Cluster-robust Standard Errors Research Articles

Fixed Effects in Unconditional Quantile Regression

Unconditional quantile regression has quickly become popular after being introduced by Firpo, Fortin, and Lemieux (2009, Econometrica 77: 953–973) and is easily implemented using the user-written command rifreg by the same authors. However, including high-dimensional fixed effects in rifreg is quite burdensome and sometimes even impossible. In this article, I show that when the number of fixed effects is large, the computational speed is massively increased by using xtreg rather than regress to fit the unconditional quantile regression models. I also introduce the xtrifreg command, which should be considered a supplement to rifreg. The xtrifreg command has many of the same features as rifreg but can be used to include a large number of fixed effects, to estimate cluster–robust standard errors, and to estimate cluster–bootstrapped standard errors.

Distrés en Hijas Adultas que Brindan Apoyo a sus Padres Mayores

The study sought to find empirical evidence of the effect of intergenerational support relationships with older parents on the well-being—operationalized as distress—of daughters aged 45 and older and to determine the moderating factors that can limit the potentially direct association between providing support and distress. Using data from Family cohesion, intergenerational solidarity and conflict: Impact on the well-being of the older adult , a survey conducted in 2009, which represents people aged 45 and older in Santiago, Chile, hierarchical linear regression models were calculated with clustered robust standard errors , using a sub-sample of 102 women with at least one living parent. No association was found between distress and providing regular care to one's father or mother; instead, an association was observed between perceived support and well-being. Even though providing support to older parents does not involve additional distress, having fewer siblings—especially having none—is associated with higher levels of emotional distress.

Party nationalization and the translation of votes into seats under single-member plurality electoral rules

This study uses empirical evidence from a nearly comprehensive set of electoral democracies that use single-member plurality systems or mixed electoral systems with single-member plurality components in order to establish empirically the impact of territorial patterns of electoral support upon vote-to-seat conversion. The analysis, employing individual parties as units of analysis and multiple linear regression with cluster-robust standard errors as its main methodological tool, confirms the hypothesis that single-member plurality rules give a representational bonus to parties with low levels of nationalization. This effect is contingent upon absolute and relative party size, so that very large parties, and particularly frontrunners in party competition, receive an advantage irrespective of their nationalization. Mixed electoral rules further facilitate their advantage, while the gains of very small parties tend to be enhanced by large assembly size. These findings contribute to a better understanding of the dynamics of party system development under Duvergerian conditions.

A randomized trial of the effects of the noble gases helium and argon on neuroprotection in a rodent cardiac arrest model.

BackgroundThe noble gas xenon is considered as a neuroprotective agent, but availability of the gas is limited. Studies on neuroprotection with the abundant noble gases helium and argon demonstrated mixed results, and data regarding neuroprotection after cardiac arrest are scant. We tested the hypothesis that administration of 50 % helium or 50 % argon for 24 h after resuscitation from cardiac arrest improves clinical and histological outcome in our 8 min rat cardiac arrest model.MethodsForty animals had cardiac arrest induced with intravenous potassium/esmolol and were randomized to post-resuscitation ventilation with either helium/oxygen, argon/oxygen or air/oxygen for 24 h. Eight additional animals without cardiac arrest served as reference, these animals were not randomized and not included into the statistical analysis. Primary outcome was assessment of neuronal damage in histology of the region I of hippocampus proper (CA1) from those animals surviving until day 5. Secondary outcome was evaluation of neurobehavior by daily testing of a Neurodeficit Score (NDS), the Tape Removal Test (TRT), a simple vertical pole test (VPT) and the Open Field Test (OFT). Because of the non-parametric distribution of the data, the histological assessments were compared with the Kruskal–Wallis test. Treatment effect in repeated measured assessments was estimated with a linear regression with clustered robust standard errors (SE), where normality is less important.ResultsTwenty-nine out of 40 rats survived until day 5 with significant initial deficits in neurobehavioral, but rapid improvement within all groups randomized to cardiac arrest. There were no statistical significant differences between groups neither in the histological nor in neurobehavioral assessment.ConclusionsThe replacement of air with either helium or argon in a 50:50 air/oxygen mixture for 24 h did not improve histological or clinical outcome in rats subjected to 8 min of cardiac arrest.

