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.     

Follower behavior renders leader behavior endogenous: The simultaneity problem,estimation challenges,and solutions

Traditionally, leadership research has focused on unidirectional questions in which leader attributes are considered to determine follower outcomes. However, many phenomena between leaders (x) and followers (y) involve a simultaneous influence process in which x affects y, and y also affects x (i.e., simultaneity). Unfortunately, this simultaneity bias creates endogeneity and is often not properly addressed in the extant leadership literature. In three studies, we demonstrate the challenges of simultaneity bias and present two methodological solutions that can help to correct problems of simultaneity bias. We focus on simultaneity that occurs between follower resistance and leader control. We mathematically demonstrate the simultaneity bias using a simulated dataset and show how this bias can be statistically solved using an instrumental variable estimation approach. Furthermore, we present how the simultaneity bias can be resolved using an experimental design. We discuss how our approach advances theory and methods for leadership research.     

An IV Model of Quantile Treatment Effects

The ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications. However, in observational studies, the variables of interest (e.g., education, prices) are often endogenous, making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes. In order to address this problem, we develop a model of quantile treatment effects (QTE) in the presence of endogeneity and obtain conditions for identification of the QTE without functional form assumptions. The principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states. This feature allows us to overcome the endogeneity problem and recover the true QTE through the use of instrumental variables. The proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors, where QTE can be interpreted as the structural quantile effects (SQE).     

Returns to Schooling in Spain: How Reliable are Instrumental Variable Estimates?

This paper studies the ordinary least–squares (OLS) and instrumental variable (IV) estimates of the returns to schooling for male workers in Spain. OLS estimates are often biased due to the endogeneity of schooling, measurement errors or omitted variables. Proper IV estimates correct this bias. The reliability of family background, natural experiments (based on changes in the education system and season of birth) and the availability of a college in the province is checked using Spanish data. The results suggest that background and college availability are valid instruments and that the IV estimates of the returns to schooling are higher than OLS estimates. These results are in line with the majority of previous results in the literature.     

半参数计量经济联立模型的变窗宽估计理论

联立方程模型在经济政策制定、经济结构分析和经济预测方面起重要作用.文章将半参数单方程计量经济模型的局部线性估计方法与传统联立方程计量经济模型的工具变量估计方法相结合, 在随机设计(模型中所有变量为随机变量)下, 提出了半参数联立方程计量经济模型的局部线性工具变量变窗宽估计方法, 并利用极限理论研究了估计的大样本性质.结果表明:参数分量的估计具有一致性和渐近正态性且收敛速度为n-1/2;非参数分量估计在内点处具有一致性和渐近正态性, 其收敛速度达到了非参数函数估计的最优收敛速度.     

Semi‐Nonparametric IV Estimation of Shape‐Invariant Engel Curves

This paper studies a shape‐invariant Engel curve system with endogenous total expenditure, in which the shape‐invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root‐n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of “low‐level” sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves.     

A Test of Exogeneity Without Instrumental Variables in Models With Bunching

This paper presents a test of the exogeneity of a single explanatory variable in a multivariate model. It does not require the exogeneity of the other regressors or the existence of instrumental variables. The fundamental maintained assumption is that the model must be continuous in the explanatory variable of interest. This test has power when unobservable confounders are discontinuous with respect to the explanatory variable of interest, and it is particularly suitable for applications in which that variable has bunching points. An application of the test to the problem of estimating the effects of maternal smoking in birth weight shows evidence of remaining endogeneity, even after controlling for the most complete covariate specification in the literature.     

Natural experiments in leadership research: An introduction,review, and guidelines

Endogeneity is a serious challenge for leadership research. To overcome the problem, researchers increasingly rely upon experimental designs, such as laboratory and field experiments. In this paper, we argue that natural experiments — in the form of standard natural experiments, instrumental variable, and regression discontinuity designs — offer additional opportunities to infer causal relationships. We conduct a systematic, cross-disciplinary review of 87 studies that leverage natural experimental designs to inquire into a leadership topic. We introduce the standard natural experiment, instrumental variable, and regression discontinuity design and use topic modeling to analyze which leadership topics have been investigated using natural experimental designs. Based on the review, we provide guidelines that we hope will assist scholars in discovering natural exogenous variations, selecting the most suitable form of natural experiment and by mobilizing appropriate statistical techniques and robustness checks. The paper is addressed to leadership and management scholars who aim to use natural experiments to infer causal relationships.     

