Decision Theory Applied to an Instrumental Variables Model

This paper applies some general concepts in decision theory to a simple instrumental variables model. There are two endogenous variables linked by a single structural equation; k of the exogenous variables are excluded from this structural equation and provide the instrumental variables (IV). The reduced‐form distribution of the endogenous variables conditional on the exogenous variables corresponds to independent draws from a bivariate normal distribution with linear regression functions and a known covariance matrix. A canonical form of the model has parameter vector (ρ, φ, ω), where φis the parameter of interest and is normalized to be a point on the unit circle. The reduced‐form coefficients on the instrumental variables are split into a scalar parameter ρand a parameter vector ω, which is normalized to be a point on the (k−1)‐dimensional unit sphere; ρmeasures the strength of the association between the endogenous variables and the instrumental variables, and ωis a measure of direction. A prior distribution is introduced for the IV model. The parameters φ, ρ, and ωare treated as independent random variables. The distribution for φis uniform on the unit circle; the distribution for ωis uniform on the unit sphere with dimension k‐1. These choices arise from the solution of a minimax problem. The prior for ρis left general. It turns out that given any positive value for ρ, the Bayes estimator of φdoes not depend on ρ; it equals the maximum‐likelihood estimator. This Bayes estimator has constant risk; because it minimizes average risk with respect to a proper prior, it is minimax. The same general concepts are applied to obtain confidence intervals. The prior distribution is used in two ways. The first way is to integrate out the nuisance parameter ωin the IV model. This gives an integrated likelihood function with two scalar parameters, φand ρ. Inverting a likelihood ratio test, based on the integrated likelihood function, provides a confidence interval for φ. This lacks finite sample optimality, but invariance arguments show that the risk function depends only on ρand not on φor ω. The second approach to confidence sets aims for finite sample optimality by setting up a loss function that trades off coverage against the length of the interval. The automatic uniform priors are used for φand ω, but a prior is also needed for the scalar ρ, and no guidance is offered on this choice. The Bayes rule is a highest posterior density set. Invariance arguments show that the risk function depends only on ρand not on φor ω. The optimality result combines average risk and maximum risk. The confidence set minimizes the average—with respect to the prior distribution for ρ—of the maximum risk, where the maximization is with respect to φand ω.     

Dummy Endogenous Variables in Weakly Separable Models

In this paper, we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term. The model is not required to be strictly increasing in the error term, and the class of models considered includes limited dependent variable models such as discrete choice models. Conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions.     

On making causal claims: A review and recommendations

Social scientists often estimate models from correlational data, where the independent variable has not been exogenously manipulated; they also make implicit or explicit causal claims based on these models. When can these claims be made? We answer this question by first discussing design and estimation conditions under which model estimates can be interpreted, using the randomized experiment as the gold standard. We show how endogeneity – which includes omitted variables, omitted selection, simultaneity, common-method variance, and measurement error – renders estimates causally uninterpretable. Second, we present methods that allow researchers to test causal claims in situations where randomization is not possible or when causal interpretation could be confounded; these methods include fixed-effects panel, sample selection, instrumental variable, regression discontinuity, and difference-in-differences models. Third, we take stock of the methodological rigor with which causal claims are being made in a social sciences discipline by reviewing a representative sample of 110 articles on leadership published in the previous 10 years in top-tier journals. Our key finding is that researchers fail to address at least 66% and up to 90% of design and estimation conditions that make causal claims invalid. We conclude by offering 10 suggestions on how to improve non-experimental research.     

A note on f statistics for instrumental variable regessions

The asymptotic distribution of the F statistic calculated from instrumental variable'two stage least squares residuals is obtained.     

仪器分析与有机化学共同开设综合性实验的尝试

该文介绍了林业院校少学时的有机化学实验和仪器分析实验共同开设综合性实验的尝试。将有机化学实验课上制备的产品,在仪器分析实验中进行测试分析,使实验教学更接近科学研究和生产实际,既节省了学时,又提高了学生对实验课的兴趣,有利于培养学生的科研能力和综合实验素质。     

A note on f statistics for instrumental variable regessions

The asymptotic distribution of the F statistic calculated from instrumental variable‘two stage least squares residuals is obtained.     

Managing stakeholder pressures: Toward a typology of corporate social performance profiles

Why do some firms ignore some stakeholders while courting others? We propose two key drivers of firms' social postures and derive from this analysis a novel typology of corporate social performance (CSP) profiles. Although we expect that other drivers exist, we argue that a useful starting point for understanding any given CSP profile is to consider the pressure exerted on an organization by its stakeholders in conjunction with its level of resource endowment. Our preliminary typology identifies six distinct CSP profiles that reflect different opportunities and risks for stakeholder management: the CSP Vanguard, Opportunist, Generalist, Minimalist, Specialist, and Laggard. All else equal, the first two CSP profiles imply more nonmarket opportunities than risk, whereas we expect Laggards and Specialists to face greater risk in their responses to social and environmental issues. According to our framework, Generalists and Minimalists probably operate between these two extremes of business risk. Our conceptual analysis seeks to advance research and practice for more strategic stakeholder management.     

Semiparametric estimation and inference for distributional and general treatment effects

Summary.  There is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome. The paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect. For distributional treatment effects, fully non-parametric and fully parametric approaches have been proposed. The fully non-parametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions. We develop a semiparametric instrumental variable method based on the empirical likelihood approach. Our method can be applied to general outcomes and general functions of outcome distributions and allows us to predict a subject's latent compliance class on the basis of an observed outcome value in observed assignment and treatment received groups. Asymptotic results for the estimators and likelihood ratio statistic are derived. A simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully non-parametric estimators. The method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices.     

A small sample confidence interval for autoregressive parameters

This paper is concerned with interval estimation of an autoregressive parameter when the parameter space allows for magnitudes outside the unit interval. In this case, intervals based on the least-squares estimator tend to require a high level of numerical computation and can be unreliable for small sample sizes. Intervals based on the asymptotic distribution of instrumental variable estimators provide an alternative. If the instrument is taken to be the sign function, the interval is centered at the Cauchy estimator and a large sample interval can be created by estimating the standard error of this estimator. The interval proposed in this paper avoids estimating this standard error and results in a small sample improvement in coverage probability. In fact, small sample coverage is exact when the innovations come from a normal distribution.     

Instrument endogeneity and identification-robust tests: Some analytical results

When some explanatory variables in a regression are correlated with the disturbance term, instrumental variable methods are typically employed to make reliable inferences. Furthermore, to avoid difficulties associated with weak instruments, identification-robust methods are often proposed. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable assumption that some of them are exogenous. In this paper, we focus on structural models and analyze the effects of instrument endogeneity on two identification-robust procedures, the Anderson–Rubin (1949, AR) and the Kleibergen (2002, K) tests, with or without weak instruments. Two main setups are considered: (1) the level of “instrument” endogeneity is fixed (does not depend on the sample size) and (2) the instruments are locally exogenous, i.e. the parameter which controls instrument endogeneity approaches zero as the sample size increases. In the first setup, we show that both test procedures are in general consistent against the presence of invalid instruments (hence asymptotically invalid for the hypothesis of interest), whether the instruments are “strong” or “weak”. We also describe cases where test consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. These include, in particular, cases where the 2SLS estimator remains consistent, but the AR and K tests are asymptotically invalid. In the second setup, we find (non-degenerate) asymptotic non-central chi-square distributions in all cases, and describe cases where the non-centrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments). Overall, our results underscore the importance of checking for the presence of possibly invalid instruments when applying “identification-robust” tests.