children has a positive impact on the children's observed educational performance three years later. In addition, the impact of child labor is negative, but it is not significantly different from zero. [ABSTRACT FROM AUTHOR]

This paper considers tests of the parameter on an endogenous variable 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 a two-sided power envelope for invariant similar tests. This allows us to assess and compare the power properties of tests such as the conditional likelihood ratio (CLR), the Lagrange multiplier, and the Anderson-Rubin tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two-sided tests. The finite-sample results of the paper are extended to the case of unknown error covariance matrix and possibly nonnormal errors via weak instrument asymptotics. Strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and strong instruments. [ABSTRACT FROM AUTHOR]

This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter-of-birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling. [ABSTRACT FROM AUTHOR]

We propose a generalized method of moments (GMM) Lagrange multiplier statistic, i.e., the K statistic, that uses a Jacobian estimator based on the continuous updating estimator that is asymptotically uncorrelated with the sample average of the moments. Its asymptotic χ² distribution therefore holds under a wider set of circumstances, like weak instruments, than the standard full rank case for the expected Jacobian under which the asymptotic χ² distributions of the traditional statistics are valid. The behavior of the K statistic can be spurious around inflection points and maxima of the objective function. This inadequacy is overcome by combining the K statistic with a statistic that tests the validity of the moment equations and by an extension of Moreira's (2003) conditional likelihood ratio statistic toward GMM. 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. [ABSTRACT FROM AUTHOR]

In this paper, we consider parameter estimation in a linear simultaneous equations model. It is well known that two-stage least squares (2SLS) estimators may perform poorly when the instruments are weak. In this case 2SLS tends to suffer from the substantial small sample biases. It is also known that LIML and Nagar-type estimators are less biased than 2SLS but suffer from large small sample variability. We construct a bias-corrected version of 2SLS based on the Jackknife principle. Using higher-order expansions we show that the MSE of our Jackknife 2SLS estimator is approximately the same as the MSE of the Nagar-type estimator. We also compare the Jackknife 2SLS with an estimator suggested by Fuller (Econometrica 45, 933–54) that significantly decreases the small sample variability of LIML. Monte Carlo simulations show that even in relatively large samples the MSE of LIML and Nagar can be substantially larger than for Jackknife 2SLS. The Jackknife 2SLS estimator and Fuller's estimator give the best overall performance. Based on our Monte Carlo experiments we conduct informal statistical tests of the accuracy of approximate bias and MSE formulas. We find that higher-order expansions traditionally used to rank LIML, 2SLS and other IV estimators are unreliable when identification of the model is weak. Overall, our results show that only estimators with well-defined finite sample moments should be used when identification of the model is weak. [ABSTRACT FROM AUTHOR]

We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log-likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The static has a x² limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting distribution does not depend on nuisance parameters. The statistic overcomes the deficiencies of the Anderon-Rubin statistic, whose limiting distribution has a degrees of freedom parameter equal to the number of instruments, and the likelihood based, Wald, likelihood ratio, and Lagrange multiplier statistics, whose limiting distributions depend on nuisance parameters. Size and power comparison reveal that the statistic is a (asymptotic) size-corrected likelihood ratio statistic. We apply the statistic to the Agrist-Krueger (1991) data and find similar results as in Staiger and Stock (1997). [ABSTRACT FROM AUTHOR]

We examine empirical relevance of three alternative asymptotic approximations to the distribution of instrumental variables estimators by Monte Carlo experiments. We find that conventional asymptotics provides a reasonable approximation to the actual distribution of instrumental variables estimators when the sample size is reasonably large. For most sample sizes, we find Bekker asymptotics provides reasonably good approximation even when the first stage R² is very small. We conclude that reporting Bekker confidence interval would suffice for most microeconometric (cross-sectional) applications, and the comparative advantage of Staiger and Stock asymptotic approximation is in applications with sample sizes typical in macroeconometric (time series) applications. [ABSTRACT FROM AUTHOR]

We develop a new specification test for IV estimators adopting a particular second order approximation of Bekker. The new specification test compares the difference of the forward (conventional) 2SLS estimator of the coefficient of the right‐hand side endogenous variable with the reverse 2SLS estimator of the same unknown parameter when the normalization is changed. Under the null hypothesis that conventional first order asymptotics provide a reliable guide to inference, the two estimates should be very similar. Our test sees whether the resulting difference in the two estimates satisfies the results of second order asymptotic theory. Essentially the same idea is applied to develop another new specification test using second‐order unbiased estimators of the type first proposed by Nagar. If the forward and reverse Nagar‐type estimators are not significantly different we recommend estimation by LIML, which we demonstrate is the optimal linear combination of the Nagar‐type estimators (to second order). We also demonstrate the high degree of similarity for k‐class estimators between the approach of Bekker and the Edgeworth expansion approach of Rothenberg. An empirical example and Monte Carlo evidence demonstrate the operation of the new specification test. [ABSTRACT FROM AUTHOR]

This manuscript lists questions from a video interview with Jim Stock at the Norges Bank on 15 March 2015. The interview covers topics ranging from time series analysis and weak instruments to climate policy. [ABSTRACT FROM AUTHOR]