非参数计量经济联立模型的变窗宽估计理论

联立方程模型在经济政策制定、经济结构分析和经济预测方面起重要作用. 文章将非参 数回归模型的局部线性估计方法与传统联立方程模型估计方法相结合,在随机设计(模型中所 有变量为随机变量) 下,提出了非参数计量经济联立模型的局部线性工具变量变窗宽估计并利 用概率论中大数定理和中心极限定理等在内点处研究了它的大样本性质,证明了它的一致性 和渐近正态性,它在内点处的收敛速度达到了非参数函数估计的最优收敛速度     

Firm‐level Evidence on Gender Wage Discrimination in the Belgian Private Economy

In this paper we explore a matched employer–employee data set to investigate the presence of gender wage discrimination in the Belgian private economy labour market. Contrary to many existing papers, we analyse gender wage discrimination using an independent productivity measure. Using firm‐level data, we are able to compare direct estimates of a gender productivity differential with those of a gender wage differential. We take advantage of the panel structure to identify gender‐related differences from within‐firm variation. Moreover, inspired by recent developments in the production function estimation literature, we address the problem of endogeneity of the gender mix using a structural production function estimator alongside instrumental variable‐general method of moments (IV‐GMM) methods where lagged value of labour inputs are used as instruments. Our results suggest that there is no gender wage discrimination inside private firms located in Belgium, on the contrary.     

Endogeneity: How Failure to Correct for it can Cause Wrong Inferences and Some Remedies

Although researchers in business and management are becoming increasingly aware of the importance of endogeneity affecting regression analysis, they frequently do not have the right methodological toolkit to adjust for this issue. In this paper we discuss such a toolkit. There are also areas in business and management research which to date seem to be mostly oblivious about the endogeneity issue. We highlight such an area, which studies the question of whether firms that are cross‐listed on a foreign stock exchange are charged premium fees by their auditors. When the same methodology (pooled ordinary least squares) as in the existing literature is used, the existence of an audit fee premium for cross‐listed firms seems to be confirmed. However, once methodologies are used which adjust for the various types of endogeneity (i.e. omitted variable bias, simultaneous and dynamic endogeneity) there is no longer support for the existence of such a generalized premium. Hence, not only do we illustrate that failure to adjust for endogeneity has severe consequences such as drawing the wrong inferences, but we also review various ways to control for the different types of endogeneity.     

Applied Nonparametric Instrumental Variables Estimation

Instrumental variables are widely used in applied econometrics to achieve identification and carry out estimation and inference in models that contain endogenous explanatory variables. In most applications, the function of interest (e.g., an Engel curve or demand function) is assumed to be known up to finitely many parameters (e.g., a linear model), and instrumental variables are used to identify and estimate these parameters. However, linear and other finite‐dimensional parametric models make strong assumptions about the population being modeled that are rarely if ever justified by economic theory or other a priori reasoning and can lead to seriously erroneous conclusions if they are incorrect. This paper explores what can be learned when the function of interest is identified through an instrumental variable but is not assumed to be known up to finitely many parameters. The paper explains the differences between parametric and nonparametric estimators that are important for applied research, describes an easily implemented nonparametric instrumental variables estimator, and presents empirical examples in which nonparametric methods lead to substantive conclusions that are quite different from those obtained using standard, parametric estimators.     

经营、投资和筹资现金流动态交互影响分析

本文提出系统现金流的面板向量自回归模型(Panel Vector Autoregression,PVAR)考察经营、投资和筹资现金流三者间的动态交互影响效应。该模型不但解决了变量内生性问题,并且有效刻画了系统变量间的冲击反应。敏感度分析与方差分解的结果表明:中国制造业上市公司投资现金流对经营现金流具有突出的敏感性,而投资现金流的波动则更多地受到筹资现金流的波动影响。正交冲击反应分析则进一步表明:经营现金流对投资、筹资现金流冲击的反应不显著,而投资现金流对经营、筹资现金流冲击的反应要持续较长时间,并且筹资现金流与经营现金流具有一定程度上的短期替代作用。以上研究结果分别从现金流敏感度和现金流波动性两个角度说明中国制造业上市公司存在外部融资约束问题。     

Effects of charismatic leadership and rewards on individual performance

We report two replication attempts for the positive main effects of charismatic leadership and performance-based rewards on individual performance from a field experiment in a charitable context (Antonakis, d'Adda, Weber, and Zehnder, 2015). Using video based treatments - instead of the live treatments in the original study - we only replicate the effect of performance-based rewards in a sample of 118 participants; we do not find an effect of charisma on performance. In a second study, we address the reasons that could explain the unsuccessful replication of the charisma effect by: (a) using a larger sample (n = 274) and (b) ensuring the experimental task context to have ingroup - cultural and hence value - fit between the workers and the beneficiaries of a charity. In the second study we fully replicate the positive effects of charisma as well as performance-based rewards on individual performance. In extending the original work we tested and found no interaction between economic incentives and charisma. Furthermore, using the manipulations as experimentally randomized instrumental variables (ERIVs, see Sajons, 2020), we find that the effect of charisma on individual performance is channelled through the vision dimension of leadership.     

