This paper is organized as follows. In Section 2, we motivate and discuss the sequential testing approach. Section 3 discusses invariance principles of the past and present, and the CUSUM and fluctuation instability detectors. Section 4 contains some illustrative Monte Carlo experiments. A summary and concluding remarks are given in Section 5. Proofs are gathered into the Mathematical Appendix

The analysis of economic phenomena at the wholistic (aggregative) level 11l8intains a long tradition that assumes the neoclassical production function Q-f(K,L) (i.e., output as a function of capital and labor) satisfies the condition of constant returns to scale.The assumed absence of any (dis-)economies of scale renders the production function useless, when the scale effect is as pronounced as is typically found at the less aggregative levels of individual firm or industry analvsis.. .The purpose of this paper is to deduce new classes of production functions that are not limited to the constant returns to scale characteristic.Hore specifically, the scale effect is described by an arbitrary function of one of the factors of production, capital in this paper.This class of production functions exhibi-ts scale sensitivity with respect to capital (SSWK).The paper shows how different fmidlies of production functions can be derived from two basic .. building blocks," a :wage share function and a scale functitm.The Cobb-])ouglas, CES and VES production fmu:tions are special cases.~e Cobb-Douglas and CES functions can be expanded to incorporate non-constant returns to scale.A smnple of firms from Taiwan is used to test among various derived functional specifications.An interesting diversity of preferred specifications was found among three industries.

In this article we generalize Harvey's (1989) empirical specification of conditional asset pricing models to allow for both time‐varying covariances between stock returns and marketwide factors and time‐varying reward‐to‐covariabilities. The model is then applied to examine the effects of firm size and book‐to‐market equity ratios. We find that the traditional asset pricing model with commonly used factors can only explain a small portion of the stock returns predicted by firm size and book‐to‐market equity ratios. The results indicate that allowing time‐varying covariances and time‐varying reward‐to‐covariabilities does little to salvage the traditional asset pricing models.