Is computer availability at home causally related to reading achievement in grade 4? A longitudinal difference in differences approach to IEA data from 1991 to 2006

Research on effects of home computer use on children’s development of cognitive abilities and skills has yielded conflicting results, with some studies showing positive effects, others no effects, and yet others negative effects. These studies have typically used non-experimental designs and one of the main reasons for the conflicting results is that studies differ with respect to how well they control for selection bias in comparisons of children with different amounts of computer use. The current study takes advantage of data from international comparative studies of educational achievement and uses the trend design of these studies to conduct longitudinal analyses at the country level. This allows for a difference in differences approach which effectively controls for within-country selection bias, time-invariant country-level omitted variables, and random errors of measurement in the independent and dependent variables. The empirical investigations are based on data from the IEA 10-Year Trend Study and the PIRLS 2001 and 2006 studies. For these studies, information about frequency of home computer use is available in the student questionnaire. The main analytical approach employed in the paper is regression estimation based on micro-data, with fixed country effects and cluster-robust standard-errors. This approach allows estimation of main effects of home computer use and interaction effects with student characteristics (gender and socio-economic status). For both data sets negative effects of home computer use on achievement are found. Results are discussed in substantive and methodological terms, focusing particularly on possible threats to valid causal inference, such as omitted variables that are not time invariant.

Inter-Industry Wage Differentials in Greece: Rent-Sharing and Unobserved Heterogeneity Hypotheses

This paper examines the structure and determinants of inter-industry wage differentials in Greece, along with the role of the rent-sharing and unobserved heterogeneity hypotheses, employing restricted least squares and quantile regression techniques with cluster robust standard errors at the firm level. To this end, a unique dataset, the European Union Structure of Earnings Survey (SES), is utilized. Data refer to 2010 when the first elements of the economic adjustment programme to deal with the chronic deficiencies of the Greek economy and restore sustainable public finances, competitiveness and set the foundation for long-term growth were beginning to be implemented. Results point to high wage dispersion across industries at the mean of the conditional wage distribution, even after controlling for personal and workplace characteristics. However, evidence for the unobserved heterogeneity hypothesis is rather scant. Therefore, there is room for efficiency wage or rent-sharing theories in accounting for a large part of inter-industry wage differentials tentatively implying that firm heterogeneity in the ability-to-pay matters more than employee unobservable attributes in the wage determination process.

Normative, Structural, and Individual Factors that Predispose Adult Children to Provide Social Support to Their Elderly Parents

This study is based on a face-to-face survey, conducted in 2009, with a representative sample of adults who were aged 45 years or above, living in the urban area of Santiago, Chile. This survey examined the exchange network between adults and their elderly parents, focusing on two of the main explanatory approaches to supportive family interrelations. That is, the norms of filial obligation and reciprocity. The article also investigates factors associated with the structure of needs and opportunities, as well as the family structures of the adult children and their parents. By estimating logistic regression models with cluster-robust standard errors the reciprocity norm is found to be significant, whereas that for filial obligation is not. The estimated models show that receiving support from the parent is one of the main factors that predisposes the adult child to the provision of parental support. That is, such action is favored by incorporation in a network of reciprocal exchanges. Thus, intergenerational ties work in two directions: parents request help from their children but also give them help. The norm of filial obligation, on the other hand, is only significant in the case of women.

Cross-Sectional Study of 24-Hour Urinary Electrolyte Excretion and Associated Health Outcomes in a Convenience Sample of Australian Primary Schoolchildren: The Salt and Other Nutrients in Children (SONIC) Study Protocol.

