Omitted Variable Bias

Omitted variable bias arises when a variable that affects price is excluded from a model and has a nonzero coefficient on an included regressor in the auxiliary regression --- partial, not merely marginal, correlation; the included regressor's coefficient then absorbs part of the omitted effect. Both conditions are necessary, and the widely held belief that any important missing variable biases a model is false as stated: an omitted variable uncorrelated with the regressors costs precision, not accuracy. This entry develops Theil's formula for the bias and verifies it exactly against a sixteen-property extension of the Pacifica dataset in which the renovation flag, disclosed in issue 1 but not recorded there, is now measured. Omitting it inflates the condition coefficient from $40,000 to $69,631 per step and deflates the view coefficient from $100,000 to $79,178 --- shifts that equal the product of the omitted coefficient and the auxiliary regression slopes to the cent. The example is used to make three defensibility points: the bias is invisible in fit statistics, with an R-squared of 0.97 concealing a coefficient off by 74 percent; it does not diminish with sample size; and a biased model can predict accurately while yielding adjustments that are unusable, failing hardest on precisely the atypical properties an appraiser is most often retained to value.