Videos and questions for Chapter 1b of the course "Market Analysis with Econometrics and Machine Learning" at Ulm University (taught by Sebastian Kranz)

The simple linear regression model

Later we will also look at the multiple linear regression model. What do you think is the difference to this simple linear regression model?

Predicted values and residuals

Assume the red line on the previous slide show the estimated regression line. What measures then the vertical black line?

Ordinary Least Squares Estimation

The disturbance \(\varepsilon\) is always modelled as a random variable. The explanatory variable \(x\) can also be a random variable. Is the OLS estimator \(\hat \beta\) also a random variable?

The estimator is a random variable

What do you think holds true for the expected value of the OLS estimator \(\hat \beta\) (which is a random variable)?

Monte-Carlo simulation of an OLS estimator

How do you think the estimates differ when we call our function several times with T=5 compared to earlier where we had T=100.

Standard Error of \(\hat \beta_1\)

Assume you run an experiment with \(T=20\) observations and get some standard error for \(\hat \beta_1\). If you want to halve the size of that standard error, how many observations would you roughly need?

Robust Standard Errors

Criteria for Estimators 1: Bias and Mean Squared Error (MSE)

Bias and MSE in our Monte-Carlo Simulation

Criteria for Estimators 2: Consistency and Efficiency

In our Monte-Carlo simulation did it look as if the estimator \(\hat \beta_1\) was consistent?

Assumptions of the linear regression model

Endogeniety and Exogeniety

Exploring Endogeniety in R

Let us look at some R code to better understand that an endogenous explanatory variable leads to an inconsistent OLS estimator

Are the prices in the regression for the simulation in the video above endogenous or exogenous?

Assume we set in the simulation prices that are always 10% above the costs c. Are prices then endogenous or exogenous when estimating the demand function?

What happens if the standard deviation of \(\varepsilon\) is very small?

What do you think holds for our estimator \(\hat \beta\) if we have such a small standard deviation of \(\varepsilon\)?

Other Assumptions

Confidence Intervals and Bias Formula

Ok, that were all videos for the first part of Chapter 1b. If you have not yet done so, it is a good time to start solving the RTutor problem set for this part.