Bias corrections for two-step fixed effects panel data estimators

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.     

Evaluating the effectiveness of private education across countries: a comparison of methods

This paper aims at estimating the effect of private vs. public education on pupils' achievement using the 2000 Organisation for Economic Co-operation and Development (OECD) Program for International Student Assessment (PISA) survey and taking into account the potential bias due to the existence of unobserved confounding factors. To deal with these selection biases, three methods are implemented in a comparative perspective: (1) instrumental variable (IV) regression; (2) Heckman's two-stage approach and (3) propensity score matching. This exercise underlines important divergences between the results of parametric and non-parametric estimators. All results, however, show that private education does not generate systematic benefits.     

The impact of consumer health information on the demand for health services

This paper empirically examines whether consumers use health information, from non-physician information sources, as a substitute or complement for health services – namely for physician visits and emergency room (ER) visits. An indicator of patient trust in physicians is developed and used as a proxy for potential unobserved heterogeneity that may drive both consumers’ propensity to seek information and to use physician services. The results, after correcting for sample selection bias and controlling for unobserved heterogeneity, concur with the literature, that consumer health information increases the likelihood of visiting a physician as well as the frequency of visits on average. However, low-trust consumers tend to substitute self-care through consumer health information for physician services. Further, better-informed consumers make significantly fewer ER visits suggesting that information may be improving efficiency in the market.     

Beyond Publication Bias

Abstract.  This review considers several meta‐regression and graphical methods that can differentiate genuine empirical effect from publication bias. Publication selection exists when editors, reviewers, or researchers have a preference for statistically significant results. Because all areas of empirical research are susceptible to publication selection, any average or tally of significant/insignificant studies is likely to be biased and potentially misleading. Meta‐regression analysis can see through the murk of random sampling error and selected misspecification bias to identify the underlying statistical structures that characterize genuine empirical effect. Meta‐significance testing and precision‐effect testing (PET) are offered as a means to identify empirical effect beyond publication bias and are applied to four areas of empirical economics research – minimum wage effects, union‐productivity effects, price elasticities, and tests of the natural rate hypothesis.     

Selection correction and sensitivity analysis for ordered treatment effect on count response

In estimating the effect of an ordered treatment τ on a count response y with an observational data where τ is self‐selected (not randomized), observed variables x and unobserved variables ε can be unbalanced across the control group (τ = 0) and the treatment groups (τ = 1, …, J). While the imbalance in x causes ‘overt bias’ which can be removed by controlling for x, the imbalance in ε causes ‘covert (hidden or selection) bias’ which cannot be easily removed. This paper makes three contributions. First, a proper counter‐factual causal framework for ordered treatment effect on count response is set up. Second, with no plausible instrument available for τ, a selection correction approach is proposed for the hidden bias. Third, a nonparametric sensitivity analysis is proposed where the treatment effect is nonparametrically estimated under no hidden bias first, and then a sensitivity analysis is conducted to see how sensitive the nonparametric estimate is to the assumption of no hidden bias. The analytic framework is applied to data from the Health and Retirement Study: the treatment is ordered exercise levels in five categories and the response is doctor office visits per year. The selection correction approach yields very large effects, which are however ruled out by the nonparametric sensitivity analysis. This finding suggests a good deal of caution in using selection correction approaches. Copyright © 2004 John Wiley & Sons, Ltd.     

Correcting for bias in retrospective data

When panel data are not available, retrospective data are used in the estimation of dynamic choice models. However, retrospective data are not reliable. Previous studies of voting choices, for example, have shown that respondents misreport their past choices in order to appear more consistent with their current choice. Such retrospective bias leads to inconsistent estimates, especially when there is state dependence in choices. Specifically, observed persistence in retrospective data may be due to (a) true state dependence, (b) unobserved heterogeneity, and (c) retrospective bias in reporting previous choices. Whereas Heckman in his 1981 study deals with (a) and (b), we introduce a method to estimate true state dependence while accounting for both unobserved heterogeneity and retrospective reporting bias. Our method is based on modeling the reporting behavior and integrating it into the estimation. The identification strategy is based on the correlation between the reported previous choices and current exogenous variables. Using data on Israeli voters, we find that the probability that a respondent whose vote intention in 1991 differed from his or her past voting choices would lie about their past choices is 0.23. Copyright © 2007 John Wiley & Sons, Ltd.     

Two-step estimation of panel data models with censored endogenous variables and selection bias

This paper presents some two-step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias. Our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity/selection bias to include as additional explanatory variables in the primary equation. These are obtained through a decomposition of the reduced form residuals. The panel nature of the data allows adjustment, and testing, for two forms of endogeneity and/or sample selection bias. Furthermore, it incorporates roles for dynamics and state dependence in the reduced form. Finally, we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions.     

