Constant-Utility Index Numbers of Real Wages: Comment
Paul Samuelson and Subramanian Swamy in their survey of index-number theory in this Review emphasized that The fundamental point about an economic quantity index, which is too little stressed by writers, Leontief and Afriat being exceptions, is that it must itself be a cardinal indicator of ordinal (p. 568). In a later article in this Review John Pencavel has endeavored to compute real wage indices in this sense. He interprets each of his indices as an of the individual's welfare (p. 93). His two series of real wages are derived from an estimated indirect Stone-Geary utility function which incorporates nonlabor income of the wage earners and an endogenous work-leisure choice. In one series the increase in real wages over the period 1934-67 was substantially less than the index of money wages deflated by the Consumer Price Index or the Bureau of Labor Statistics series of real spendable weekly earnings of production workers, whereas in the second series the increase was substantially greater than in these other series over the same period. He has also constructed an index of real nonlabor income. My contention is that none of these indices is a true quantity index, but a genuine true quantity index can be obtained from the indirect utility function by using a slightly different definition of income. Moreover, this can be done for any regular utility function. For a family of functions which includes the Stone-Geary, this index is equal to an index of deflated incomes and is the canonical dual of the true price index. For any utility function one can obtain a quantity index of real income across incomeprice situations directly and simply by taking the ratio of the indirect utility function in period t to that at the situation in a base period 0. That is,