Construct redundancy in leader behaviors: A review and agenda for the future

Leadership remains a popular and heavily researched area in the social sciences. Such popularity has led to a proliferation of new constructs within the leadership domain. Here, we argue that such construct proliferation without pruning is unhealthy and violates the principle of parsimony. Our purpose was to examine construct redundancy via a comprehensive review of task-oriented, relational, passive, and inspirational leader behaviors as well as values-based and moral leadership behaviors. Our findings, as indexed via meta-analytic correlations, reveal that construct redundancy remains problematic for the leadership literature. In addition, many of the values-based and moral behavior models correlated heavily with constructs traditionally examined as outcome variables (e.g., trust, LMX, justice). Implications for future research are discussed in regards to construct redundancy and how to avoid endogeneity bias in primary studies in the leadership literature.     

Structural Nonparametric Cointegrating Regression

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill‐posed inverse problems. In functional cointegrating regressions where the regressor is an integrated or near‐integrated time series, it is shown here that inverse and ill‐posed inverse problems do not arise. Instead, simple nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving straightforward asymptotics that are useable in practical work. It is further shown that use of augmented regression, as is common in linear cointegration modeling to address endogeneity, does not lead to bias reduction in nonparametric regression, but there is an asymptotic gain in variance reduction. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series when there is a single integrated or near‐integrated regressor. The methods may be applied to a range of empirical models where functional estimation of cointegrating relations is required.     

Instrumental variables estimation: Assumptions,pitfalls, and guidelines

Researchers striving to ensure rigor in their scientific findings face a common pitfall: Endogeneity. To tackle this problem, scholars have increasingly adopted instrumental variables estimation (IVE). Although there are many published works showing how IVE should be used, many applied researchers still have trouble understanding how to use the method correctly. In this article, we provide a methodological overview of IVE by discussing the underlying conditions valid instruments must satisfy as well as common mistakes made in using IVE. Using simulated data, we further demonstrate the sensitivity of IVE to violations of its conditions. We then take stock of the literature in a social science discipline (i.e., leadership research) and provide insights regarding trends and shortcomings in the application of IVE. Based on our review, we categorize the different types of instruments used and discuss the potential appropriateness of each type. We conclude by providing non–technical guidelines targeted at the study design, analysis, and reporting phases, which will help applied social science researchers to ensure they use IVE correctly.     

On Completeness and Consistency in Nonparametric Instrumental Variable Models

This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.     

The Implications of Temporary Jobs on the Distribution of Wages in Italy: An Unconditional IVQTE Approach

Using Italian data, this paper investigates the wage implications of temporary jobs across the whole pay profile using unconditional quantile regression (UQR) models. Results clearly indicate that the wage penalty associated to temporary jobs is significantly larger at the bottom of wage profile and is almost absent for high‐wage jobs. This is in line with the sticky floors hypothesis, supporting the idea that the wage gap for temporary employees depends on their position in the wage distribution for low‐paid jobs. To recover a causal interpretation, I employ an instrumental variable (IV) strategy. I adopt the unconditional instrumental variable quantile treatment effects (IVQTE) estimator proposed by Frolich and Melly, which corrects for endogenous selection in temporary contracts. The IVQTE estimates yield similar results to standard UQR, even if the wage penalty is larger in size at the bottom of the wage distribution and disappears at the top quantiles. This evidence highlights that policies aimed at increasing flexibility may reinforce the two‐tier nature of the Italian labour market and the relative wage inequality.     

Practice-Specific Risk Perceptions and Self-Reported Food Safety Practices

The relationship between risk perception and risk avoidance is typically analyzed using self-reported measures. However, in domains such as driving or food handling, the validity of responses about usual behavior is threatened because people think about the situations in which they are self-aware, such as when they encounter a hazard. Indeed, researchers have often noted a divergence between what people say about their behavior and how they actually behave. Thus, in order to draw conclusions about risk perceptions and risk avoidance from survey data, it is important to identify particular cognitive elements, such as those measured by questions about risk and safety knowledge, risk perceptions, or information search behavior, which may be effective antecedents of self-reported safety behavior. It is also important to identify and correct for potential sources of bias that may exist in the data. The authors analyze the Food and Drug Administration's 1998 Food Safety Survey to determine whether there are consistent cognitive antecedents for three types of safe food practices: preparation, eating, and cooling of foods. An assessment of measurement biases shows that endogeneity of food choices affects reports of food preparation. In addition, response bias affects reports of cooling practices as evidenced by its relation to knowledge and information search, a pattern of cognitive effects unique to cooling practices. After correcting for these biases, results show that practice-specific risk perceptions are the primary cognitive antecedents of safe food behavior, which has implications for the design of effective education messages about food safety.