On the Rental Price of Capital and the Profit Rate: The Perils and Pitfalls of Total Factor Productivity Growth

This paper considers the implications of the conceptual difference between the rental price of capital, embedded in the neoclassical cost identity (output equals the cost of labor plus the cost of capital), which is used in growth accounting studies; and the accounting profit rate, which can be derived from the National Income and Product Accounts (NIPA). The neoclassical identity is a 'virtual' identity in that it depends on a series of assumptions (constant returns to scale and perfectly competitive factor markets). The income side of the NIPA also provides an accounting identity for output as the sum of the wage bill plus the gross operating surplus. This identity, however, is a 'real' one, in the sense that it does not depend on any assumption and thus it always holds. It is shown that because the neoclassical cost identity and the income accounting identity according to the NIPA may be expressed as formally equivalent expressions, estimations of aggregate production functions and growth accounting studies are tautologies. Likewise, the test of the hypothesis of competitive markets using Hall's (1988) framework gives rise to a null hypothesis that cannot be rejected statistically. Finally, it is argued that the NIPA identity does hold in constant prices, pace Denison (1972a, 1972b).