Testing Missing at Random Using Instrumental Variables

Breunig, Christoph

doi:10.1080/07350015.2017.1302879

Cited by 20 publications

(22 citation statements)

References 44 publications

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“…In our application, P(∆ = 1|V * ) denotes the probability that a company reports sales or costs of intermediates given potential productivity Prod * and other controls (that is P(∆ = 1|V * ) = P(∆ = 1|Prod * , ITout, L, K, Y2K)). As we show below, identification of the function v → P(∆ = 1|V * = v) is key to identifying the structural parameter through inverse probability weighting but is also of interest on its own, because it illustrates whether the MAR assumption is violated (see also Breunig [2015] for a formal test of it). In our application, we see that the conditional probability depends on the potential productivity realizations in a nonlinear fashion (see chapter 3).…”

Section: Now Taking the Difference Of Both Equation Yieldsmentioning

confidence: 99%

Information technology outsourcing and firm productivity: eliminating bias from selective missingness in the dependent variable

Breunig

Kummer

Ohnemus

et al. 2019

The Econometrics Journal

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Summary Missing values are a major problem in all econometric applications based on survey data. A standard approach assumes data are missing at random and uses imputation methods or even listwise deletion. This approach is justified if item nonresponse does not depend on the potentially missing variables’ realization. However, assuming missingness at random may introduce bias if nonresponse is, in fact, selective. Relevant applications range from financial or strategic firm-level data to individual-level data on income or privacy-sensitive behaviors. In this paper, we propose a novel approach to deal with selective item nonresponse in the model’s dependent variable. Our approach is based on instrumental variables that affect selection only through a partially observed outcome variable. In addition, we allow for endogenous regressors. We establish identification of the structural parameter and propose a simple two-step estimation procedure for it. Our estimator is consistent and robust against biases that would prevail when assuming missingness at random. We implement the estimation procedure using firm-level survey data and a binary instrumental variable to estimate the effect of outsourcing on productivity.

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Section: Now Taking the Difference Of Both Equation Yieldsmentioning

confidence: 99%

Information technology outsourcing and firm productivity: eliminating bias from selective missingness in the dependent variable

Breunig

Kummer

Ohnemus

et al. 2019

The Econometrics Journal

Self Cite

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“…In this paper, we propose two score tests for MAR under a linear logistic model when a completely parametric model and a semiparametric location model, respectively, are imposed on the outcome regression model, respectively. Compared with the tests proposed by Breunig (2019) and Duan et al (2020), the new tests have at least three advantages. The first remarkable advantage is that no identification condition is required under MNAR, which implies that no instrumental variable is needed.…”

Section: Introductionmentioning

confidence: 99%

“…The first remarkable advantage is that no identification condition is required under MNAR, which implies that no instrumental variable is needed. However, without an instrumental variable, the tests of Breunig (2019) and Duan et al (2020) may fail to work. The second advantage is that the new tests involve much easier calculations, because the underlying unknown parameters need only be estimated under MAR.…”

Section: Introductionmentioning

confidence: 99%

Score test for missing at random or not

Wang,

Lu,

Liu

2021

Preprint

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Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR. A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The score tests require only parameter estimation under the null MAR assumption, which completely circumvents the identification issue. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

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“…In addition, Molenberghs et al (2008) showed that an MNAR model may be replaced with a MAR model that fits the observed data exactly. Further, while statistical tests exist for checking the MCAR mechanism on the data set (e.g., Little 1988; see Rhoads 2012 for a review), tests for the MAR assumption against the MNAR alternative require additional assumptions to be refutable (Breunig 2019;Jaeger 2006;Rhoads 2012). Nonetheless, in practice, much statistical modeling still relies on the assumption of an ignorable missing-data mechanism and thus robust methods that offer improved estimation and inference approaches to deal with models of ignorable missing-data mechanisms are of critical importance.…”

Section: Introductionmentioning

confidence: 99%

Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data

et al. 2019

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Researchers are often faced with the challenge of developing statistical models with incomplete data. Exacerbating this situation is the possibility that either the researcher’s complete-data model or the model of the missing-data mechanism is misspecified. In this article, we create a formal theoretical framework for developing statistical models and detecting model misspecification in the presence of incomplete data where maximum likelihood estimates are obtained by maximizing the observable-data likelihood function when the missing-data mechanism is assumed ignorable. First, we provide sufficient regularity conditions on the researcher’s complete-data model to characterize the asymptotic behavior of maximum likelihood estimates in the simultaneous presence of both missing data and model misspecification. These results are then used to derive robust hypothesis testing methods for possibly misspecified models in the presence of Missing at Random (MAR) or Missing Not at Random (MNAR) missing data. Second, we introduce a method for the detection of model misspecification in missing data problems using recently developed Generalized Information Matrix Tests (GIMT). Third, we identify regularity conditions for the Missing Information Principle (MIP) to hold in the presence of model misspecification so as to provide useful computational covariance matrix estimation formulas. Fourth, we provide regularity conditions that ensure the observable-data expected negative log-likelihood function is convex in the presence of partially observable data when the amount of missingness is sufficiently small and the complete-data likelihood is convex. Fifth, we show that when the researcher has correctly specified a complete-data model with a convex negative likelihood function and an ignorable missing-data mechanism, then its strict local minimizer is the true parameter value for the complete-data model when the amount of missingness is sufficiently small. Our results thus provide new robust estimation, inference, and specification analysis methods for developing statistical models with incomplete data.

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Testing Missing at Random Using Instrumental Variables

Cited by 20 publications

References 44 publications

Information technology outsourcing and firm productivity: eliminating bias from selective missingness in the dependent variable

Information technology outsourcing and firm productivity: eliminating bias from selective missingness in the dependent variable

Score test for missing at random or not

Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data

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