Multiple Regression and Model Specification
EVIDENCE LAB · 08
Multiple Regression
& Specification.
Economic outcomes have multiple determinants. Learn to estimate partial associations, choose controls from theory and recognise when specification choices alter the story.
CONTROLBIASSPECIFY
01 · THE MULTIVARIATE MODEL
One outcome.
Several economic forces.
Partial association
The change in expected Y associated with one unit of Xⱼ, holding included regressors constant.
Ceteris paribus
Comparison between observations with equal values of the other included explanatory variables.
Unobserved influences
Relevant omitted factors remain in the error term and threaten causal interpretation when correlated with included X.
02 · OMITTED-VARIABLE BIAS
Leaving something out
can move everything else.
Wage = f(education)
The education coefficient absorbs its own relationship with wages and any correlated omitted influences.
→
Wage = f(education, experience, region)
The education coefficient becomes a partial association conditional on the added controls.
MODEL SPECIFICATION STUDIO
Choose controls.
Watch the estimate change.
Construct a wage model and observe how theoretically relevant controls change the focal coefficient, fit and specification warning.
Wage = β₀ + β₁Education + ε
| VARIABLE | COEFFICIENT | STD. ERROR | STATUS |
|---|
SPECIFICATION AUDITThe education coefficient may absorb experience, geography, occupation and unobserved ability.
03 · SPECIFICATION DISCIPLINE
Controls require theory.
Not a fishing expedition.
Start from mechanism
Specify variables because the economic model requires them.
Avoid bad controls
Do not condition mechanically on variables caused by treatment.
Check collinearity
Highly related regressors inflate uncertainty and weaken interpretation.
Report alternatives
Show how key estimates behave across defensible specifications.
