Identification, Weak Instruments and Statistical Inference in Econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

Semi-Parametric Weak Instrument Regressions with an Application to the Risk-Return Trade-off

Recent work shows that a low correlation between the instruments and the included variables leads to serious inference problems. We extend the local-to-zero analysis of models with weak instruments to models with estimated instruments and regressors and with higher-order dependence between instruments and disturbances. This makes this framework applicable to linear models with expectation variables that are estimated non-parametrically. Two examples of such models are the risk-return trade-off in finance and the impact of inflation uncertainty on real economic activity. Results show that inference based on Lagrange Multiplier (LM) tests is more robust to weak instruments than Wald-based inference. Using LM confidence intervals leads us to conclude that no statistically significant risk premium is present in returns on the S&P 500 index, excess holding yields between 6-month and 3-month Treasury bills, or in yen-dollar spot returns.

Exogeneity, weak identification and instrument selection in econometrics

La dernière décennie a connu un intérêt croissant pour les problèmes posés par les variables instrumentales faibles dans la littérature économétrique, c’est-à-dire les situations où les variables instrumentales sont faiblement corrélées avec la variable à instrumenter. En effet, il est bien connu que lorsque les instruments sont faibles, les distributions des statistiques de Student, de Wald, du ratio de vraisemblance et du multiplicateur de Lagrange ne sont plus standard et dépendent souvent de paramètres de nuisance. Plusieurs études empiriques portant notamment sur les modèles de rendements à l’éducation [Angrist et Krueger (1991, 1995), Angrist et al. (1999), Bound et al. (1995), Dufour et Taamouti (2007)] et d’évaluation des actifs financiers (C-CAPM) [Hansen et Singleton (1982,1983), Stock et Wright (2000)], où les variables instrumentales sont faiblement corrélées avec la variable à instrumenter, ont montré que l’utilisation de ces statistiques conduit souvent à des résultats peu fiables. Un remède à ce problème est l’utilisation de tests robustes à l’identification [Anderson et Rubin (1949), Moreira (2002), Kleibergen (2003), Dufour et Taamouti (2007)]. Cependant, il n’existe aucune littérature économétrique sur la qualité des procédures robustes à l’identification lorsque les instruments disponibles sont endogènes ou à la fois endogènes et faibles. Cela soulève la question de savoir ce qui arrive aux procédures d’inférence robustes à l’identification lorsque certaines variables instrumentales supposées exogènes ne le sont pas effectivement. Plus précisément, qu’arrive-t-il si une variable instrumentale invalide est ajoutée à un ensemble d’instruments valides? Ces procédures se comportent-elles différemment? Et si l’endogénéité des variables instrumentales pose des difficultés majeures à l’inférence statistique, peut-on proposer des procédures de tests qui sélectionnent les instruments lorsqu’ils sont à la fois forts et valides? Est-il possible de proposer les proédures de sélection d’instruments qui demeurent valides même en présence d’identification faible? Cette thèse se focalise sur les modèles structurels (modèles à équations simultanées) et apporte des réponses à ces questions à travers quatre essais. Le premier essai est publié dans Journal of Statistical Planning and Inference 138 (2008) 2649 – 2661. Dans cet essai, nous analysons les effets de l’endogénéité des instruments sur deux statistiques de test robustes à l’identification: la statistique d’Anderson et Rubin (AR, 1949) et la statistique de Kleibergen (K, 2003), avec ou sans instruments faibles. D’abord, lorsque le paramètre qui contrôle l’endogénéité des instruments est fixe (ne dépend pas de la taille de l’échantillon), nous montrons que toutes ces procédures sont en général convergentes contre la présence d’instruments invalides (c’est-à-dire détectent la présence d’instruments invalides) indépendamment de leur qualité (forts ou faibles). Nous décrivons aussi des cas où cette convergence peut ne pas tenir, mais la distribution asymptotique est modifiée d’une manière qui pourrait conduire à des distorsions de niveau même pour de grands échantillons. Ceci inclut, en particulier, les cas où l’estimateur des double moindres carrés demeure convergent, mais les tests sont asymptotiquement invalides. Ensuite, lorsque les instruments sont localement exogènes (c’est-à-dire le paramètre d’endogénéité converge vers zéro lorsque la taille de l’échantillon augmente), nous montrons que ces tests convergent vers des distributions chi-carré non centrées, que les instruments soient forts ou faibles. Nous caractérisons aussi les situations où le paramètre de non centralité est nul et la distribution asymptotique des statistiques demeure la même que dans le cas des instruments valides (malgré la présence des instruments invalides). Le deuxième essai étudie l’impact des instruments faibles sur les tests de spécification du type Durbin-Wu-Hausman (DWH) ainsi que le test de Revankar et Hartley (1973). Nous proposons une analyse en petit et grand échantillon de la distribution de ces tests sous l’hypothèse nulle (niveau) et l’alternative (puissance), incluant les cas où l’identification est déficiente ou faible (instruments faibles). Notre analyse en petit échantillon founit plusieurs perspectives ainsi que des extensions des précédentes