The Identification Problem
In economics, establishing causality is notoriously difficult because randomized controlled trials (RCTs) are often unethical or impossible. Observational data is plagued by Endogeneity, where an independent variable is correlated with the error term in a regression model.
Omitted Variable Bias (OVB)
Consider a simple regression estimating the effect of education ($X$) on wages ($Y$):
$$ Y_i = \beta_0 + \beta_1 X_i + \epsilon_i $$
If we omit unobservable “innate ability” ($A$), which is correlated with both higher education and higher wages, our estimate of $\beta_1$ will be biased upward. The true model is $Y_i = \beta_0 + \beta_1 X_i + \beta_2 A_i + u_i$. The bias is mathematically expressed as:
$$ E[\hat{\beta_1}] = \beta_1 + \beta_2 \frac{Cov(X, A)}{Var(X)} $$
Natural Experiments
To solve endogeneity, economists use quasi-experimental methods like Instrumental Variables (IV) or Difference-in-Differences (DiD). These methods leverage exogenous shocks (e.g., a sudden policy change in one state but not another) to isolate causal effects from correlated noise.