### Center for Effective Global Action

CEGACenter of Evaluation for Global Action
The CEGA toolbox includes randomized evaluation (long-trusted in the medical field) as well as regression discontinuity, panel analysis, instrumental variables, and other rigorous quasi-experimental methods. When used appropriately, each of these methods can create equivalent treatment and comparison groups for use in estimating an intervention's impact. CEGA is unique among development research centers, in that it integrates business and economic approaches with expertise from various sectors—including agriculture, engineering and computer science, public health, education, political science, and environment.

### Steven Levitt

Steven D. LevittSteve Levitt
In a 1997 paper on the effect of police hiring on crime rates, Levitt used the timing of mayoral and gubernatorial elections as an instrumental variable to identify a causal effect of police on crime. Past studies had been inconclusive because of the simultaneity inherent in police hiring (when crime increases, more police are hired to combat crime). The findings of this paper were found to be the result of a programming error. This was pointed out in a comment by Justin McCrary published in the American Economic Review in 2002. In a response published with McCrary's comment Levitt admits to the error and then goes on to offer alternative evidence to support his original conclusions.

### Quasi-experiment

quasi-experimentalQuasi-experimental designquasi-experiments
Case-control design. time-series designs. multiple time series design. interrupted time series design. propensity score matching. instrumental variables. Panel analysis.

### Henri Theil

TheilTheil, Henri
Henri (Hans) Theil (October 13, 1924 – August 20, 2000) was a Dutch econometrician, Professor at the Netherlands School of Economics in Rotterdam, known for his contributions to the field of econometrics.

### Endogeneity with an exponential regression function

The variables z_i serve as instrumental variables for the potentially endogenous x_i. One can assume a linear relationship between these two variables or alternatively project the endogenous variable x_i onto the instruments to get the following reduced form equation: The usual rank condition is needed to ensure identification. The endogeneity is then modeled in the following way, where \rho determines the severity of endogeneity and v_i is assumed to be independent of e_i.

### Fiscal multiplier

multiplierSpending multipliermultiplier effect
The economists used mafia influence as an instrumental variable to help estimate the effect of central funds given to local councils. In October 2012 the International Monetary Fund released their Global Prospects and Policies document in which an admission was made that their assumptions about fiscal multipliers had been inaccurate. This admission has serious implications for economies such as the UK where the OBR used the IMF's assumptions in their economic forecasts about the consequences of the government's austerity policies.

### Caroline Hoxby

Caroline M. Hoxby
Jesse Rothstein published a paper in which he stated that Hoxby's result depended on her hand-count of the main instrumental variable, and that he was unable to replicate her results with any of several alternative measures. Hoxby later published a response in defense of her original work. The debate received coverage in the mainstream press. Among the awards and honors that Hoxby has received are: * Caroline M. Hoxby (editor). 2003. The Economics of School Choice. University of Chicago Press. ISBN: 978-0-226-35533-7. Caroline M. Hoxby (editor). 2004. College Choices: The Economics of Where to Go, When to Go, and How to Pay for It. University of Chicago Press. ISBN: 978-0-226-35535-1.

### Robert Basmann

BasmannR. L. Basmann
Robert Leon Basmann (born January 15, 1926) is an American econometrician. He was a Professor of Econometrics at Texas A&M University until his retirement. He served as a lecturer at Binghamton University after his retirement.

### Rubin causal model

potential outcomescausal modelcausal modeling from observational data
The Rubin causal model has also been connected to instrumental variables (Angrist, Imbens, and Rubin, 1996) and other techniques for causal inference. For more on the connections between the Rubin causal model, structural equation modeling, and other statistical methods for causal inference, see Morgan and Winship (2007). Principal stratification. Propensity score matching. Causation. Guido Imbens & Donald Rubin (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge: Cambridge University Press. doi:10.1017/CBO9781139025751.

### Methodology of econometrics

econometric methodsmethodological aspectsnon-structural econometric approaches
One widely used remedy is the method of instrumental variables (IV). For an economic model described by more than one equation, simultaneous-equation methods may be used to remedy similar problems, including two IV variants, Two-Stage Least Squares (2SLS), and Three-Stage Least Squares (3SLS). Computational concerns are important for evaluating econometric methods and for use in decision making. Such concerns include mathematical well-posedness: the existence, uniqueness, and stability of any solutions to econometric equations. Another concern is the numerical efficiency and accuracy of software. A third concern is also the usability of econometric software.

### Durbin–Wu–Hausman test

Hausman specification testHausman testThe Hausman test, ''or'' Hausman specification test
This test can be used to check for the endogeneity of a variable (by comparing instrumental variable (IV) estimates to ordinary least squares (OLS) estimates). It can also be used to check the validity of extra instruments by comparing IV estimates using a full set of instruments Z to IV estimates that use a proper subset of Z. Note that in order for the test to work in the latter case, we must be certain of the validity of the subset of Z and that subset must have enough instruments to identify the parameters of the equation. Hausman also showed that the covariance between an efficient estimator and the difference of an efficient and inefficient estimator is zero.

### Gauss–Markov theorem

best linear unbiased estimatorGauss–Markovbest linear unbiased estimation
Instrumental variable techniques are commonly used to address this problem. The sample data matrix \mathbf{X} must have full column rank. :Otherwise is not invertible and the OLS estimator cannot be computed. A violation of this assumption is perfect multicollinearity, i.e. some explanatory variables are linearly dependent. One scenario in which this will occur is called "dummy variable trap," when a base dummy variable is not omitted resulting in perfect correlation between the dummy variables and the constant term. Multicollinearity (as long as it is not "perfect") can be present resulting in a less efficient, but still unbiased estimate.

