Alphabetical order by author’s Last name. Update by May 13, 2017

Donald Andrews (Yale University, United States)

A Note on Optimal Inference in the Linear IV Model

This paper considers tests and confidence sets (CS’s) concerning the coe¢ cient on the endogenous variable in the linear IV regression model with homoskedastic normal errors and one right-hand side endogenous variable. The paper derives a finite-sample lower bound function for the probability that a CS constructed using a two-sided invariant similar test has infinite length and shows numerically that the conditional likelihood ratio (CLR) CS of Moreira (2003) is not always “very close”to this lower bound function. This implies that the CLR test is not always very close to the two-sided asymptotically-e¢ cient (AE) power envelope for invariant similar tests of Andrews, Moreira, and Stock (2006) (AMS). On the other hand, the paper establishes the finite-sample optimality of the CLR test when the correlation between the structural and reduced-form errors, or between the two reduced-form errors, goes to 1 or -1 and other parameters are held constant, where optimality means achievement of the two-sided AE power envelope of AMS. These results cover the full range of (non-zero) IV strength. The paper investigates in detail scenarios in which the CLR test is not on the two-sided AE power envelope of AMS. Also, the paper shows via theory and numerical work that the CLR test is close to having greatest average power, where the average is over a grid of concentration parameter values and over pairs alternative hypothesis values of the parameter of interest, uniformly over pairs of alternative hypothesis values and uniformly over the correlation between the structural and reduced-form errors. The paper concludes that, although the CLR test is not always very close to the two-sided AE power envelope of AMS, CLR tests and CS’s have very good overall properties. Joint with Vadim Marmer and Zhengfei Yu

Isaiah Andrews (MIT, United States)

Identification of and Correction for Publication Bias

We consider linear IV regression models and we propose two new inference procedures that are easy to implement and robust to any identification pattern. Our tests are based on generalized ICM-type tests, see Bierens (1982). We combine his idea, first with the Anderson and Rubin’s (1949) idea of fixing the value of the coefficient under test, and second with the conditionality principle developed by Moreira (2003). Our procedures avoid any parametric assumption or approximation about the reduced form of the model, and are powerful irrespective of its particular
form. Our tests control size irrespective of identification strength and are competitive with existing procedures in simulations and applications. Joint with Pascal Lavergne, TSE.

Bertille Antoine (Simon Fraser University, Canada)

Identification-Robust Nonparametric Inference in a Linear IV Model

Not all empirical results are published, and the probability that a given result is published may depend on the result. Such selective publication can lead to biased estimators and distorted inference. We discuss identification of selectivity, and in particular of the conditional probability of publication as a function of a study’s results. We propose two approaches to identification, the first based on systematic replication studies, and the second based on meta-studies. Having identified the form of selectivity, we propose median-unbiased estimators and associated confidence sets. We apply our methods to recent large-scale replication studies in experimental economics and experimental psychology, where we find strong evidence of selection based on statistical significance. We also apply our methods to a meta-study of minimum wage effects, where we find larger publication probabilities for studies reporting a negative effect on employment, and to a meta-study of de-worming programs, where our findings are ambiguous. Joint with Max Kasy.

Otilia Boldea (Tilburg University)

