Competitive Selection and Market Data: The Mixed-Index Problem
指出，当价格具有配置功能时，以价格为因变量的横截面回归可能存在“混合指数”偏差，这种偏差源于竞争性选择机制，而非经典联立性，并建立了分析框架来界定其发生条件。
If prices have an allocational role, then in addition to their economic signalling, they may act as a statistical signal for the existence of selection bias in cross-sectional studies with some form of price (wages, rental, yield etc.) as dependent variable. Elements of competitive selection appear in the pricing theory of real or financial assets and in the determination of wage rates, where prices correlate the characteristics of the asset or job with those of the individuals, under the equilibrium allocation. If prices achieve such an allocation, then regressions with price as dependent variable are prima facie "mixed-index" in character, with adverse bias or consistency properties, no matter that the right-hand regressors are apparently exogenous. We set up a paradigm for competitive selection and use the concepts so generated to codify the conditions under which mixed index bias will occur. The problem may be regarded as one of selection bias, but does not necessarily derive from classical simultaneity, and is a problem of data-generation structures rather than sample selection.