Tag Archives: OLS

Derivation of the Least Squares Estimator for Beta in Matrix Notation – Proof Nr. 1

In the post that derives the least squares estimator, we make use of the following statement:

\frac{\partial b'X'Xb}{\partial b} =2X'Xb

This post shows how one can prove this statement. Let’s start from the statement that we want to prove:

\frac{\partial \hat{\beta}'X'X\hat{\beta}}{\partial \hat{\beta}}=2 X'X \hat{\beta}'

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Graphically Illustrate Multicollinearity: Venn Diagram

Multicollinearity is a common problem in econometrics. As explained in a previous post, multicollinearity arises when we have too few observations to precisely estimate the effects of two or more highly correlated variables on the dependent variable. This post tries to graphically illustrate the problem of multicollinearity using venn-diagrams. The venn-diagrams below all represent the following regression model Continue reading Graphically Illustrate Multicollinearity: Venn Diagram

The Problem of Multicollinearity

Multicollinearity or collinearity refers to a situation where two or more variables of a regression model are highly correlated. Because of the high correlation, it is difficult to disentangle the pure effect of one single explanatory variables x on the dependent variable y. From a mathematical point of view, multicollinearity only becomes an issue when we face perfect multicollinearity. That is, when we have identical variables in our regression model. Continue reading The Problem of Multicollinearity

Cluster Robust Standard Errors in Stargazer

In a previous post, we discussed how to obtain clustered standard errors in R. While the previous post described how one can easily calculate cluster robust standard errors in R, this post shows how one can include cluster robust standard errors in stargazer and create nice tables including clustered standard errors.

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Omitted Variable Bias

The omitted variable bias is a common and serious problem in regression analysis. Generally, the problem arises if one does not consider all relevant variables in a regression. In this case, one violates the third assumption of the assumption of the classical linear regression model. The following series of blog posts explains the omitted variable bias and discusses its consequences.

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