Of the Impossibility to Estimate the Marginal Propensity to Consume Because the Aggregate Consumption Function Is an Accounting Semi Identity

The coefficients of a model estimated with a linear regression fail to represent a causal relation when this model is part of an accounting (semi) identity, because the coefficient is constrained to fulfill this identity. The aggregate consumption function suffers from this problem and its estimated coefficient does not serve to infer a causal relation, as it depends on the value of the rest of the accounting identity. This problem sheds light to some of the unexpected results obtained throughout the last decades