BackgroundDietary sodium and potassium are involved in the pathogenesis of cardiovascular disease. Data exploring the cardiovascular outcomes associated with these electrolytes within Australian children is sparse. Furthermore, an objective measure of sodium and potassium intake within this group is lacking.ObjectiveThe primary aim of the Salt and Other Nutrient Intakes in Children (“SONIC”) study was to measure sodium and potassium intakes in a sample of primary schoolchildren located in Victoria, Australia, using 24-hour urine collections. Secondary aims were to identify the dietary sources of sodium and potassium, examine the association between these electrolytes and cardiovascular risk factors, and assess children’s taste preferences and saltiness perception of manufactured foods.MethodsA cross-sectional study was conducted in a convenience sample of schoolchildren attending primary schools in Victoria, Australia. Participants completed one 24-hour urine collection, which was analyzed for sodium, potassium, and creatinine. Completeness of collections was assessed using collection time, total volume, and urinary creatinine. One 24-hour dietary recall was completed to assess dietary intake. Other data collected included blood pressure, body weight, height, waist and hip circumference. Children were also presented with high and low sodium variants of food products and asked to discriminate salt level and choose their preferred variant. Parents provided demographic information and information on use of discretionary salt. Descriptive statistics will be used to describe sodium and potassium intakes. Linear and logistic regression models with clustered robust standard errors will be used to assess the association between electrolyte intake and health outcomes (blood pressure and body mass index/BMI z-score and waist circumference) and to assess differences in taste preference and discrimination between high and low sodium foods, and correlations between preference, sodium intake, and covariates.ResultsA total of 780 children across 43 schools participated. The results from this study are expected at the end of 2015.ConclusionsThis study will provide the first objective measure of sodium and potassium intake in Australian schoolchildren and improve our understanding of the relationship of these electrolytes to cardiovascular risk factors. Furthermore, this study will provide insight into child taste preferences and explore related factors. Given the cardiovascular implications of consuming too much sodium and too little potassium, monitoring of these nutrients during childhood is an important public health initiative.

A Practitioner’s Guide to Cluster-Robust Inference

We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.

Macro-level drivers of multidimensional poverty in sub-Saharan Africa: Explaining change in the Human Poverty Index

Poverty is increasingly recognised as a multidimensional phenomenon in the development literature, encompassing not only income, but also a range of factors related to broadening an individual’s freedoms to live a life of their own choosing. Poverty so understood suggests that alternative approaches to poverty measurement reflecting this multidimensionality may point towards alternative policies for poverty alleviation. The imperative to reinforce pro-poor policy development in sub-Saharan Africa with evaluation findings that reflect improvements in well-being, rather than solely improvements in national economies, has become self-evident as, despite decades of market-led development policies, much of the subcontinent remains mired in deprivation. As recognised by the 2014 African Evaluation Association’s biannual conference, fresh thinking and new evaluation metrics are required in order to create policies that more effectively increase well-being. This article explores the factors that may account for changes in one metric of multidimensional poverty in developing countries, the United Nation Development Program’s Human Poverty Index (HPI), and will be primarily concerned with measuring the effects on the HPI of policies and activities that relate to, or are explicitly meant to encourage, economic growth, increased literacy and improved health. The study focuses on the outcomes of a panel data set, created for the purpose of this study, of HPI scores for a set of 47 sub-Saharan countries, between 1990 and 2010, and a range of indicators that the development literature and theory suggest should have an effect on income poverty, asking, what is the relationship between these indicators and multidimensional poverty? A parallel set of models has been developed to measure the response of household consumption expenditure to changes in economic growth and human capabilities indicators. All models are estimated using fixed effects estimators and cluster robust standard errors in Stata 12. Consistent with the development literature, household expenditure appears to be significantly and positively related to changes in gross domestic product (GDP) per capita. However, when the HPI is regressed on GDP per capita, no statistically significant relationshipis observed, even when controlling for a range of other indicators, calling into question the relationship between economic growth and well-being in much of sub-Saharan Africa. This finding suggests that development policies that focus primarily on economic growth as a means to addressing multidimensional deprivation may be misplaced.

