Heteroskedasticity-robust Standard Errors Research Articles

Disclosure-based regulation and municipal security trade prices

Purpose This paper aims to measure the trade price impact of a recent regulatory disclosure intervention in municipal securities secondary markets, which required broker-dealers to disclose securities trading information on a near-real-time and continuing basis. Design/methodology/approach The author analyzes trade price outcomes in the preintervention and postintervention regimes using a suite of time series estimations that give heteroskedasticity-robust standard errors (Prais–Winsten and Cochrain–Orcutt), accommodate higher-order lag structure in the error term (autoregressive integrated moving average) and account for volatility clustering in the time series (generalized autoregressive conditional heteroskedasticity). Findings Results show that regulatory disclosure intervention significantly improved trade price efficiency in municipal securities secondary markets as daily trade price differential and volatility both declined market-wide after the disclosure intervention. Research limitations/implications The sample consists of trades in State of California general obligation bonds; therefore, empirical findings may not be generalizable to other states, local governments and different types of bonds. Practical implications The findings highlight voluntary information disclosure as a practical and effective mechanism in disclosure regulation of municipal securities secondary markets. Originality/value Only a small body of work exists that examines information disclosure regulation in municipal securities secondary markets; therefore, this paper expands knowledge on the topic and should provide renewed impetus for regulatory efforts aimed at improving the efficiency of municipal capital markets.

Effects of digital chatbot on gender attitudes and exposure to intimate partner violence among young women in South Africa.

South Africa has among the highest rates of intimate partner violence (IPV) globally, with young women at heightened risk due to inequitable gender roles, limited relationship skills, and inadequate social support. Despite an urgent need for violence prevention in low- and middle-income settings, most efficacious approaches are time-intensive and costly to deliver. Digital, interactive chatbots may help young women navigate safer relationships and develop healthier gender beliefs and skills. Young women (18-24 years old) across South Africa were recruited via Facebook for participation in an individually randomised controlled trial (n = 19,643) during the period of June 2021-September 2021. Users were randomly allocated, using a pipeline algorithm, to one of four trial arms: Pure Control (PC) had no user engagement outside of study measures; Attention Treatment (T0) provided didactic information about sexual health through a text-based chatbot; Gamified Treatment (T1) was a behaviourally-informed gamified text-based chatbot; Narrative Treatment (T2) was a behaviourally-informed drama delivered through pre-recorded voice notes. All chatbots were delivered in WhatsApp, through which users were invited to complete brief "quizzes" comprising adapted versions of validated scales. Primary outcomes were short-form adaptations of scales for gender attitudes (Gender Relations Scale) and past-month IPV (WHO Multi-country Study Instrument). Secondary outcomes were identification of unhealthy relationship behaviours (Intimate Partner Violence Attitudes Scale) and brief screener for depressive symptoms (Patient Health Questionnaire). A direct chat link to a trained counsellor was a safety measure (accessed by 4.5% of the sample). We estimated treatment effects using ordinary least squares and heteroskedasticity robust standard errors. The trial retained 11,630 (59.2%) to the primary endpoint of gender attitudes. Compared to control, all treatments led to moderate and significant changes in attitudes towards greater gender equity (Cohen's D = 0.10, 0.29, 0.20 for T0, T1, and T2, respectively). The gamified chatbot (T1) had modest but significant effects on IPV: 56% of young women reported past-month IPV, compared to 62% among those without treatment (marginal effects = -0.07, 95%CI = -0.09to-0.05). The narrative treatment (T2) had no effect on IPV exposure. T1 increased identification of unhealthy relationship behaviours at a moderate and significant level (Cohen's D = 0.25). Neither T1 nor T2 had a measurable effect on depressive symptoms as measured by the brief screener. Interpretation: A behaviourally-informed, gamified chatbot increased gender equitable attitudes and was protective for IPV exposure among young women in South Africa. These effects, while modest in magnitude, could represent a meaningful impact given potential to scale the low-cost intervention.

VALID HETEROSKEDASTICITY ROBUST TESTING

Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions, and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly used test statistics. Furthermore, sufficient and often also necessary conditions for their existence are given that are easy to check. Granted their existence, these critical values are the canonical choice: larger critical values result in unnecessary power loss, whereas smaller critical values lead to overrejections under the null hypothesis, make spurious discoveries more likely, and thus are invalid. We suggest algorithms to numerically determine the proposed critical values and provide implementations in accompanying software. Finally, we numerically study the behavior of the proposed testing procedures, including their power properties.

