Instrumental Variables

Endogeneity and the need for Instrumental Variables: Endogeneity occurs when the independent variable is correlated with the error term in a regression model, leading to biased and inconsistent coefficient estimates. Instrumental Variables (IVs) are used to address this issue by providing a way to estimate causal effects when there is endogeneity.

Identification: Identification is the process of determining the causal effect of an independent variable on the dependent variable. In IV analysis, identification requires finding an instrument that is correlated with the endogenous independent variable but uncorrelated with the error term.

Two-Stage Least Squares Regression (2SLS): SLS is a widely used method for estimating causal effects in IV analysis. It involves finding a relevant instrument and then using it to obtain predicted values of the endogenous variable. These predicted values are then used as a replacement for the endogenous variable in the regression equation to obtain unbiased estimates of the causal effect.

Weak Instruments: Weak instruments are instruments with low correlation with the endogenous variable. When weak instruments are used, the 2SLS estimates can be biased and inconsistent. Various tests have been developed to detect and correct for weak instruments.

Over-Identification: Over-identification occurs when there are more instruments than endogenous variables, providing more information than necessary to identify the causal effect. Over-identification tests can be conducted to assess the suitability of the instruments used.

Local Average Treatment Effect (LATE): LATE is the causal effect of the treatment on the subgroup of the population that is affected by the instrument. It is a key concept in IV analysis and is sometimes referred to as the “complier average causal effect.”.

Endogenous Treatment: Endogenous treatment occurs when the treatment variable is correlated with the error term in a regression model. IV analysis can be used to estimate the causal effect of endogenous treatment, just as it is used to estimate the causal effect of an endogenous independent variable.

Panel Data Instrumental Variables: Panel data analysis involves the use of time-series data for multiple individuals or entities. In panel data IV analysis, instruments are used to control for time-invariant omitted variables that are correlated with the endogenous variable.

Nonlinear Instrumental Variables: Nonlinear IV analysis is used when the relationship between the endogenous variable and the instrument is nonlinear. This requires specialized estimation techniques, such as maximum likelihood estimation or nonlinear IV regression.

Bayesian Instrumental Variables: Bayesian IV analysis involves the incorporation of prior distributions on the parameters of the regression model. This can additional information and improve estimation accuracy, especially when dealing with small sample sizes.

GMM Estimation: Generalized Method of Moments (GMM) Estimation is a way to estimate models when assumptions regarding normal distribution and/or variance fail.

Treatment Effects with Multiple Outcomes: It's common in practice that interventions or treatments have multiple effects on different outcomes simultaneously, Instrumental Variables can be used for this purpose.

Cross-validation techniques: Cross-validation techniques can be used to study the robustness of the estimates and the power of the instruments.

Causality and the Concept of "Falsification Test": In the research design, researchers often use 'falsification test,' where they investigate the effects of a treatment on an outcome that is not plausibly associated with the instrument. By doing this, researchers can identify whether the instrument has any effect on the given outcome.

Estimating Binary models: Estimating binary models that involve instrumental variables followed by the rigorous validation of these estimates.

Heterogeneity: There is often heterogeneity between individuals that could impact the accuracy of the estimates for a model, the estimation techniques should capture and account for these variations.

Structural Equation Model: Structural Equation Model is an approach to analyzing a data set using a combination of different relationships among independent, mediating, intervening and dependent variables.

Semiparametric and nonparametric estimation methods that are based on using instrumental variables.: Semiparametric and nonparametric estimation methods based on instrumental variables involve using statistical techniques that allow for flexibility in modeling the relationship between variables without relying on specific functional form assumptions.

Endogenous sample selection models: Model of selection that aims to address the issue of self-selection of the samples.

Fixed Effects and Local Instruments: This technique involves the use of fixed effects models to address endogeneity in observational studies.

Natural experiments: This refers to situations where an external event or natural occurrence creates an exogenous variation in a variable, allowing the researcher to isolate its effect on another variable of interest.

Regression discontinuity design (RDD): This is a method to estimate causal effects in situations where assignment to a treatment is determined by a score on a continuous measure that has a known threshold, such as a passing grade on a test.

Difference-in-difference (DiD): This is a quasi-experimental design used to estimate causal effects, which compares changes in an outcome variable across two or more groups that were exposed to different levels of a treatment or intervention.

Two-stage least squares (2SLS): This is a method to estimate causal effects in situations where there is endogeneity, by utilizing an instrumental variable that is correlated with the endogenous variable of interest, but uncorrelated with the error term.

Propensity score matching (PSM): This is a method to estimate causal effects in situations where there is selection bias, by matching subjects that share a common set of observed characteristics, but differ in their exposure to a treatment or intervention.

Instrumental variable regression (IVR): This is a linear regression model that uses instrumental variables to address endogeneity and identify causal effects between two variables, by removing the correlation between the endogenous variable and the error term.

Fixed effects models: This approach controls for unobserved heterogeneity by including time-invariant characteristics of individuals, groups, or other units as explanatory variables, allowing researchers to isolate the causal effect of a treatment or intervention.

Synthetic control: This is a method to estimate causal effects in situations where there is no control group, by selecting a weighted average of comparison units that mimic the pre-treatment trends of the treated unit.