Regression and Causality: Binary Outcomes

The causal effect of schooling on wage

Yi = Y0i + (Y1i − Y0i )Di

E[Y1i |Di = 1] − E[Y0i |Di = 1]

<p>A further assumption, such as Conditional Independence Assumption</p> Signup and view all the answers

<p>Omitted variable bias, selection bias, or bad controls</p> Signup and view all the answers

<p>Omitted variable bias</p> Signup and view all the answers

<p>A model that assumes the causal effect of schooling on wage is the same for all individuals</p> Signup and view all the answers

<p>It can lead to biased estimates of the causal effect of schooling on wage</p> Signup and view all the answers

<p>Variables that introduce bias when controlled for, but leaving them out is fine.</p> Signup and view all the answers

<p>It may not have a causal interpretation, even if the treatment is randomized.</p> Signup and view all the answers

<p>It opens a path between two variables that were previously blocked.</p> Signup and view all the answers

<p>The treatment effect is the same for all individuals.</p> Signup and view all the answers

<p>If an omitted variable affects both the treatment and the outcome, and is not accounted for in the model.</p> Signup and view all the answers

<p>Conditional Independence Assumption (CIA)</p> Signup and view all the answers

<p>To ensure that the treatment is independent of the error term, conditional on the controls.</p> Signup and view all the answers

<p>The CIA focuses on identifying one causal effect, whereas the traditional assumption assumes all regressors are independent of the error term.</p> Signup and view all the answers

<p>A direct effect is the effect of the treatment on the outcome, while an indirect effect is the effect of the treatment on the outcome through a mediator.</p> Signup and view all the answers

<p>They have no causal interpretation.</p> Signup and view all the answers

<p>A DAG can help identify bad controls by visualizing the causal relationships between variables.</p> Signup and view all the answers

<p>Omitted variable bias</p> Signup and view all the answers

<p>A model that assumes the causal effect is constant across different levels of the control variables.</p> Signup and view all the answers

<p>d and v are independent, conditional on x.</p> Signup and view all the answers

<p>Regression focuses on estimating associations, while causality focuses on identifying causal effects.</p> Signup and view all the answers

<p>It can lead to biased estimates of the causal effect and incorrect inference.</p> Signup and view all the answers

<p>β = Cov(Yi, Xi) / Var(Xi)</p> Signup and view all the answers

<p>To estimate the linear effect of each regressor, controlling for the other variables in the model.</p> Signup and view all the answers

<p>Omitted variable bias, resulting in an estimator of the coefficient of D that is biased by γδXD.</p> Signup and view all the answers

<p>The assumption that the error term is independent of the regressors, i.e., εi ⊥ Xki.</p> Signup and view all the answers

<p>A model that assumes the effect of a regressor on the outcome is constant across all observations.</p> Signup and view all the answers

<p>Variables that are correlated with both the outcome and the regressor of interest, but are not causally related to the outcome.</p> Signup and view all the answers

<p>The non-normality of the outcome variable, which can lead to biased estimates of the regression coefficients.</p> Signup and view all the answers

<p>The estimator is biased by γδXD, where δXD is the coefficient of D in the regression of X on D.</p> Signup and view all the answers

<p>The primary assumption of the Constant Effect Model is that the effect of the independent variable on the dependent variable is constant across all observations. This assumption is central to regression analysis, as it allows us to estimate the average effect of the independent variable on the dependent variable.</p> Signup and view all the answers

<p>The Conditional Independence Assumption (CIA) states that the error term is independent of the independent variable, given the control variables. This assumption is necessary for identifying causal relationships between variables in regression analysis.</p> Signup and view all the answers

<p>Bad controls refer to the inclusion of variables in a regression model that are not truly exogenous, but are instead correlated with the error term. This can lead to biased estimates, as the model may attribute the effect of the bad control to the independent variable of interest.</p> Signup and view all the answers

<p>Omitted variable bias occurs when a relevant variable is omitted from a regression model, leading to biased estimates of the independent variable's effect. This can be addressed by including the omitted variable in the model or using instrumental variable techniques.</p> Signup and view all the answers

<p>Binary outcomes are discrete variables that take on only two values, whereas continuous outcomes are continuous variables that take on any value within a range. The assumptions of regression analysis differ for binary outcomes, as the dependent variable is not normally distributed, and specialized techniques such as logistic regression are required.</p> Signup and view all the answers

<p>The F-statistic tests the overall significance of the regression model, while the R-squared value measures the proportion of variance explained by the model. Together, they provide a comprehensive evaluation of the model's goodness of fit.</p> Signup and view all the answers

<p>The residual plot is a graphical representation of the residuals against the fitted values, and it can be used to identify potential problems such as non-normality, heteroscedasticity, and non-linear relationships.</p> Signup and view all the answers

<p>The Coef. column represents the estimated change in the dependent variable for a one-unit change in the independent variable, while holding all other variables constant.</p> Signup and view all the answers