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 (B)

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

<p>1</p> Signup and view all the answers

Match the following terms with their definitions:

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

What is the purpose of the regression anatomy approach?

<p>To check assumptions A1-A4 and apply results of chapter 1b (A)</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

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

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

What is the ideal method to estimate a causal effect?

<p>Conducting a randomized experiment (A)</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

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

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

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

<p>x, u</p> Signup and view all the answers

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

<p>We get an inconsistent estimate of β (B)</p> Signup and view all the answers

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

<p>True (A)</p> Signup and view all the answers

Match the following methods with their purposes:

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

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

<p>Randomized experiments</p> Signup and view all the answers

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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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