A Replication of “The Political Determinants of Federal Expenditure at the State Level” (Public Choice, 2005)

This article replicates and analyzes a study by Hoover and Pecorino (H&P) on federal spending in US states. H&P followed on pathbreaking research by Atlas et al. in which evidence was claimed in favor of the “small state effect”; namely, that since every state is represented by two senators, small states have a disproportionate influence on federal spending relative to their population size. Using H&P’s data, we both replicate their results and demonstrate strong support for the small-state effect when we formally test their predictions. The contribution of this study is that we demonstrate that this empirical support vanishes when we (i) employ cluster robust standard errors rather than conventional ordinary least squares (OLS) standard errors and (ii) include a variable for population growth as suggested in a recent study by Larcinese, Rizzo, and Testa. We conclude that there is insufficient evidence to support the hypothesis of a “small-state effect.”

A general framework for parametric survival analysis.

Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User-friendly Stata software is provided, which significantly extends parametric survival models available in standard software.

Impact of a pertussis epidemic on infant vaccination in Washington state.

Washington State experienced a pertussis epidemic from October 2011 to December 2012. There was wide variation in incidence by county. The objectives of this study were to determine how the pertussis epidemic affected infant vaccination in Washington State and whether the incidence in counties modified this effect. We conducted an ecologic before-after study to compare the proportion of infants up to date (UTD) with a pertussis-containing vaccine at time points before (September 30, 2011), during (September 30, 2012), and after (September 30, 2013) the epidemic. Children aged 3 to 8 months enrolled in the Washington State Immunization Information System with documented county of residence were included. UTD status was determined as ≥ 1, ≥ 2, or ≥ 3 doses of a pertussis-containing vaccine at ages 3, 5, and 7 months, respectively. Generalized linear models with extension to the binomial family and clustered robust standard errors were used to examine differences in the proportion of UTD infants between preepidemic and either epidemic or postepidemic points. The potential modifying effect of pertussis incidence by county was examined. We found no significant difference in statewide UTD status with a pertussis-containing vaccine between preepidemic and either epidemic (absolute difference 2.1%; 95% confidence interval, -1.6 to 5.9) or postepidemic (absolute difference 0.2%; 95% confidence interval, -4.0 to 4.5) time points. There was no significant modification by county pertussis incidence. There was wide variation in the absolute difference in UTD status across counties. A statewide pertussis epidemic does not appear to have significantly changed the proportion of infants who were UTD with a pertussis-containing vaccine.

Assessing the connection between health and education: identifying potential leverage points for public health to improve school attendance.

We examined multiple variables influencing school truancy to identify potential leverage points to improve school attendance. A cross-sectional observational design was used to analyze inner-city data collected in Los Angeles County, California, during 2010 to 2011. We constructed an ordinal logistic regression model with cluster robust standard errors to examine the association between truancy and various covariates. The sample was predominantly Hispanic (84.3%). Multivariable analysis revealed greater truancy among students (1) with mild (adjusted odds ratio [AOR] = 1.57; 95% confidence interval [CI] = 1.22, 2.01) and severe (AOR = 1.80; 95% CI = 1.04, 3.13) depression (referent: no depression), (2) whose parents were neglectful (AOR = 2.21; 95% CI = 1.21, 4.03) or indulgent (AOR = 1.71; 95% CI = 1.04, 2.82; referent: authoritative parents), (3) who perceived less support from classes, teachers, and other students regarding college preparation (AOR = 0.87; 95% CI = 0.81, 0.95), (4) who had low grade point averages (AOR = 2.34; 95% CI = 1.49, 4.38), and (5) who reported using alcohol (AOR = 3.47; 95% CI = 2.34, 5.14) or marijuana (AOR = 1.59; 95% CI = 1.06, 2.38) during the past month. Study findings suggest depression, substance use, and parental engagement as potential leverage points for public health to intervene to improve school attendance.

