Coefficient of determination

R-squaredR'' 2 R 2
In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

Cochran's Q test

Cochran's QQ statistic
In statistics, in the analysis of two-way randomized block designs where the response variable can take only two possible outcomes (coded as 0 and 1), Cochran's Q test is a non-parametric statistical test to verify whether k treatments have identical effects. It is named after William Gemmell Cochran. Cochran's Q test should not be confused with Cochran's C test, which is a variance outlier test. Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups.

Fixed effects model

fixed effectsFixed effectFixed effects estimation
Such models assist in controlling for omitted variable bias due to unobserved heterogeneity when this heterogeneity is constant over time. This heterogeneity can be removed from the data through differencing, for example by subtracting the group-level average over time, or by taking a first difference which will remove any time invariant components of the model. There are two common assumptions made about the individual specific effect: the random effects assumption and the fixed effects assumption. The random effects assumption is that the individual-specific effects are uncorrelated with the independent variables.

Panel data

longitudinal datapanel(panel)
Instrumental variables or GMM techniques are commonly used in this situation, such as the Arellano–Bond estimator. *Panel study * Russia Longitudinal Monitoring Survey (RLMS). German Socio-Economic Panel (SOEP). Household, Income and Labour Dynamics in Australia Survey (HILDA). British Household Panel Survey (BHPS). Survey of Family Income and Employment (SoFIE). Survey of Income and Program Participation (SIPP). Lifelong Labour Market Database (LLMDB). Longitudinal Internet Studies for the Social sciences (LISS). Panel Study of Income Dynamics (PSID). Korean Labor and Income Panel Study (KLIPS). China Family Panel Studies (CFPS). German Family Panel (pairfam).

Optimal instruments

A common statistical and econometric problem deals with conditional moment models, that satisfy regression relationships of the form where. [How can you say "where" followed by an expression involving epsilon when the foregoing statement does not mention epsilon? ] No additional constraints are imposed on the class of probability distributions that have generated the data. However, this means that we can use infinitely many moments. More specifically, the moments,, are all consistent with the conditional moment restriction. A natural question to ask then, is whether an optimal set of instruments is available. Both econometricians and statisticians have extensively studied this subject.

Daniel McFadden

Daniel L. McFaddenDaniel Little McFaddenMcFadden
Daniel Little McFadden (born July 29, 1937) is an American econometrician who shared the 2000 Nobel Memorial Prize in Economic Sciences with James Heckman. McFadden's share of the prize was "for his development of theory and methods for analyzing discrete choice". He is the Presidential Professor of Health Economics at the University of Southern California and Professor of the Graduate School at University of California, Berkeley.

Mark Thoma

Mark Allen Thoma (born December 15, 1956) is a macroeconomist and econometrician and a Professor of Economics at the Department of Economics of the University of Oregon. Thoma is best known as a regular columnist for The Fiscal Times through his blog "Economist's View", which Paul Krugman called "the best place by far to keep up with the latest in economic discourse", and as an analyst at CBS MoneyWatch. He is also a regular contributor to EconoMonitor.

Denis Sargan

John Denis SarganJohn D. SarganSargan
He made many contributions, notably in instrumental variables estimation, Edgeworth expansions for the distributions of econometric estimators, identification conditions in simultaneous equations models, asymptotic tests for overidentifying restrictions in homoskedastic equations and exact tests for unit roots in autoregressive and moving average models (co-authored with Alok Bhargava). At the LSE, Sargan was Professor of Econometrics from 1964–84. Sargan was President of the Econometric Society, a Fellow of the British Academy and an (honorary foreign) member of the American Academy of Arts and Sciences. Sargan is known for having been doctoral advisor to several renowned econometricians.

