Econometrics and Machine Learning: Causal Effect Estimation

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Questions and Answers

What is the purpose of adding control variables in a multiple linear regression?

To increase the complexity of the model

To make the model more difficult to interpret

To decrease the accuracy of the model

To remove factors from the error term and make the explanatory variable of interest exogenous (correct)

The OLS estimator of a multiple linear regression is different from the OLS estimator of a simple linear regression.

False

What is the condition for an explanatory variable to be exogenous in a regression with control variables?

It must be uncorrelated with the error term.

The regression anatomy approach reduces a multiple linear regression to a simple linear regression, where the OLS estimator is the same as the OLS estimator from the simple linear regression: y = β0 + β______x~ + ε

1 Signup and view all the answers

Match the following terms with their definitions:

Exogenous = Uncorrelated with the error term Endogenous = Correlated with the error term Control variable = Additional explanatory variable to remove factors from the error term Signup and view all the answers

What is the purpose of the regression anatomy approach?

To check assumptions A1-A4 and apply results of chapter 1b Signup and view all the answers

The OLS estimator of a multiple linear regression is always biased.

False Signup and view all the answers

What is the formula for the OLS estimator in a multiple linear regression?

β^ = (X′X)−1X′y Signup and view all the answers

What is the ideal method to estimate a causal effect?

Conducting a randomized experiment Signup and view all the answers

It is always possible to run a randomized experiment to estimate a causal effect.

False Signup and view all the answers

What is the purpose of adding control variables in regression analysis?

To overcome endogeneity problems and consistently estimate regression parameters that describe causal effects. Signup and view all the answers

The demand function for ice is given by the following regression formula with two explanatory variables: and .

x, u Signup and view all the answers

If we estimate the short regression model without controlling for unobserved demand shocks, what can we expect?

We get an inconsistent estimate of β Signup and view all the answers

Instrumental variable estimation is a method to consistently estimate causal effects.

True Signup and view all the answers

Match the following methods with their purposes:

Conducting a randomized experiment = To establish causal effects Adding control variables = To overcome endogeneity problems Using instrumental variable estimation = To consistently estimate causal effects Signup and view all the answers

What is the 'Scientific Gold Standard' in establishing causal effects?

Randomized experiments Signup and view all the answers

Study Notes

Methods to Consistently Estimate Causal Effects

Several methods can be used to overcome endogeneity problems and consistently estimate regression parameters that describe causal effects:
- Conducting a randomized experiment
- Adding control variables
- Using instrumental variable estimation

Conducting a Randomized Experiment

The ideal method to estimate a causal effect is to run a randomized experiment
Randomized experiments are often called the "Scientific Gold Standard" to establish causal effects
They are required by regulators when a pharmaceutical company wants to establish that a new drug has positive effects on patients

Control Variables

Motivating example: demand function for ice with two explanatory variables: price and sunny day
If we estimate the short regression model without control variables, we may not get a consistent estimate of the coefficient of interest
Adding control variables: multiple linear regression can help to consistently estimate the coefficient of interest
Control variables are additional explanatory variables that are included in the regression to remove factors from the error term

Regression Anatomy

The regression anatomy approach reduces a multiple linear regression to a simple linear regression
This approach can be used to check assumptions A1-A4 and apply results of chapter 1b
The OLS estimator of a multiple linear regression is the same as the OLS estimator of a simple linear regression of the residual on the variable of interest

Exogeneity in a Regression with Control Variables

Exogeneity in a regression with control variables means that the variable of interest is uncorrelated with the error term
Adding control variables can remove factors from the error term and make the explanatory variable of interest exogenous
However, the explanatory variable of interest can still be correlated with the control variables

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Description

This quiz covers methods to estimate causal effects in econometrics, including randomized experiments, control variables, and instrumental variable estimation.