Democracy and Health in Developing Countries: New Cross-National Evidence, 1990–2016

Scholars have long investigated the factors that affect health outcomes in less-developed countries. One debate that has increasingly intensified in recent years is the democracy and health relationship in comparative international context. Scholars argue that democracy does affect country-level health outcomes in less-developed countries, while others argue democracy does not affect country-level health outcomes. I estimate the effect of numerous democracy indexes on child mortality and infant mortality in developing countries using fixed effects regression models with heteroskedasticity-robust standard errors clustered by country. I find that multiple aspects of democracy exert significant beneficial effects on child mortality and infant mortality in less-developed countries.

Analysis of the Ecuadorian government's proposed methodology of brand valuation: application in agricultural sector brands

PurposeThe purpose of this work is to analyze a brand valuation methodology proposed by the current Ecuadorian National Service for Intellectual Rights, assessing the relevance of the proposed marketing variables: awareness, associations and evaluation of purchase determinants, and their relationship within the proposed methodology.Design/methodology/approachThe authors used data from surveys of 482 consumers of two agricultural brands in Ecuador (supplies, equipment and services). The authors applied linear multiple regressions estimated by generalized least squares with heteroskedasticity-robust standard errors. “Intention to repurchase” and “recommend” the brands were selected as dependent variables due to their relationship with brand value.FindingsBrand awareness and associations positively influence the two dependent variables. However, the interaction between brand awareness and associations is negative, suggesting that, for the upper level of awareness, associations have no effect over intentions. This result holds for both brands. Brand evaluation of purchase determinants was a significant predictor of intentions only for the brand which belongs to a product category in which the purchase decision process is more extensive and with more effort.Research limitations/implicationsThis study is focused only on agricultural brands, which limits the generalization of the findings.Originality/valueThe agricultural sector is very important in Ecuador due to its contribution to GDP and employment, and the country's position as the fifth exporter of bananas worldwide. Understanding consumer behavior is important for brands and firms' managers in order to preserve or increase brand value, for which a reliable valuation model is useful.

Geographic distribution of bed occupancy during the COVID-19 epidemic in the United States: A nationwide study.

Geographic distribution of bed occupancy during the COVID-19 epidemic in the United States: A nationwide study.

A Regression Analysis of the Carbon Footprint of Megacities

Urbanization and climate change are two major issues that humanity faces in the 21st century. Megacities are large urban agglomerations with more than 10 million inhabitants that emerged in the 20th century. The world’s top 100 economies include many North and South American megacities, such as New York, Los Angeles, Mexico City, Sao Paulo and Buenos Aires; European cities such as London and Paris; and Asian cities such as Tokyo, Osaka, Seoul, Beijing and Mumbai. This paper addresses a dearth of megacity energy metabolism models in the literature. Cross-sectional data for 36 global megacities were collected from many literature and Internet sources. Variables included megacity name, country and region; population; area; population density; (per capita) GDP; income inequality measures; (per capita) energy consumption; household electricity prices; (per capita) carbon and ecological footprint; degree days; average urban heat island intensity; and temperature and precipitation. A descriptive comparison of the characteristics of megacities was followed by ordinary least squares with heteroskedasticity-robust standard errors that were used to estimate four alternative multiple regression models. The per-capita carbon footprint of megacities was positively associated with the megacity GDP per capita, and the megacity ecological footprint; and negatively associated with country income inequality, a low-income country dummy, the country household electricity price, and the megacity annual precipitation. Targeted policies are needed, but more policy autonomy should be left to megacities. Collecting longitudinal data for megacities is very challenging but should be a next step to overcome misspecification and bias issues that plague cross-sectional approaches.

Democracy and deforestation: The role of spillover effects

This paper is a replication and extension of Buitenzorgy and Mol (2011). We recreate the data and analyses from that paper on the impact of democracy on deforestation from 1990 through 2000 with great precision before extending the data set and analyses to include the period from 2000 through 2010. We find that the original results of Buitenzorgy and Mol (2011) were spurious and inconsistent in the replication once heteroskedasticity robust standard errors were employed. When combining the two time periods and running analyses on panel data and differenced data for robust outcomes and better policy inferences, we find different results for the effect of democracy on deforestation, indicating that model specification is critical to studying this relationship. The more econometrically sound method, the differenced models, reject the Environmental Kuznet's Curve (EKC) hypothesis for democracy and deforestation, instead indicating that democracy decreased deforestation rates. When adding democracy spillover effects to the model, i.e., the impact on deforestation rates due to changes in democracy levels in neighboring countries, we still find that democracy leads to decreased rates of deforestation. We also find that having more democratic neighbors leads to further decreases in democracy. These outcomes have far-reaching implications for the blocs examined, which are highlighted in this study.