Sensitivity analyses for clustered data: An illustration from a large-scale clustered randomized controlled trial in education

In this paper, we demonstrate the importance of conducting well-thought-out sensitivity analyses for handling clustered data (data in which individuals are grouped into higher order units, such as students in schools) that arise from cluster randomized controlled trials (RCTs). This is particularly relevant given the rise in rigorous impact evaluations that use cluster randomized designs across various fields including education, public health and social welfare. Using data from a recently completed cluster RCT of a school-based teacher professional development program, we demonstrate our use of four commonly applied methods for analyzing clustered data. These methods include: (1) hierarchical linear modeling (HLM); (2) feasible generalized least squares (FGLS); (3) generalized estimating equations (GEE); and (4) ordinary least squares (OLS) regression with cluster-robust (Huber–White) standard errors. We compare our findings across each method, showing how inconsistent results – in terms of both effect sizes and statistical significance – emerged across each method and our analytic approach to resolving such inconsistencies.

Long-Acting Reversible Contraceptive Training Intervention

INTRODUCTION: Unintended pregnancy remains persistently high in the United States. Few randomized interventions have effectively reduced pregnancy. METHODS: We conducted a cluster randomized trial in 40 Planned Parenthood sites, including family planning and abortion, to assess the effect of a clinic-wide training in long-acting reversible contraceptives (LARCs) on patient outcomes. A cohort of 1,500 patients, 18–25 years, who received contraceptive counseling and did not want to become pregnant in the next 12 months, were recruited from intervention and control clinics. Pregnancy was measured over 12 months with questionnaires, pregnancy tests, and medical record review. In blinded intent-to-treat analyses, we used survival analysis with shared frailty for clustered data to measure the intervention effect compared with standard care. The trial was registered with ClinicalTrials.gov and followed CONSORT (Consolidated Standards of Reporting Trials) guidelines. RESULTS: Participants were similar in baseline characteristics by arm. At enrollment, after counseling, participants in arm 1 were twice as likely to choose a LARC method as those in arm 2 using generalized estimating equation models for clustered data and robust standard errors (odds ratio 2.0, 95% confidence interval [CI] 1.3–2.9). In family planning settings, pregnancy during the study was lower in arm 1 (7.5%) than in arm 2 (13.8%). Analyses of the intervention effect in a model with an interaction for setting type showed a highly significant effect on reduced pregnancy in family planning settings (hazard ratio 0.5, 95% CI 0.3–0.8). However, there were no significant differences in pregnancy by arm in the abortion setting. CONCLUSIONS: A half-day replicable LARC intervention effectively reduced pregnancy in family planning clinics.

Are We Really Doing What We Think We Are Doing? A Note on Finite-Sample Estimates of Two-Way Cluster-Robust Standard Errors

Archival researchers heavily rely on statistics software to deliver large sample analyses. To provide valid empirical analyses, an author needs to know the best statistical solution to the research issue and also the correct computer language that exactly carries out such statistical tests. However, unfortunately, researchers rarely explain what they exactly do in empirical analyses. Consequently, it is difficult for a reader to figure out the validity of the empirical results. This note uses two-way cluster-robust standard errors as an example to explain these points. Two-way cluster-robust standard errors are getting widely used in the accounting and finance literature. There are multiple different alternative specifications of two-way cluster-robust standard errors, which could result in very different significance levels than unadjusted asymptotic estimates. However, researchers rarely explain which estimate of two-way cluster-robust standard errors they use, though they may all call their standard errors “two-way cluster-robust standard errors”. Specifically, I first provide a short-discussion on alternative estimates of two-way cluster-robust standard errors. Second, I discuss two common mistakes in calculating two-way cluster-robust standard errors. Third, I show that popular statistics software (SAS and STATA) have options that could generate several alternative estimates of two-way cluster-robust standard errors. Therefore, if not explained, no reader would know which estimate is used. Finally, I suggest that future empirical research should carefully explain how it implements estimates of two-way cluster-robust standard errors in finite samples. In addition, a SAS macro code for two-way clustered standard errors is available at my website. If you use this code, please add the following footnote “To obtain unbiased estimates, the clustered standard errors are adjusted by (N-1)/ (N-P) × G/(G-1), where N is the sample size, P is the number of independent variables, and G is the number of clusters.”

