QQM Topic 6

• The average treatment effect (ATE) is the expected difference in outcomes between the treated and untreated groups.

  $ATE=$$E[Y 1 ​ ]−E[Y 0 ​ ]$
• $E[Y 1 ​ ]$


  The expected outcome if the individual receives the treatment
• $E[Y 0 ​ ]$


  The expected outcome if the individual does not receive the treatment
• The Average Treatment Effect on the Treated (ATET) is the expected difference in outcomes between the treated group and the hypothetical outcomes if these same individuals had not received the treatment.

  $ATT=$$E[Y 1 ​ ∣D=1]−E[Y 0 ​ ∣D=1]$
• $E[Y 1 ​ ∣D=1]$


  The expected outcome for individuals who received the treatment
• $E[Y 0 ​ ∣D=1]$


  The expected outcome for those same individuals if they had not received the treatment
• Selection Bias happens when there's a non-random selection of participants or when participants choose themselves into groups, leading to skewed results.

  $Selection Bias=$$E[Y 1 ​ ∣D=0]−E[Y 0 ​ ∣D=1]$