P. K. Trivedi, B. M. S. Lee; Seasonal Variability in a Distributed Lag Model, The Review of Economic Studies, Volume 48, Issue 3, 1 July 1981, Pages 497–505, ht

THE RESEARCH on the economic theory of the cost-of-living index has not paid much attention to the proposals made by Frisch and Wald in the thirties. In Frisch [3,4] the was developed and tested on certain examples. Wald [8] succeeded in deriving a new for the index of cost of living in an article containing a curious editorial footnote by Frisch on the comparative advantages of both methods. Banerjee [1] presented a simplification of the derivation of Wald's new formula. In an article commemorating Frisch, Samuelson [7] asked for a study of the relative merits of Frisch's and Wald's proposals to which he added a variant of his own. Recently Banerjee [2] succeeded in showing that Wald's new formula is the true cost-of-living index for a general quadratic utility function. In this paper I give an alternative, mathematically equivalent but economically more meaningful, derivation which highlights the resemblance of Wald's index to the true cost-of-living index corresponding to the familiar Klein-Rubin-Stone-Geary utility function (Section 2). This derivation provides a convenient framework for discussing Frisch's double-expenditure method (Section 3) and Samuelson's proposal (Section 4) and for assessing the relative merits of them. I hope this note is a (partial) answer to Samuelson's question.

We consider economies with preferences drawn from a very general class of strongly convex preferences, closely related to the class of convex (but intransitive and incomplete) preferences for which Mas-Colell proved the existence of competitive equilibria [13]. We prove a strong core limit theorem for sequences of such economies with a mild assumption on endowments (the largest endowment is small compared to the total endowment) and a uniform convexity condition. The results extend corresponding results in Hildenbrand's book [8]. The proof, which is based on our earlier result for economies with more general preferences [2], is elementary.

One of the perennial problems of business cyde theory has been the search for a convincing empirical description and theoretical explanation of the behaviour of wage rates during fluctuations in output and employment. Even the empirical question is hardly settled, although the most recent careful study (Geary and Kennan) confirms the prevailing view that real-wage movements are more or less independent of the business cycle. There are really two subquestions here. The first presumes that nominal wage stickiness is the main route by which nominal disturbances have real macroeconomic effects, and asks why nominal wages should be sticky. The second focuses on real wages, and asks why fluctuations in the demand for labour should so often lead to large changes in employment and small, unsystematic, changes in the real wage.