procédures. En effet, la caractérisation de la distribution de ces statistiques en petit échantillon permet la construction des tests de Monte Carlo exacts pour l’exogénéité même avec les erreurs non Gaussiens. Nous montrons que ces tests sont typiquement robustes aux intruments faibles (le niveau est contrôlé). De plus, nous fournissons une caractérisation de la puissance des tests, qui exhibe clairement les facteurs qui déterminent la puissance. Nous montrons que les tests n’ont pas de puissance lorsque tous les instruments sont faibles [similaire à Guggenberger(2008)]. Cependant, la puissance existe tant qu’au moins un seul instruments est fort. La conclusion de Guggenberger (2008) concerne le cas où tous les instruments sont faibles (un cas d’intérêt mineur en pratique). Notre théorie asymptotique sous les hypothèses affaiblies confirme la théorie en échantillon fini. Par ailleurs, nous présentons une analyse de Monte Carlo indiquant que: (1) l’estimateur des moindres carrés ordinaires est plus efficace que celui des doubles moindres carrés lorsque les instruments sont faibles et l’endogenéité modérée [conclusion similaire à celle de Kiviet and Niemczyk (2007)]; (2) les estimateurs pré-test basés sur les tests d’exogenété ont une excellente performance par rapport aux doubles moindres carrés. Ceci suggère que la méthode des variables instrumentales ne devrait être appliquée que si l’on a la certitude d’avoir des instruments forts. Donc, les conclusions de Guggenberger (2008) sont mitigées et pourraient être trompeuses. Nous illustrons nos résultats théoriques à travers des expériences de simulation et deux applications empiriques: la relation entre le taux d’ouverture et la croissance économique et le problème bien connu du rendement à l’éducation. Le troisième essai étend le test d’exogénéité du type Wald proposé par Dufour (1987) aux cas où les erreurs de la régression ont une distribution non-normale. Nous proposons une nouvelle version du précédent test qui est valide même en présence d’erreurs non-Gaussiens. Contrairement aux procédures de test d’exogénéité usuelles (tests de Durbin-Wu-Hausman et de Rvankar- Hartley), le test de Wald permet de résoudre un problème courant dans les travaux empiriques qui consiste à tester l’exogénéité partielle d’un sous ensemble de variables. Nous proposons deux nouveaux estimateurs pré-test basés sur le test de Wald qui performent mieux (en terme d’erreur quadratique moyenne) que l’estimateur IV usuel lorsque les variables instrumentales sont faibles et l’endogénéité modérée. Nous montrons également que ce test peut servir de procédure de sélection de variables instrumentales. Nous illustrons les résultats théoriques par deux applications empiriques: le modèle bien connu d’équation du salaire [Angist et Krueger (1991, 1999)] et les rendements d’échelle [Nerlove (1963)]. Nos résultats suggèrent que l’éducation de la mère expliquerait le décrochage de son fils, que l’output est une variable endogène dans l’estimation du coût de la firme et que le prix du fuel en est un instrument valide pour l’output. Le quatrième essai résout deux problèmes très importants dans la littérature économétrique. D’abord, bien que le test de Wald initial ou étendu permette de construire les régions de confiance et de tester les restrictions linéaires sur les covariances, il suppose que les paramètres du modèle sont identifiés. Lorsque l’identification est faible (instruments faiblement corrélés avec la variable à instrumenter), ce test n’est en général plus valide. Cet essai développe une procédure d’inférence robuste à l’identification (instruments faibles) qui permet de construire des régions de confiance pour la matrices de covariances entre les erreurs de la régression et les variables explicatives (possiblement endogènes). Nous fournissons les expressions analytiques des régions de confiance et caractérisons les conditions nécessaires et suffisantes sous lesquelles ils sont bornés. La procédure proposée demeure valide même pour de petits échantillons et elle est aussi asymptotiquement robuste à l’hétéroscédasticité et l’autocorrélation des erreurs. Ensuite, les résultats sont utilisés pour développer les tests d’exogénéité partielle robustes à l’identification. Les simulations Monte Carlo indiquent que ces tests contrôlent le niveau et ont de la puissance même si les instruments sont faibles. Ceci nous permet de proposer une procédure valide de sélection de variables instrumentales même s’il y a un problème d’identification. La procédure de sélection des instruments est basée sur deux nouveaux estimateurs pré-test qui combinent l’estimateur IV usuel et les estimateurs IV partiels. Nos simulations montrent que: (1) tout comme l’estimateur des moindres carrés ordinaires, les estimateurs IV partiels sont plus efficaces que l’estimateur IV usuel lorsque les instruments sont faibles et l’endogénéité modérée; (2) les estimateurs pré-test ont globalement une excellente performance comparés à l’estimateur IV usuel. Nous illustrons nos résultats théoriques par deux applications empiriques: la relation entre le taux d’ouverture et la croissance économique et le modèle de rendements à l’éducation. Dans la première application, les études antérieures ont conclu que les instruments n’étaient pas trop faibles [Dufour et Taamouti (2007)] alors qu’ils le sont fortement dans la seconde [Bound (1995), Doko et Dufour (2009)]. Conformément à nos résultats théoriques, nous trouvons les régions de confiance non bornées pour la covariance dans le cas où les instruments sont assez faibles.

