Lecture 3: Empirical Methods Part 2

What is omitted variable bias?

Failure of regression estimates to account for unmeasured, confounding differences between the treatment and control group

Without random assignment, why is a simple comparison of means (i.e. simple OLS regression) so misleading?

Potential confounding factors (e.g. store type) are not guaranteed to be balanced between treatment and control groups

What is the main limitation of regression analysis?

• Can never be sure all possible confounding factors are measured → leading to omitted variables bias

• Thus multiple regression studies can never give as definite an estimate of the true effectiveness of a treatment as a well-designed randomised controlled trial (RCT)

Why do people still do regression-based analysis?

RCTs are often not possible for both practical and ethical reasons:

• e.g. consider randomly assigning a more generous retirement package to subset of one’s employees

• Could generate morale issues over concerns about fairness + take decades to reveal package’s effects

Given speed of modern business → regressions on existing data (or even worse, simple before-after comparisons) are often the best we can do

What is single linear regression?

Statistical technique to study effects of single observable factor in situations where treatment of interest has been assigned by non-random process

• Can give misleading estimates of causal effects → don’t control for other, confounding factors affecting the outcome of interest (i.e. omitted variable bias)

What is multiple linear regression?

Statistical technique for removing confounding effects of one or multiple observable factors in situations where treatment of interest assigned by non-random process

• Can easily control for large no. of confounding factors → but only if those factors can be measured and entered into your analysis

• Any relevant factors left out → can still cause omitted variable bias