The Climate Crisis and Export Intensity: A Comparative International Study of Greenhouse Gas Emissions in the Global South, 1990–2014

The climate crisis is among the gravest threats to humanity and the planet. Combatting the climate crisis requires understanding of the sociostructural causes of anthropogenic greenhouse gas emissions. Social scientists have long debated the environmental implications of trade openness for developing countries, with world-systems analysis/dependency theory suggesting that trade openness is associated with increased environmental degradation. Conversely, neoliberal thought argues that trade openness is associated with decreased environmental harm. I use fixed effects panel regression models with heteroskedasticity-robust standard errors to estimate the effect of trade openness on carbon dioxide emissions, methane emissions, and nitrous oxide emissions. I find that trade openness positively affects carbon dioxide emissions, methane emissions, and nitrous oxide emissions, which supports world-systems analysis/dependency theory expectations. This analysis underscores the need to consider the extent to which international trade contributes to the emission of greenhouse gases.

Clustering and External Validity in Randomized Controlled Trials

In the literature studying randomized controlled trials (RCTs), it is often assumed that the potential outcomes of units participating in the experiment are deterministic. This assumption is unlikely to hold, as stochastic shocks may take place during the experiment. In this paper, we consider the case of an RCT with individual-level treatment assignment, and we allow for individual-level and cluster-level (e.g. village-level) shocks to affect the potential outcomes. We show that one can draw inference on two estimands: the ATE conditional on the realizations of the cluster-level shocks, using heteroskedasticity-robust standard errors; the ATE netted out of those shocks, using cluster-robust standard errors. By clustering, researchers can test if the treatment would still have had an effect, had the stochastic shocks that occurred during the experiment been different. Then, the decision to cluster or not depends on the level of external validity one would like to achieve.

Testing for episodic predictability in stock returns

Standard tests based on predictive regressions estimated over the full available sample data have tended to find little evidence of predictability in stock returns. Recent approaches based on the analysis of subsamples of the data suggest in fact that predictability where it occurs might exist only within so-called “pockets of predictability” rather than across the entire sample. However, these methods are prone to the criticism that the subsample dates are endogenously determined such that the use of standard critical values appropriate for full sample tests will result in incorrectly sized tests leading to spurious findings of stock returns predictability. To avoid the problem of endogenously-determined sample splits, we propose new tests derived from sequences of predictability statistics systematically calculated over subsamples of the data. Specifically, we will base tests on the maximum of such statistics from sequences of forward and backward recursive, rolling, and double-recursive predictive subsample regressions. We develop our approach using the over-identified instrumental variable-based predictability test statistics of Breitung and Demetrescu (2015). This approach is based on partial-sum asymptotics and so, unlike many other popular approaches including, for example, those based on Bonferroni corrections, can be readily adapted to implementation over sequences of subsamples. We show that the limiting null distributions of our proposed test statistics depend in general on whether the putative predictor is strongly or weakly persistent and on any heteroskedasticity present (indeed on any time-variation present in the unconditional variance matrix of the innovations), the latter even if the subsample statistics are based on heteroskedasticity-robust standard errors. As a consequence, we develop fixed regressor wild bootstrap implementations of the tests which we demonstrate to be first-order asymptotically valid. Finite sample behaviour against a variety of temporarily predictable processes is considered. An empirical application to US stock returns illustrates the usefulness of the new predictability testing methods we propose.

Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

Abstract In regression discontinuity designs (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the “fixed-bandwidth” alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators as locally parametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

In regression discontinuity design (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators as locally parametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel, bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