Density and Proximity of Tobacco Outlets to Homes and Schools: Relations with Youth Cigarette Smoking

This study investigated the associations of youth cigarette smoking with tobacco outlet densities and proximity of tobacco outlets to youth homes and schools across different buffers in 45 midsized California communities. The sample comprised 832 youths who were surveyed about their smoking behaviors. Inclusion criteria included both home and school addresses within city boundaries. Observations in the 45 cities were conducted to document addresses of tobacco outlets. City- and buffer-level demographics were obtained and negative binomial regression analyses with cluster robust standard errors were conducted. All models were adjusted for youth gender, age, and race. Greater densities of tobacco outlets within both a 0.75 and 1-mile buffer of youth homes were associated with higher smoking frequency. Neither tobacco outlet densities around schools nor distance to the nearest tobacco outlet from home or school were associated with youths past-30-day smoking frequency. Lower population density and percent of African Americans in areas around homes and lower percent of unemployed in areas around schools were associated with greater smoking frequency. Results of this study suggest that restricting outlet density within at least 1-mile surrounding residential areas will help to reduce youth smoking.

Neighborhood safety and green space as predictors of obesity among preschool children from low-income families in New York City

BackgroundNeighborhood safety, green space, walkability, and sociodemographics may influence physical activity and childhood obesity. MethodsData on measured height and weight, demographic characteristics, and home ZIP code were collected from year 2004 enrollees in a means-tested preschool program in New York City. Each ZIP code was surrounded by a 400-m buffer and characterized using data from the US census, local government departments, New York Times website, and Transportation Alternatives. Linear and Poisson models were constructed using cluster robust standard errors and adjusting for child's sex, race, ethnicity, age, and neighborhood characteristics. ResultsAnalyses included 11,562 children ages 3–5years living in 160 residential ZIP codes. A higher homicide rate (at the 75th vs 25th percentile) was associated with a 22% higher prevalence of obesity (95% CI for the prevalence ratio (PR): 1.05 to 1.41). A higher density of street trees (at the 75th vs 25th percentile) was associated with 12% lower prevalence of obesity (95% CI for the PR: 0.79 to 0.99). Other neighborhood characteristics did not have significant associations with childhood obesity. ConclusionsAmong preschool children from low-income families, neighborhood homicide rate was associated with more obesity and street tree density was associated with less obesity.

Panel data in accounting and finance: theory and application

The use of models that involve longitudinal data in accounting and finance is common. However, there is often a lack of proper care regarding the criteria for adopting one model over another as well as an insufficiently detailed discussion of the possible estimators to be studied in each situation. This article presents, in conceptual and applied form, the main panel data estimators that can be used in these areas of knowledge and discusses the definition of the most consistent model to be adopted in function of the data characteristics. The models covered for short panels are the POLS with clustered robust standard errors, with between estimator, fixed effects, fixed effects with clustered robust standard errors, random effects and random effects with clustered robust standard errors. In turn, for long panels, the models discussed are fixed effects, random effects, fixed effects with AR(1) error terms, random effects with AR(1) error terms, POLS with AR(1) errors and pooled FGLS with AR(1) errors. The models are also applied to a real case, based on data from Compustat Global. At the end, the main routines for applying each of the models in Stata are presented.