Aggregate Production Functions Are a Pervasive, But Unpersuasive, Fairytale

 Briefly, an examination of the conditions required for aggregation yields results such as:

• Except under constant returns, aggregate production functions are unlikely to exist at all.
• Even under constant returns, the conditions for aggregation are so very stringent as to make the existence of aggregate production functions in real economies a non-event. This is true not only for the existence of an aggregate capital stock but also for the existence of such constructs as aggregate labor or even aggregate output.
• One cannot escape the force of these results by arguing that aggregate production functions are only approximations. While, over some restricted range of the data, approximations may appear to fit, good approximations to the true underlying technical relations require close approximation to the stringent aggregation conditions, and this is not a sensible thing to suppose. . . .

All these facts should be well known. They are not, or, if they are, their implications are simply ignored by macroeconomists who go on treating the aggregate production function as the most fundamental construct of neoclassical macroeconomics. Yet the implications of the points I have listed are not merely theoretical. As this symposium’s papers show, they include:

• The specification and estimation of the aggregate demand curve for labor;
• The measurement of productivity and, especially, the interpretation (or, perhaps more properly, the misinterpretation) of the Solow residual; and
• The use of aggregate production functions to validate the neoclassical theory of distribution.

—Franklin M. Fisher, “Aggregate Production Functions: A Pervasive, But Unpersuasive, Fairytale,” Eastern Economic Journal 31, no. 3 (Winter 2005): 489-490.