On the effect of obesity on employment in the presence of observed and unobserved confounding

The aim of this paper was to estimate the effect of obesity on the employment probability for Italian men and women accounting for both observed and unobserved confounding. We use microdata collected by the Italian National Statistical Office for the year 2009 during a multi‐scope survey of Italian households. The employment–obesity relationship is estimated after controlling for observed confounding by using probit regression and a propensity score weighting approach. To control for both observed and unobserved confounding (endogeneity), a semiparametric recursive bivariate probit model is employed instead. Our findings suggest that obesity has a significant negative effect on the employment probability and that endogeneity might not be an important issue.     

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

A Social Interactions Model with Endogenous Friendship Formation and Selectivity

This paper analyzes the endogeneity bias problem caused by associations of members within a network when the spatial autoregressive (SAR) model is used to study social interactions. When there are unobserved factors that affect both friendship decisions and economic outcomes, the spatial weight matrix (sociomatrix; adjacency matrix) in the SAR model, which represents the structure of a friendship network, might correlate with the disturbance term of the model, and consequently result in an endogenous selection problem in the outcomes. We consider this problem of selection bias with a modeling approach. In this approach, a statistical network model is adopted to explain the endogenous network formation process. By specifying unobserved components in both the network model and the SAR model, we capture the correlation between the processes of network and outcome formation, and propose a proper estimation procedure for the system. We demonstrate that the estimation of this system can be effectively done by using the Bayesian method. We provide a Monte Carlo experiment and an empirical application of this modeling approach on the friendship networks of high school students and their interactions on academic performance in the Add Health data. Copyright © 2015 John Wiley & Sons, Ltd.     

STATE DEPENDENCE AND HETEROGENEITY IN HEALTH USING A BIAS‐CORRECTED FIXED‐EFFECTS ESTIMATOR

This paper estimates a dynamic ordered probit model of self‐assessed health with two fixed effects: one in the linear index equation and one in the cut‐points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model. Copyright © 2012 John Wiley & Sons, Ltd.     

Time and causality: A Monte Carlo assessment of the timing-of-events approach

We present new Monte Carlo evidence regarding the feasibility of separating causality from selection within non-experimental duration data, by means of the non-parametric maximum likelihood estimator (NPMLE). Key findings are: (i) the NPMLE is extremely reliable, and it accurately separates the causal effects of treatment and duration dependence from sorting effects, almost regardless of the true unobserved heterogeneity distribution; (ii) the NPMLE is normally distributed, and standard errors can be computed directly from the optimally selected model; and (iii) unjustified restrictions on the heterogeneity distribution, e.g., in terms of a pre-specified number of support points, may cause substantial bias.     

Sampling and Selection Bias in International Collaborative Alliance Research

Abstract

This paper argues that our understanding of international collaborative alliances is limited by selection bias. Bias in data sets developed both from published announcements of alliance formation and in more narrowly focused studies are discussed. The results of an empirical test of geographic bias are reported.     

Hospital competition under pay‐for‐performance: Quality,mortality, and readmissions

Health outcomes, such as mortality and readmission rates, are commonly used as indicators of hospital quality and as a basis to design pay‐for‐performance (P4P) incentive schemes. We propose a model of hospital behavior under P4P where patients differ in severity and can choose hospital based on quality. We assume that risk‐adjustment is not fully accounted for and that unobserved dimensions of severity remain. We show that the introduction of P4P which rewards lower mortality and/or readmission rates can weaken or strengthen hospitals' incentive to provide quality. Since patients with higher severity have a different probability of exercising patient choice when quality varies, this introduces a selection bias (patient composition effect) which in turn alters quality incentives. We also show that this composition effect increases with the degree of competition. Critically, readmission rates suffer from one additional source of selection bias through mortality rates since quality affects the distribution of survived patients. This implies that the scope for counterproductive effects of P4P is larger when financial rewards are linked to readmission rates rather than mortality rates.     

Publication Bias in the Economic Freedom and Economic Growth Literature

Abstract.  The impact of institutions on economic performance has attracted significant attention from researchers, as well as from policy reformers. A rapidly growing area in this literature is the impact of economic freedom on economic growth. The aim of this paper was to explore publication bias in this literature by means of traditional funnel plots, meta‐significance testing, as well as by bootstrapping these meta‐significance tests. When all the available estimates are combined and averaged, there seems to be evidence of a genuine and positive economic freedom – economic growth effect. However, it is also shown that the economic freedom – economic growth literature is tainted strongly with publication bias. The existence of publication bias makes it difficult to identify the magnitude of the genuine effect of economic freedom on economic growth. The paper explores the differences between aggregate and disaggregate measures of economic freedom and shows that selection effects are stronger when aggregate measures are used.     

