Introduction to the matrix formulation of econometrics

The matrix formulation of econometrics - example

How to differentiate with respect to a vector - part 1

How to differentiate with respect to a vector - part 2

How to differentiate with respect to a vector - part 3

Ordinary Least Squares Estimators - derivation in matrix form - part 1

Ordinary Least Squares Estimators - derivation in matrix form - part 2

Ordinary Least Squares Estimators - derivation in matrix form - part 3

Expectations and variance of a random vector - part 1

Expectations and variance of a random vector - part 2

Expectations and variance of a random vector - part 3

Expectations and variance of a random vector - part 4

Least Squares as an unbiased estimator - matrix formulation

Variance of Least Squares Estimators - Matrix Form

The Gauss-Markov Theorem proof - matrix form - part 1

The Gauss-Markov Theorem proof - matrix form - part 2

The Gauss-Markov Theorem proof - matrix form - part 3

Geometric Interpretation of Ordinary Least Squares: An Introduction

Geometric Interpretation of Ordinary Least Squares: An Example

Geometric Least Squares Column Space Intuition

Geometric intepretation of least squares - orthogonal projection

Geometric interpretation of Least Squares: geometrical derivation of estimator

Orthogonal Projection Operator in Least Squares - part 1

Orthogonal Projection Operator in Least Squares - part 2

Orthogonal Projection Operator in Least Squares - part 3

Estimating the error variance in matrix form - part 1

Estimating the error variance in matrix form - part 2

Estimating the error variance in matrix form - part 3

Estimating the error variance in matrix form - part 4

Estimating the error variance in matrix form - part 5

Estimating the error variance in matrix form - part 6

Proof that the trace of Mx is p

Representing homoscedasticity and no autocorrelation in matrix form - part 1

Representing homoscedasticity and no autocorrelation in matrix form - part 2

Representing heteroscedasticity in matrix form

BLUE estimators in presence of heteroscedasticity - GLS - part 1

BLUE estimators in presence of heteroscedasticity - GLS - part 2

GLS estimators in matrix form - part 1

GLS estimators in matrix form - part 2

GLS estimators in matrix form - part 3

The variance of GLS estimators

GLS - example in matrix form

GLS estimators in the presence of autocorrelation and heteroscedasticity in matrix form

The Kronecker Product of two matrices - an introduction

SURE estimation - an introduction - part 1

SURE estimation - an introduction - part 2

SURE estimation - autocorrelation and heteroscedasticity

SURE estimator derivation - part 1

SURE estimator derivation - part 2

Kronecker Matrix Product - properties

SURE estimator - same independent variables - part 1

SURE estimator - same independent variables - part 2

SURE estimator - same independent variables - part 3

Causality - an introduction

The Rubin Causal model - an introduction

Causation in econometrics - a simple comparison of group means

Causation in econometrics - selection bias and average causal effect

Random assignment - removes selection bias

How to check if treatment is randomly assigned?

The conditional independence assumption: introduction

The conditional independence assumption - intuition

The average causal effect - an example

The average causal effect with continuous treatment variables

Conditional Independence Assumption for Continuous Variables

Linear regression and causality

Selection bias as viewed as a problem with samples

Sample balancing via stratification and matching

Propensity score - introduction and theorem

The Law of Iterated Expectations: an introduction

The Law of Iterated Expectations: introduction to nested form

Propensity score theorem proof - part 1

Propensity score theorem proof - part 2

Propensity score matching: an introduction

Propensity score matching - mathematics behind estimation