Inference for Iterated GMM Under Misspecification and Clustering

This paper develops a new distribution theory and inference methods for over-identified Generalized Method of Moments (GMM) estimation focusing on the iterated GMM estimator, allowing for moment misspecification, and for clustered dependence with heterogeneous and growing cluster sizes. This paper is the first to provide a rigorous theory for the iterated GMM estimator. We provide conditions for its existence by demonstrating that the iteration sequence is a contraction mapping. Our asymptotic theory allows the moments to be possibly misspecified, which is a general feature of approximate over-identified models. This form of moment misspecification causes bias in conventional standard error estimation. Our results show how to correct for this standard error bias. Our paper is also the first to provide a rigorous distribution theory for the GMM estimator under cluster dependence. Our distribution theory is asymptotic, and allows for heterogeneous and growing cluster sizes. Our results cover standard smooth moment condition models, including dynamic panels, which is a common application for GMM with cluster dependence. Our simulation results show that conventional heteroskedasticity-robust standard errors are highly biased under moment misspecification, severely understating estimation uncertainty, and resulting in severely over-sized hypothesis tests. In contrast, our misspecification-robust standard errors are approximately unbiased and properly sized under both correct specification and misspecification. We illustrate the method by extending the empirical work reported in Acemoglu, Johnson, Robinson, and Yared (2008, American Economic Review) and Cervellati, Jung, Sunde, and Vischer (2014, American Economic Review). Our results reveal an enormous effect of iterating the GMM estimator, demonstrating the arbitrari- ness of using one-step and two-step estimators. Our results also show a large effect of using misspecification robust standard errors instead of the Arellano-Bond standard errors. Our results support Acemoglu, Johnson, Robinson, and Yared’s conclusion of an insignificant effect of income on democracy, but reveal that the heterogeneous effects documented by Cervellati, Jung, Sunde, and Vischer are less statistically significant than previously claimed.

Corporate governance: evidence from Islamic banks

PurposeThis paper aims to examine the impact of Shari’ah supervisory boards (SSBs) on the performance of Islamic banks (IBs). It also tests whether SSBs’ attributes affect the performance of IBs. Based on a sample of 1,803 Islamic bank-year observations from 82 banks in 15 countries over the period 1993-2014 and controlling for factors known to affect bank performance, this study reveals a robust and significant positive relationship between SSBs and Islamic bank performance. This study also shows that the characteristics of SSBs affect the performance of IBs. This research reveals how SSBs influence the performance of IBs, as well as the processes and roles SSBs use to ensure Shari’ah compliance in business transactions.Design/methodology/approachThe purpose of this study design is to relate SSB presence, size and diversity to financial performance using three techniques. The first technique is a multivariate data analysis that analyzes data arising from more than one variable. The second technique is a clustered regression (clustering by bank), which corrects for serial correlation and produces unbiased t-statistics. Because this sample is drawn from panel data, it is expected serial autocorrelation of the independent variables and error term within banks. In cases where within-company correlation exists, t-statistics based on average regression coefficients from year-by-year regression are upwardly biased and potentially severe (Peterson, 2009). Therefore, this study uses a technique that agrees with Stock and Watson (2002), who show that the standard method of calculating heteroskedasticity-robust standard errors for the fixed-effects estimator generates inconsistent variance estimates. Thus, using the clustered regression is consistent with the fixed-effects estimator. The third technique is a two-stage least-squares regression that helps build an instrumental variable for robustness tests purposes.FindingsThe findings suggest that large corporate boards and large SSBs are more efficient in dealing with different monitoring and advisory roles than small SSBs. Consequently, this suggests that increasing the size of corporate boards and SSBs should improve monitoring and advisory functions, management behavior and organizational performance.Research limitations/implicationsIt is possible that there is an upper limit to this benefit, however; we do not explore this limit, which therefore provides opportunities for additional research. Because Shari’ah compliance relates only to a rational legal framework of negative screening relegated to interest prohibition and limiting uncertainty. The interest prohibition and limiting uncertainty have not been investigated between the two samples due to data unavailability. In addition, limited accounting-based measures of financial performance may not accurately portray IB performance; hence, an additional market measure is implemented, which is Tobin’s Q.Practical implicationsUltimately, these findings could help IBs improve their financial results by enhancing their internal and external governance mechanisms (Walsh and Seward, 1990). They provide a basis for developing larger, more diverse SSBs that are more focused on complying with Shari’ah and corporate governance. The results also have significant policy implications for improving firm-level corporate governance versus improving country-level institutional factors. Both views have their advocates. However, it is very difficult to reform the legal system in a short time. Still, this study shows that struggling IBs have a way to improve their corporate governance and simultaneously improve their financing environment.Originality/valueThis research contributes to the literature on the effects of SSBs on IBs’ organizational financial performance, processes and roles. It is the first to examine empirically the underpinnings of how SSBs affect organizational financial performance via agency theory and contingency theory.

Robust methods for heteroskedastic regression

Heteroskedastic regression data are modelled using a parameterized variance function. This procedure is robustified using a method with high breakdown point and high efficiency, which provides a direct link between observations and the weights used in model fitting. This feature is vital for the application, the analysis of international trade data from the European Union. Heteroskedasticity is strongly present in such data, as are outliers. A further example shows that the new method outperforms ordinary least squares with heteroskedasticity robust standard errors, even when the form of heteroskedasticity is mis-specified. A discussion of computational matters concludes the paper. An appendix presents the new scoring algorithm for estimation of the parameters of heteroskedasticity.

