Omitted-variable bias

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Omitted-variable bias (OVB) is the bias that appears in estimates of parameters in a regression analysis when the assumed specification is incorrect, in that it omits an independent variable that should be in the model.

Omitted-variable bias in linear regression

Two conditions must hold true for omitted variable bias to exist in linear regression:

  • the omitted variable must be a determinant of the dependent variable (i.e., its true regression coefficient is not zero); and
  • the omitted variable must be correlated with one or more of the included independent variables.

Omitted variable bias is a type of least squares bias. Although an incomplete predictive equation (i.e., an equation without one or more relevant variables) does not necessarily have an increased least squares bias, more often this bias is increased. In a linear least squares regression, omitted-variable bias can affect the slope and/or the intercept estimates.

Omitted variables can also cause an ineffectual use of the multiple linear regression technique. This occurs when a multiple linear regression study concludes that A predicts C, but there exists another variable, B, that was not included in the study, and B also predicts C; and also, if this omitted variable had been included, one would have discovered that and A and B together are a stronger predictor of C than A or B alone.

References

  • Greene, WH (1993). Econometric Analysis, 2nd ed. Macmillan. pp. 245–246.

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