Neonatal palliative care attitude scale : development of an instrument to measure the barriers to and facilitators of palliative care in neonatal nursing

OBJECTIVE The aim of this research project was to obtain an understanding of the barriers to and facilitators of providing palliative care in neonatal nursing. This article reports the first phase of this research: to develop and administer an instrument to measure the attitudes of neonatal nurses to palliative care. METHODS The instrument developed for this research (the Neonatal Palliative Care Attitude Scale) underwent face and content validity testing with an expert panel and was pilot tested to establish temporal stability. It was then administered to a population sample of 1285 neonatal nurses in Australian NICUs, with a response rate of 50% (N 645). Exploratory factor-analysis techniques were conducted to identify scales and subscales of the instrument. RESULTS Data-reduction techniques using principal components analysis were used. Using the criteria of eigenvalues being 1, the items in the Neonatal Palliative Care Attitude Scale extracted 6 factors, which accounted for 48.1% of the variance among the items. By further examining the questions within each factor and the Cronbach’s of items loading on each factor, factors were accepted or rejected. This resulted in acceptance of 3 factors indicating the barriers to and facilitators of palliative care practice. The constructs represented by these factors indicated barriers to and facilitators of palliative care practice relating to (1) the organization in which the nurse practices, (2) the available resources to support a palliative model of care, and (3) the technological imperatives and parental demands. CONCLUSIONS The subscales identified by this analysis identified items that measured both barriers to and facilitators of palliative care practice in neonatal nursing. While establishing preliminary reliability of the instrument by using exploratory factor-analysis techniques, further testing of this instrument with different samples of neonatal nurses is necessary using a confirmatory factor-analysis approach.

An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics; and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics.

Employing the five-factor mentoring instrument : analysing mentoring practices for teaching primary science.

Primary science education is a concern around the world and quality mentoring within schools can develop preservice teachers’ practices. A five-factor model for mentoring has been identified, namely, personal attributes, system requirements, pedagogical knowledge, modelling, and feedback. Final-year preservice teachers (mentees, n=211) from three Turkish universities were administered a previously validated instrument to gather perceptions of their mentoring in primary science teaching. ANOVA indicated that each of these five factors was statistically significant (p<.001) with mean scale scores ranging from 3.36 to 4.12. Although mentees perceived their mentors to provide evaluation feedback (95%), model classroom management (88%), guide their preparation (96%), and outline the science curriculum (92%), the majority of mentors were perceived not to assist their mentees in 10 of the 34 survey items. Professional development programmes that target the specific needs of these mentors may further enhance mentoring practices for advancing primary science teaching.

