Omitting relevant variables in an econometric model can have several theoretical consequences, including:
Bias in parameter estimates: When relevant variables are omitted from a model, the estimated coefficients of the remaining variables may be biased. This happens because the omitted variable(s) can influence the relationship between the dependent variable and the included independent variables. In other words, the estimated coefficients of the included variables do not capture the full effect of the omitted variable(s) on the dependent variable, leading to biased estimates.
Inefficiency in estimation: Omitting relevant variables can also lead to inefficient estimates of the remaining coefficients. This is because the omitted variable(s) contain information about the relationship between the dependent variable and the included independent variables. If this information is not included in the model, the estimator may not be able to use all the available information to estimate the coefficients of the included variables.
Misspecification of the model: Omitting relevant variables can result in a misspecified model. A misspecified model is one that does not accurately capture the underlying relationship between the dependent variable and the independent variables. This can lead to incorrect inferences about the relationship between the variables and can also affect the accuracy of predictions made using the model.
Increased variance of errors: Omitting relevant variables can increase the variance of the error term in the model. This happens because the omitted variable(s) contain information that can explain some of the variation in the dependent variable that is not accounted for by the included independent variables. As a result, the error term may be larger than it would be if all relevant variables were included in the model.
Poor policy decisions: Finally, omitting relevant variables can lead to poor policy decisions. If the model does not accurately capture the relationship between the variables, policymakers may make decisions based on incorrect information. This can lead to suboptimal outcomes and wasted resources.