Bootstrapping Structural Change Tests

Bootstrap methods have been applied extensively in testing for structural breaks in the past few decades, but the conditions under which they are valid are, for the most part, unknown. In this paper, we fill this gap for the empirically important scenario in which supremum-type tests are used to test for discrete parameter change in linear models estimated by least squares methods. Our analysis covers models with exogenous regressors estimated by Ordinary Least Squares (OLS), and models with endogenous regressors estimated by Two Stage Least Squares (2SLS). Specifically, we show the asymptotic validity of the (IID and wild) recursive and fixed-regressors bootstraps for inference based on sup-F and sup-Wald statistics for testing both the null hypothesis of no parameter change versus an alternative of parameter change at k > 0 unknown break points, and also the null hypothesis of parameter change at l break points versus an alternative of parameter change at l + 1 break points. For the case of exogenous regressors, Bai and Perron (1998) derive and tabulate the limiting distributions of the test statistics based on OLS under the appropriate null hypothesis; for the case of endogenous regressors, Hall, Han and Boldea (2012) show that the same limiting distributions hold for the analogous test statistics based on 2SLS when the first stage model is stable. As part of our analysis, we derive the limiting distribution of the test statistics based on 2SLS when the regressors are endogenous and the first stage regression exhibits discrete parameter change. We show that the asymptotic distributions of the second-stage break-point tests are non-pivotal, and as a consequence the usual Bai and Perron (1998) critical values cannot be used. Thus, our bootstrapbased methods represent the most practically feasible approach to testing for multiple discrete parameter changes in the empirically relevant scenario of endogenous regressors and an unstable first stage regression. Our simulation results show very good finite sample properties with all the versions of the bootstrap considered here, and indicate that the bootstrap tests are preferred over the asymptotic tests, especially in the presence of conditional heteroskedasticity of unknown form. Joint with Adriana Cornea-Madeira and Alastair R. Hall

Federico Bugni (Duke University, United States)

Regression-based inference for covariate-adaptive randomization with multiple treatments

Joint with Ivan A. Canay, and Azeem M. Shaikh

Matias D. Cattaneo (University of Michigan, United States)

Coverage Error Optimal Confidence Intervals for Regression Discontinuity Designs

Gregory Cox (Yale University, United States)

Weak Identification in a Class of Generically Identified Models with an Application to Factor Models

This paper provides new theorems for calculating the asymptotic distribution of extremum estimators along sequences of parameters that lead to an unidentified limit. These theorems are formulated for models that are doubly parameterized by structural and reduced form parameters. This paper applies these theorems to weak identification in factor models. Identification in factor models can be characterized in terms of a rank condition on the factor loadings. Weak identification in factor models is complicated by the fact that the boundary of the identified set may not be differentiable and the limit of the objective function may be degenerate. The new theorems are capable of handling these difficulties, yielding inference that is robust to failure of the rank condition. Explicit robust inference procedures are proposed for two example models: one model with one weak factor and one model with two factors that may be weak or entangled. This paper also provides an empirical application of inference for entangled factors in a model of parents investing in their children.

Geert Dhaene (University of Leuven, Belgium)

Second-order corrected likelihood for nonlinear panel models with fixed effects

We propose a second-order correction for nonlinear fixed-effect panel models. The correction is made via the log-likelihood function. It removes the two leading terms of the bias of the log-likelihood that arises from estimating the fixed effects. Maximizing the corrected likelihood gives a second-order bias-corrected estimator, with bias O(T −3), where T is the number of time periods. The correction applies to general nonlinear fixed-effect models with independent observations. The bias reduction properties are confirmed in simulations for binary-choice models. Joint with Yutao Sun

Prosper Dovonon (Concordia University, Canada)