### Galton's problem

Galton's problem, named after Sir Francis Galton, is the problem of drawing inferences from cross-cultural data, due to the statistical phenomenon now called autocorrelation. The problem is now recognized as a general one that applies to all nonexperimental studies and to experimental design as well. It is most simply described as the problem of external dependencies in making statistical estimates when the elements sampled are not statistically independent. Asking two people in the same household whether they watch TV, for example, does not give you statistically independent answers. The sample size, n, for independent observations in this case is one, not two.

### Mendelian randomization

epidemiologyMendelian randomisationrandom Mendelian sampling
From a statistical perspective, Mendelian randomization (MR) is an application of the technique of instrumental variables with genotype acting as an instrument for the exposure of interest. The method has also been used in economic research studying the effects of obesity on earnings, and other labor market outcomes. Accuracy of MR depends on a number of assumptions: That there is no direct relationship between the instrumental variable and the dependent variables, and that there are no direct relation between the instrumental variable and any possible confounding variables.

### Experimentalist approach to econometrics

experimentalist
The experimentalist approach looks for an instrumental variable that is correlated with X but uncorrelated with the unobservables. Instrumental variables. Difference in differences.

### Generated regressor

generated regressors
With minor modifications in the model, the above formulation is also applicable to Instrumental Variable estimation. Suppose the model of interest is linear in parameter. Error term is correlated with some of the regressors, and the model specifies some instrumental variables, which are not observable but have the representation. If a consistent estimator of \gamma of \hat\gamma is available using as instruments, the parameter of interest can be estimated by IV. Similar to the above case, consistency and asymptotic normality follows under mild conditions, and the asymptotic variance has a different form than observed IV case.

### Linear regression

regression coefficientmultiple linear regressionregression
When controlled experiments are not feasible, variants of regression analysis such as instrumental variables regression may be used to attempt to estimate causal relationships from observational data. The capital asset pricing model uses linear regression as well as the concept of beta for analyzing and quantifying the systematic risk of an investment. This comes directly from the beta coefficient of the linear regression model that relates the return on the investment to the return on all risky assets. Linear regression is the predominant empirical tool in economics.

### Instrument

Instrument (disambiguation)
Instrumental variable, a method used in statistics. Financial instrument, a formal documentation of a financial transaction. Legal instrument, a formal documentation of a status or transaction. Negotiable instrument, a type of contract. Statutory instrument, a form of legislation. Instrumental case, in linguistics, a grammatical case expressing the instrument by which an action is performed. Tool. Instrumentation (disambiguation).

### Overdispersion

underdispersionover-dispersionoverdispersed
However, in the presence of study heterogeneity where studies have different sampling bias, the distribution is instead a compound distribution and will be overdistributed relative to the predicted distribution. For example, given repeated opinion polls all with a margin of error of 3%, if they are conducted by different polling organizations, one expects the results to have standard deviation greater than 3%, due to pollster bias from different methodologies. Over- and underdispersion are terms which have been adopted in branches of the biological sciences.

### Natural experiment

natural experimentsnaturalexperimental variable
Using statistical methods developed in econometrics, Angrist capitalized on the approximate random assignment of the Vietnam War draft lottery, and used it as an instrumental variable associated with eligibility (or non-eligibility) for military service. Because many factors might predict whether someone serves in the military, the draft lottery frames a natural experiment whereby those drafted into the military can be compared against those not drafted because the two groups should not differ substantially prior to military service. Angrist found that the earnings of veterans were, on average, about 15 percent less than the earnings of non-veterans.

### Mixture distribution

mixture densitymixturedensity mixture
In meta-analysis of separate studies, study heterogeneity causes distribution of results to be a mixture distribution, and leads to overdispersion of results relative to predicted error. For example, in a statistical survey, the margin of error (determined by sample size) predicts the sampling error and hence dispersion of results on repeated surveys.

### Principal stratification

Instrumental variable. Preprint. Zhang, Junni L.; Rubin, Donald B. (2003) "Estimation of Causal Effects via Principal Stratification When Some Outcomes are Truncated by “Death”", Journal of Educational and Behavioral Statistics, 28: 353–368. Barnard, John; Frangakis, Constantine E.; Hill, Jennifer L.; Rubin, Donald B. (2003) "Principal Stratification Approach to Broken Randomized Experiments", Journal of the American Statistical Association, 98, 299–323. Roy, Jason; Hogan, Joseph W.; Marcus, Bess H. (2008) "Principal stratification with predictors of compliance for randomized trials with 2 active treatments", Biostatistics, 9 (2), 277–289.

### Thomas Kane (economist)

Thomas KaneKane
Thomas Joseph Kane (born September 5, 1961) is a U.S.-American education economist who currently holds the position of Walter H. Gale Professor of Education and Economics at the Harvard Graduate School of Education. He has performed research on education policy, labour economics and econometrics. During Bill Clinton's first term as U.S. President, Kane served on the Council of Economic Advisers.

### Comparison of statistical packages

Econometric softwareEconometrics softwarestatistical computer packages
The following tables compare general and technical information for a number of statistical analysis packages.

### Instrumental (disambiguation)

Instrumental variable, in statistics. Instrumental value, one of two poles of an ancient dichotomy.