The Melbourne Decision-Making Questionnaire : an instrument for measuring patterns for coping with decisional conflict

A study was conducted to examine the factorial validity of the Flinders Decision Making Questionnaire (Mann, 1982), a 31-item self-report inventory designed to measure tendencies to use three major coping patterns identified in the conflict theory of decision making (Janis and Mann, 1977): vigilance, hypervigilance, and defensive avoidance (procrastination, buck-passing, and rationalization). A sample of 2051 university students, comprising samples from Australia (n=262), New Zealand (n=260), the USA (n=475), Japan (n=359), Hong Kong (n=281) and Taiwan (n=414) was administered the DMQ. Factorial validity of the instrument was tested by confirmatory factor analysis with LISREL. Five different substantive models, representing different structural relationships between the decision-coping patterns had unsatisfactory fit to the data and could not be validated. A shortened instrument, containing 22 items, yielded a revised model comprising four identifiable factors-vigilance, hypervigilance, buck-passing, and procrastination. The revised model had adequate fit with data for each country sample and for the total sample, and was confirmed. It is recommended that the 22-item instrument, named the Melbourne DMQ, replace the Flinders DMQ for measurement of decision-coping patterns.

The Autistic Behavioural Indicators Instrument (ABII) : development and instrument utility in discriminating autistic disorder from speech and language impairment and typical development

The Autistic Behavioural Indicators Instrument (ABII) is an 18-item instrument developed to identify children with Autistic Disorder (AD) based on the presence of unique autistic behavioural indicators. The ABII was administered to 20 children with AD, 20 children with speech and language impairment (SLI) and 20 typically developing (TD) children aged 2-6 years. Results indicated that the ABII discriminated children diagnosed with AD from those diagnosed with SLI and those who were TD, based on the presence of specific social attention, sensory, and behavioural symptoms. A combination of symptomology across these domains correctly classified 100% of children with and without AD. The paper concludes that the ABII shows considerable promise as an instrument for the early identification of AD.

Establishing content validity of a survey research instrument : the older patients in acute care survey - United States

Geriatric nursing competency in the acute care setting is a social mandate for the 21st century. This article reports on the content validation of an Australian research instrument, the Older Patients in Acute Care Survey (OPACS) that examines the attitudes, the knowledge, and the practices of nurses working with acute care patients. The OPACS tool was developed primarily to assist nurse educators to assess attitudes, knowledge, and practices of nursing staff in caring for older patients in the acute care setting; to evaluate the implementation of institution-specific educational interventions; and to improve quality of care given to older patients. An overall content validity index (CVI) for the OPACS was calculated (CVI = .918), revealing high content validity. Opinions (CVI = .92) and practices (CVI = .97) subconstructs revealed high content validity as well. Therefore, results indicate that the OPACS has high content validity in the U.S. acute care setting and could assist nurse educators in establishing and enhancing nurse competency in the care for geriatric patients in the future.

An instrument to measure the approach to learning for assessment in economics

Economics education research studies conducted in the UK, USA and Australia to investigate the effects of learning inputs on academic performance have been dominated by the input-output model (Shanahan and Meyer, 2001). In the Student Experience of Learning framework, however, the link between learning inputs and outputs is mediated by students' learning approaches which in turn are influenced by their perceptions of the learning contexts (Evans, Kirby, & Fabrigar, 2003). Many learning inventories such as Biggs' Study Process Questionnaires and Entwistle and Ramsden' Approaches to Study Inventory have been designed to measure approaches to academic learning. However, there is a limitation to using generalised learning inventories in that they tend to aggregate different learning approaches utilised in different assessments. As a result, important relationships between learning approaches and learning outcomes that exist in specific assessment context(s) will be missed (Lizzio, Wilson, & Simons, 2002). This paper documents the construction of an assessment specific instrument to measure learning approaches in economics. The post-dictive validity of the instrument was evaluated by examining the association of learning approaches to students' perceived assessment demand in different assessment contexts.

Validation of an Australian sign language instrument of outcome measurement for adults in mental health settings