Inference in Second-Order Identified Models

First-order asymptotic analyses of the Generalized Method of Moments (GMM) estimator and its associated statistics are based on the assumption that the population moment condition identifies the parameter vector both globally and locally at first order. In linear models, global and firstorder local identification are equivalent but in nonlinear models they are not. In certain econometric models of interest, parameters are globally identified but only identified locally at second order. In these scenarios the standard GMM inference techniques based on first-order asymptotics are invalid, see Dovonon and Renault (2013) and Dovonon and Hall (2016). In this paper, we explore how to perform inference in moment condition models that only identify the parameters locally to second order. For inference about the parameters, we consider inference based on conventional Wald and LM statistics, and also the Generalized Anderson Rubin (GAR) statistic (Anderson and Rubin, 1949; Dufour, 1997; Staiger and Stock, 1997; Stock and Wright, 2000) and the KLM statistic (Kleibergen, 2002, 2005). Both the GAR and KLM statistics have been proposed as methods of inference in the presence of weak identification and are known to be “identification robust” in the sense that their limiting distribution is the same under first-order and weak identification. For inference about the model specification, we consider the identification-robust J statistic (Kleibergen, 2005) and the GAR statistic. In each case, we derive the limiting distribution of statistics under both null and local alternative hypotheses. We show that under their respective null hypotheses the GAR, KLM and J statistics have the same limiting distribution as would apply under first-order or weak identification, thus showing their identification robustness extends to second-order identification. We explore the power properties in detail in two empirically relevant models with second-order identification. In the panel autoregressive (AR) model of order one, our analysis indicates that the Wald test of whether the AR parameter is one has superior power to the corresponding GAR test which, in turn, dominates the KLM and LM tests. For the conditionally heteroskedastic factor model, we compare Kleibergen’s (2005) J and the GAR statistics to Hansen’s (1982) overidentifying restrictions test (previously analyzed in this context by Dovonon and Renault, 2013) and find the power ranking depends on the sample size. Collectively, our results suggest that tests with meaningful power can be conducted in second-order identified models. Joint with Alastair R. Hall and Frank Kleibergen.

Jean-Marie Dufour (McGill University, Canada)
Wald Tests of Nonlinear Hypotheses when Restrictions are Singular
Patrik Guggenberger (The Pennsylvania State University, United States)

On the Subvector Anderson Rubin test in Linear IV Regression with conditional heteroskedasticity

Joint work with Frank Kleibergen and Sophocles Mavroeidis

Grant Hillier (University of Southampton, United Kingdom)

Nonparametric Testing for Exogeneity with Discrete Regressors and Instruments

This paper presents new approaches to testing for exogeneity in nonparametric models with discrete regressors and instruments. Under endogeneity, the identifying power of a discrete instrument depends on the number of support points of the instrument relative to that of the regressor. For the pointidentified case, the test for exogeneity is an adapted version of the familiar Durbin-Wu-Hausman approach. For the partially identiÖed case, the teststatistic is derived from a constrained minimization problem. Both tests are shown to be consistent with satisfactory Önite-sample properties. The practicability of the suggested testing procedures is illustrated in an application to the modelling of returns to schooling. Joint with Katarzyna Bech

Michael Jansson (University of California, Berkeley, United States)

Bootstrap-Based Inference for Cube Root Consistent Estimators
Joint with Matias Cattaneo and Kenichi Nagasawa

Philipp Ketz (Paris School of Economics, France)

A Simple Solution to Invalid Inference in the Random Coeffcients Logit Model

Toru Kitagawa (University College London, United Kingdom)

Uncertain Identification
Uncertainty about the choice of identifying assumptions is common in causal studies, but has been often ignored in empirical practice. This paper considers uncertainty over a class of models that impose different sets of identifying assumptions, which, in general, leads to a mix of point- and set-identified models. We propose a method for performing inference in the presence of this type of uncertainty by generalizing Bayesian model averaging. Our proposal is to consider ambiguous belief (multiple posteriors) for the set-identified models, and to combine them with a single posterior in a model that is either point-identified or that imposes non-dogmatic identifying assumptions in the form of a Bayesian prior. The output is a set of posteriors (post-averaging ambiguous belief ) that are mixtures of the single posterior and any element of the class of multiple posteriors, with mixture weights the posterior probabilities of the models. We propose to summarize the post-averaging ambiguous belief by reporting the range of posterior means and the associated credible regions, and offer a simple algorithm to compute these quantities. We establish conditions under which the data are informative about model probabilities, which occurs when the models are distinguishable for some distribution of data and/or specify different priors for reduced-form parameters, and examine the asymptotic behavior of the posterior model probabilities. The method is general and allows for dogmatic and non-dogmatic identifying assumptions, multiple point-identified models, multiple set-identified models, and nested or non-nested models.