Simultaneous equations model

simultaneous equationsIndirect least squaresLimited information maximum likelihood
One can estimate these models equation by equation; however, estimation methods that exploit the system of equations, such as generalized method of moments (GMM) and instrumental variables estimation (IV) tend to be more efficient. Suppose there are m regression equations of the form : where i is the equation number, and is the observation index. In these equations x it is the k i ×1 vector of exogenous variables, y it is the dependent variable, y −i,t is the n i ×1 vector of all other endogenous variables which enter the i th equation on the right-hand side, and u it are the error terms.

Heterogeneity (disambiguation)

Heterogeneity is a diverseness of constituent structure. Heterogeneity or heterogeneous may also refer to: * Heterogeneity in landscape ecology, the measure of how different parts of a landscape are from one another. Heterogeneity in statistics. Heterogeneity in econometrics. Study heterogeneity, a concept in statistics. Heterogeneous relation. Heterogeneous conditions in medicine are those conditions which have several causes/etiologies. A heterogeneous taxon, a taxon that contains a great variety of individuals or sub-taxa; usually this implies that the taxon is an artificial grouping. Genetic heterogeneity, multiple origins causing the same disorder in different individuals.

Generalizing the local average treatment effect

By leveraging instrumental variable, Aronow and Carnegie (2013) propose a new reweighting method called Inverse Compliance Score weighting (ICSW), with a similar intuition behind IPW. This method assumes compliance propensity is a pre-treatment covariate and compliers would have the same average treatment effect within their strata. ICSW first estimates the conditional probability of being a complier (Compliance Score) for each subject by Maximum Likelihood estimator given covariates control, then reweights each unit by its inverse of compliance score, so that compliers would have covariate distribution that matches the full population.

International inequality

inequalityglobal inequalityinternational
International inequality refers to the idea of inequality between countries. This can be compared to global inequality which is inequality between people across countries. This may refer to economic differences between countries. As well as medical care and education differences.

Plot (graphics)

plotdata plotplots
It is used primarily as a visual aid to detecting bias or systematic heterogeneity. Dot plot (statistics) : A dot chart or dot plot is a statistical chart consisting of group of data points plotted on a simple scale. Dot plots are used for continuous, quantitative, univariate data. Data points may be labelled if there are few of them. Dot plots are one of the simplest plots available, and are suitable for small to moderate sized data sets. They are useful for highlighting clusters and gaps, as well as outliers. Forest plot : is a graphical display that shows the strength of the evidence in quantitative scientific studies.

Multiple treatments

Nevertheless, the general instrumental variable framework used to analyze binary treatment effects has been extended to allow for multiple treatments. There are different approaches available to analyze multiple treatment effects. One can think of treatment effects within this framework as the difference in the counterfactual outcomes that would have been observed if the agent faced different general choice sets, with multinomial choices being a natural way to analyze multiple treatments. More formally, assume there are J options available and the value to the agent of choosing option j is R j (Z j )=v j (Z j ) -ϵ j where ε j is some unobserved random shock.


acupuncturistacupuncture pointacupuncture points
A 2013 systematic review found that acupuncture may be effective for nonspecific lower back pain, but the authors noted there were limitations in the studies examined, such as heterogeneity in study characteristics and low methodological quality in many studies. A 2012 systematic review found some supporting evidence that acupuncture was more effective than no treatment for chronic non-specific low back pain; the evidence was conflicting comparing the effectiveness over other treatment approaches.

Funnel plot

It is used primarily as a visual aid for detecting bias or systematic heterogeneity. A symmetric inverted funnel shape arises from a ‘well-behaved’ data set, in which publication bias is unlikely. An asymmetric funnel indicates a relationship between treatment effect estimate and study precision. This suggests the possibility of either publication bias or a systematic difference between studies of higher and lower precision (typically ‘small study effects’). Asymmetry can also arise from use of an inappropriate effect measure.