Objective: There are currently no adult mental health outcome measures that have been translated into Australian sign language (Auslan). Without a valid and reliable Auslan outcome measure, empirical research into the efficacy of mental health interventions for sign language users is unattainable. To address this research problem the Outcome Rating Scale (ORS), a measure of general functioning, was translated into Auslan and recorded on to digital video disk for use in clinical settings. The purpose of the present study was therefore to examine the reliability, validity and acceptability of an Auslan version of the ORS (ORS-Auslan). Method: The ORS-Auslan was administered to 44 deaf people who use Auslan as their first language and who identify as members of a deaf community (termed ‘Deaf’ people) on their first presentation to a mental health or counselling facility and to 55 Deaf people in the general community. The community sample also completed an Auslan version of the Depression Anxiety Stress Scale-21 (DASS-21). Results: t-Tests indicated significant differences between the mean scores for the clinical and community sample. Internal consistency was acceptable given the low number of items in the ORS-Auslan. Construct validity was established by significant correlations between total scores on the DASS-21-Auslan and ORS-Auslan. Acceptability of ORS-Auslan was evident in the completion rate of 93% compared with 63% for DASS-21-Auslan. Conclusions: This is the only Auslan outcome measure available that can be used across a wide variety of mental health and clinical settings. The ORS-Auslan provides mental health clinicians with a reliable and valid, brief measure of general functioning that can significantly distinguish between clinical and non-clinical presentations for members of the Deaf community.

The properties of the international classification of the external cause of injury when used as an instrument for injury prevention research

Objective: To demonstrate properties of the International Classification of the External Cause of Injury (ICECI) as a tool for use in injury prevention research. Methods: The Childhood Injury Prevention Study (CHIPS) is a prospective longitudinal follow up study of a cohort of 871 children 5–12 years of age, with a nested case crossover component. The ICECI is the latest tool in the International Classification of Diseases (ICD) family and has been designed to improve the precision of coding injury events. The details of all injury events recorded in the study, as well as all measured injury related exposures, were coded using the ICECI. This paper reports a substudy on the utility and practicability of using the ICECI in the CHIPS to record exposures. Interrater reliability was quantified for a sample of injured participants using the Kappa statistic to measure concordance between codes independently coded by two research staff. Results: There were 767 diaries collected at baseline and event details from 563 injuries and exposure details from injury crossover periods. There were no event, location, or activity details which could not be coded using the ICECI. Kappa statistics for concordance between raters within each of the dimensions ranged from 0.31 to 0.93 for the injury events and 0.94 and 0.97 for activity and location in the control periods. Discussion: This study represents the first detailed account of the properties of the ICECI revealed by its use in a primary analytic epidemiological study of injury prevention. The results of this study provide considerable support for the ICECI and its further use.

Parents’ self-efficacy, outcome expectations, and self-reported task performance when managing atopic dermatitis in children: Instrument reliability and validity

BACKGROUND: Support and education for parents faced with managing a child with atopic dermatitis is crucial to the success of current treatments. Interventions aiming to improve parent management of this condition are promising. Unfortunately, evaluation is hampered by lack of precise research tools to measure change. OBJECTIVES: To develop a suite of valid and reliable research instruments to appraise parents' self-efficacy for performing atopic dermatitis management tasks; outcome expectations of performing management tasks; and self-reported task performance in a community sample of parents of children with atopic dermatitis. METHODS: The Parents' Eczema Management Scale (PEMS) and the Parents' Outcome Expectations of Eczema Management Scale (POEEMS) were developed from an existing self-efficacy scale, the Parental Self-Efficacy with Eczema Care Index (PASECI). Each scale was presented in a single self-administered questionnaire, to measure self-efficacy, outcome expectations, and self-reported task performance related to managing child atopic dermatitis. Each was tested with a community sample of parents of children with atopic dermatitis, and psychometric evaluation of the scales' reliability and validity was conducted. SETTING AND PARTICIPANTS: A community-based convenience sample of 120 parents of children with atopic dermatitis completed the self-administered questionnaire. Participants were recruited through schools across Australia. RESULTS: Satisfactory internal consistency and test-retest reliability was demonstrated for all three scales. Construct validity was satisfactory, with positive relationships between self-efficacy for managing atopic dermatitis and general perceived self-efficacy; self-efficacy for managing atopic dermatitis and self-reported task performance; and self-efficacy for managing atopic dermatitis and outcome expectations. Factor analyses revealed two-factor structures for PEMS and PASECI alike, with both scales containing factors related to performing routine management tasks, and managing the child's symptoms and behaviour. Factor analysis was also applied to POEEMS resulting in a three-factor structure. Factors relating to independent management of atopic dermatitis by the parent, involving healthcare professionals in management, and involving the child in the management of atopic dermatitis were found. Parents' self-efficacy and outcome expectations had a significant influence on self-reported task performance. CONCLUSIONS: Findings suggest that PEMS and POEEMS are valid and reliable instruments worthy of further psychometric evaluation. Likewise, validity and reliability of PASECI was confirmed.