The information content of small business earnings

Purpose– This paper starts from the observation that small businesses in France report a significant fraction of their net income in the form of non-core earnings. Consequently, the purpose of this paper is to examine the persistence and informativeness of both core and non-core earnings of small businesses listed on the Euronext Paris market.Design/methodology/approach– Panel regressions estimated with heteroskedasticity robust standard errors are used to investigate the relationships between earnings components, future performance and stock market valuation of small businesses.Findings– The findings show that core and non-core earnings of the current year (t), contrary to those of the previous year (t−1), make it possible to predict the performance of the next year (t+1). However, only the persistence of current core earnings is valued by the stock market.Research limitations/implications– The study puts forward an anomaly of market efficiency. Thus, it shows that investors in the French stock market do not appropriately price a part of the available financial information (i.e. non-core earnings) that may contribute to a better assessment of the future performance of listed small businesses.Practical implications– The persistence of non-core earnings is certainly less important than that of core elements but able to help investors appraise the future performance of listed small businesses. Hence, it represents useful financial information for investors.Originality/value– This paper contributes to the existing literature by investigating the relationships between earnings, future performance and stock market valuation of listed SMEs, especially. Thus, the findings of this research allow a better understanding of earnings components properties (i.e. persistence) and their implication on the stock market valuation (i.e. informativeness) of listed SMEs. Given the observed specificities of earnings for this category of firms, these findings may be of particular interest to both researchers and investors.

School Performance: A Matter of Health or Socio-Economic Background? Findings from the PIAMA Birth Cohort Study.

BackgroundPerformance in primary school is a determinant of children’s educational attainment and their socio-economic position and health inequalities in adulthood. We examined the relationship between five common childhood health conditions (asthma symptoms, eczema, general health, frequent respiratory infections, and overweight), health related school absence and family socio-economic status on children’s school performance.MethodsWe used data from 1,865 children in the Dutch PIAMA birth cohort study. School performance was measured as the teacher’s assessment of a suitable secondary school level for the child, and the child’s score on a standardized achievement test (Cito Test). Both school performance indicators were standardised using Z-scores. Childhood health was indicated by eczema, asthma symptoms, general health, frequent respiratory infections, overweight, and health related school absence. Children’s health conditions were reported repeatedly between the age of one to eleven. School absenteeism was reported at age eleven. Highest attained educational level of the mother and father indicated family socio-economic status. We used linear regression models with heteroskedasticity-robust standard errors for our analyses with adjustment for sex of the child.ResultsThe health indicators used in our study were not associated with children’s school performance, independently from parental educational level, with the exception of asthma symptoms (-0.03 z-score / -0.04 z-score with Cito Test score after adjusting for respectively maternal and paternal education) and missing more than 5 schooldays due to illness (-0.18 z-score with Cito Test score and -0.17 z-score with school level assessment after adjustment for paternal education). The effect estimates for these health indicators were much smaller though than the effect estimates for parental education, which was strongly associated with children’s school performance.ConclusionChildren’s school performance was affected only slightly by a number of common childhood health problems, but was strongly associated with parental education.

Inference Problems Under a Special Form of Heteroskedasticity

In the presence of heteroskedasticity, conventional standard errors (which assume homoskedasticity) can be biased up or down. The most common form of heteroskedasticity leads to conventional standard errors that are too small. When Wald tests based on these standard errors are insignificant, heteroskedasticity robust standard errors do not change inference. On the other hand, inference is conservative in a setting with upward-biased conventional standard errors. We discuss the power gains when using robust standard errors in this case and also potential problems of heteroskedasticity tests. As a solution for the poor performance of the usual heteroskedasticity tests in this setting, we propose a modification of the White test which has better properties. We illustrate our findings using a study in labor economics. The correct standard errors turn out to be around 15 percent lower, leading to different policy conclusions. Moreover, only our modified test is able to detect heteroskedasticity in this application.

Heteroskedasticity-robust inference in finite samples

Since the advent of heteroskedasticity-robust standard errors, several papers have proposed adjustments to the original White formulation. We replicate earlier findings that each of these adjusted estimators performs quite poorly in finite samples. We propose a class of alternative heteroskedasticity-robust tests of linear hypotheses based on an Edgeworth expansion of the test statistic distribution. Our preferred test outperforms existing methods in both size and power for low, moderate, and severe levels of heteroskedasticity.