Cowles Foundation

Cowles CommissionCowles Commission for Research in EconomicsCowles Commission for Economic Research
Consequently, Cowles researchers developed new methods such as the indirect least squares, instrumental variable methods, the full information maximum likelihood method, and the limited information maximum likelihood method. All of these methods used theoretical, a priori restrictions. According to an article by Carl F. Christ, the Cowles approach was grounded on certain assumptions: Several Cowles associates have won Nobel prizes for research done while at the Cowles Commission. These include Tjalling Koopmans, Kenneth Arrow, Gérard Debreu, James Tobin, Franco Modigliani, Herbert A. Simon, Joseph E. Stiglitz, Lawrence Klein, Trygve Haavelmo, Leonid Hurwicz and Harry Markowitz.

Linear discriminant analysis

discriminant analysisDiscriminant function analysisFisher's linear discriminant
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition, and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.


causalcause and effectcausation
Instrumental variable. Root cause analysis. Self-fulfilling prophecy. Supply and demand. Unintended consequence. Virtuous circle and vicious circle. Environmental issues. Causes of global warming. Causes of deforestation. Causes of land degradation. Causes of soil contamination. Causes of habitat fragmentation. Azamat Abdoullaev (2000). The Ultimate of Reality: Reversible Causality, in Proceedings of the 20th World Congress of Philosophy, Boston: Philosophy Documentation Centre, internet site, Paideia Project On-Line: Arthur Danto (1965). Analytical Philosophy of History. Cambridge University Press.

Impact evaluation

impactimpact analysis
Instrumental variables estimation accounts for selection bias by modelling participation using factors ('instruments') that are correlated with selection but not the outcome, thus isolating the aspects of program participation which can be treated as exogenous. The pipeline approach (stepped-wedge design) uses beneficiaries already chosen to participate in a project at a later stage as the comparison group. The assumption is that as they have been selected to receive the intervention in the future they are similar to the treatment group, and therefore comparable in terms of outcome variables of interest.

Seed-based d mapping

SDM meta-analysesseed based
This mean is weighted by the inverse of the variance and accounts for inter-study heterogeneity (QH maps). Subgroup analyses are mean analyses applied to groups of studies to allow the study of heterogeneity. Linear model analyses (e.g. meta-regression) are a generalization of the mean analysis to allow comparisons between groups and the study of possible confounds. A low variability of the regressor is critical in meta-regressions, so they are recommended to be understood as exploratory and to be more conservatively thresholded.

Arellano–Bond estimator

Anderson and Hsiao (1981) first proposed a solution by utilising instrumental variables (IV) estimation. However, the Anderson–Hsiao estimator is asymptotically inefficient, as its asymptotic variance is higher than the Arellano–Bond estimator, which uses a similar set of instruments, but uses generalized method of moments estimation rather than instrumental variables estimation. In the Arellano–Bond method, first difference of the regression equation are taken to eliminate the fixed effects. Then, deeper lags of the dependent variable are used as instruments for differenced lags of the dependent variable (which are endogenous).

Twin study

twin studiestwinstudies of twins
Twin studies are studies conducted on identical or fraternal twins. They aim to reveal the importance of environmental and genetic influences for traits, phenotypes, and disorders. Twin research is considered a key tool in behavioral genetics and in content fields, from biology to psychology. Twin studies are part of the broader methodology used in behavior genetics, which uses all data that are genetically informative – siblings studies, adoption studies, pedigree, etc. These studies have been used to track traits ranging from personal behavior to the presentation of severe mental illnesses such as schizophrenia.

Colonial origins of comparative development

2001 paperThe Colonial Origins of Comparative DevelopmentThe Colonial Origins of Comparative Development: An Empirical Investigation
It is considered a seminal contribution to development economics through its use of European settler mortality as an instrumental variable of institutional development in former colonies. The theory proposed in the article is that Europeans only set up growth-inducing institutions in areas where the disease environment was favourable, so that they could settle. In areas with unfavourable disease environment to Europeans, such as central Africa, they instead set up extractive institutions which persist to the present day and explain much of the variation in income across countries, it is claimed. Law and economics. New institutional economics.