Three Factors to Signal Non‐Response Bias With Applications to Categorical Auxiliary Variables

Non‐response causes bias in survey estimates. The unknown bias can be reduced, for example as in this paper by the use of a calibration estimator built on powerful auxiliary information. Still, some bias will always remain. A bias reduction indicator is proposed and expressed as a product of three factors reflecting familiar statistical ideas. These factors provide a useful perspective on the components that constitute non‐response bias in estimates. To illustrate the indicator, we focus on the important case with information defined by one or more categorical auxiliary variables, each expressed by two or more properties or traits. Together, the auxiliary variables may represent a large number of traits, more or less important for bias reduction. An examination of the three factors of the bias reduction indicator brings the insight that the ultimate auxiliary vector for calibration need not or should not contain all available traits; some are unimportant or detrimental to bias reduction. The question becomes one of selection of traits, not of complete auxiliary variables. Empirical examples are given, and a stepwise procedure for selecting important traits is proposed.     

Intergenerational mobility and sample selection in short panels

Using data from the first 11 waves of the BHPS, this paper measures the extent of the selection bias induced by standard coresidence conditions—bias that is expected to be severe in short panels—on measures of intergenerational mobility in occupational prestige. We try to limit the impact of other selection biases, such as those induced by labour market restrictions that are typically imposed in intergenerational mobility studies, by using different measures of socio‐economic status that account for missing labour market information. We stress four main results. First, there is evidence of an underestimation of the true intergenerational elasticity, the extent of which ranges between 12% and 39%. Second, the proposed methods used to correct for the selection bias seem to be unable to attenuate it, except for the propensity score weighting procedure, which performs well in most circumstances. This result is confirmed both under the assumption of missing‐at‐random data as well as under the assumption of not‐missing‐at‐random data. Third, the two previous sets of results (direction and extent of the bias, and differential abilities to correct for it) are also robust when we account for measurement error. Fourth, restricting the sample to a period shorter than the 11 waves under analysis leads to a severe sample selection bias. In the cases when the analysis is limited to eight waves, this bias ranges from about 40% to 65%. Copyright © 2006 John Wiley & Sons, Ltd.     

Self-serving Bias in Annual Report Narratives: An Empirical Analysis of the Impact of Economic Crises

Consistently, management's explanations of corporate performance in accounting narratives have been found to suffer from self-serving bias. Yet there is no unequivocal evidence as to whether this bias is the product of conscious efforts to manage the impressions of the audience or the result of unintentional cognitive biases. The present study contributes to this discussion by comparing the narratives of the letters addressed to shareholders of Europe's most highly-capitalized companies in crisis and non-crisis settings. We find that a crisis situation leads to more extensive use of self-serving bias as adverse external economic conditions are used by managers to present themselves in the best possible light. Given that the letters to shareholders are widely used for capital allocation decisions and considering the evidence that intentional self-serving behavior can be successful, our results imply that investors need to be alert to misleading explanations of performance, particularly during external crises. The International Accounting Standards Board (IASB) has formulated a practice statement proposing non-mandatory guidance on the management commentary that accompanies financial statements. Our results suggest that the quality of narrative information in annual reports is unlikely to be augmented by guidelines that encourage the discussion of corporate performance through the eyes of management.     

Does joining social media groups help to reduce students’ dropout within the first university year?

Using observational data, the aim of our study paper was to investigate whether university students’ dropout within the first year is influenced by participation in social media groups such as Facebook pages created and run by other students. Specifically, in this paper such participation is considered as a treatment and represents a means to help promote and strengthen social relationships amongst students but also to help share information on courses and other material useful for studying and preparing for exams. For this purpose, data from a sample survey of students enrolled in a major Italian university were used. Given a non-random treatment assignment, analysis was carried out using propensity score matching (PSM) in order to correct for selection bias due to a set of observable pretreatment covariates. Several matching techniques and sensitivity analyses suggested that the results were robust for estimating an average treatment effect on the treated group. The estimated effect indicated that participation in social media groups is effective for lowering the dropout rate.     

Bias in estimating multivariate and univariate diffusions

Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that when the mean reversion is slow, the approximation methods work better than ML, the bias formulae are accurate, and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ML. For the square root process, the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman’s method and the Milstein method.