Adam McCloskey (Brown University, United States)

Estimation and Inference with a (Nearly) Singular Jacobian

This paper develops extremum estimation and inference results for nonlinear models with very general forms of potential identification failure when the source of this identification failure is known. We examine models that may have a general defficient rank Jacobian in certain parts of the parameter space. When identification fails in one of these models, it becomes under-identified and the identification status of individual parameters is not generally straightforward to characterize. We provide a systematic reparameterization procedure that leads to a reparameterized model with straightforward identification status. Using this reparameterization, we determine the asymptotic behavior of standard extremum estimators and Wald statistics under a comprehensive class of parameter sequences characterizing the strength of identification of the model parameters, ranging from non-identification to strong identification. Using the asymptotic results, we propose hypothesis testing methods that make use of a standard Wald statistic and data-dependent critical values, leading to tests with correct asymptotic size regardless of identification strength and good power properties. Importantly, this allows one to directly conduct uniform inference on low-dimensional functions of the model parameters, including one-dimensional subvectors. The paper illustrates these results in three examples: a sample selection model, a triangular threshold crossing model and a collective model for household expenditures. Joint with Sukjin Han.

Marcelo J. Moreira (Getúlio Vargas Foundation, Brazil)

Invariant Tests in the Instrumental Variable Model

Anders Rahbek (University of Copenhagen, Denmark)

Bootstrapping non-causal autoregressions: with applications to explosive bubble modelling

In this paper we develop bootstrap-based inference for non-causal autoregressions with heavy tailed innovations. This class of models is widely used for modelling bubbles and explosive dynamics in economic and financial time series. In the non-causal, heavy tail framework, a major drawback of asymptotic inference is that it is not feasible in practice, as the relevant limiting distributions depend crucially on the (unknown) decay rate of the tails of the distribution of the innovations. In addition, even in the unrealistic case where the tail behavior is known, asymptotic inference may su¤er from small-sample issues. To overcome these difficulties, in this paper we study novel bootstrap inference procedures, using parameter estimates obtained with the null hypothesis imposed (the so-called restricted bootstrap). We discuss three di¤erent choices of bootstrap innovations: wild bootstrap, based on Rademacher errors; permutation bootstrap; a combination of the two (permutation wild bootstrap). Crucially, implementation of these bootstraps do not require any a priori knowledge about the distribution of the innovations, such as the tail index or the convergence rates of the estimators. We establish sufficient conditions ensuring that, under the null hypothesis, the bootstrap statistics estimate consistently particular conditional distributions of the original statistics. In particular, we show that validity of the permutation bootstrap holds without any restrictions on the distribution of the innovations, while the permutation wild and the standard wild bootstraps require further assumptions such as symmetry of the innovation distribution. Extensive Monte Carlo simulations show that the finite sample performance of the proposed bootstrap tests is exceptionally good, both in terms of size and of empirical rejection probabilities under the alternative hypothesis. We conclude by applying the proposed bootstrap inference to Bitcoin/USD exchange rates and to crude oil prices data. We find that indeed non-causal models with heavy tailed innovations are able to fit the data quite well, also in periods of bubble dynamics.

Kees Jan van Garderen (University of Amsterdam)

Confidence Regions for Spatial Autoregressive Models

Spatial autoregressive models may have likelihood functions with multiple local maxima. The parameter space is often restricted to allow for only one maximum and to rule out singular points of the loglikelihood associated with eigenvalues of the spatial correlation matrix. In this paper we will not restrict the parameter space and allow for the distribution of the MLE to be multimodal. This has implications for inference, including disjoint confidence regions. We use an adapted version of Barndorff-Nielsen’s p^{∗}-approximation to the conditional density of the MLE to construct confidence sets that have correct coverage levels, conditionally on an ancillary statistic that is indicative of the degree of bimodality, as well as unconditionally. Standard confidence intervals based on the normal approximation can have coverage rates that are much below their stated nominal level and connected confidence intervals with correct coverage are much wider when bimodality is considerable. Our confidence regions remain accurate even in small samples.