Except in special cases, market work and household membership are jointly chosen. A Nash bargaining model of family behavior is used to specify stochastic structural relationships (two indirect utility functions and a market and a reservation wage function) that jointly determine work, consumption, and household membership. The maximum likelihood estimates of the implied trinomial probit model differ sharply from those obtained when either market work or household membership is taken as exogenous. This application to white male youths from the National Longitudinal Surveys shows the insurance function of families: parents insure their sons against poor market opportunities.

Many empirical studies of production specify a deterministic model of the firm, derive the implied behavioral equat ions (input demand or share system), and then "embed this system in a stochastic framework" by tacking on linear error terms. In contras t, this paper proposes general error models (GEMs) in which the error specification is an integral part of the optimization model. These m odels are the statistical embodiment of Stigler's view that apparent observed inefficiencies reflect the investigator's ignorance of the t rue optimization problems. Additive GEMs are proposed and interpreted Specification tests indicate that a translog additive GEM is superi or to the standard translog specification.

The APT is represented as a multivariate regression model with across-equations restrictions. Both observed and unobserved (latent) macroeconomic factors are included, thus generalizing and unifying two previous strands of literature. Large portfolios representing unobserved factors are treated as endogenous, and nonlinear 3SLS estimates are shown to differ sharply from estimates that ignore this endogeneity. Using monthly stock returns and six factors, we cannot reject January effects. The following results are invariant with respect to the inclusion of January effects: we reject the CAPM in favor of the APT; however, we cannot reject the APT restrictions on the linear factor model.

The APT is represented as a multivariate regression model with across‐equations restrictions. Both observed and unobserved (latent) macroeconomic factors are included, thus generalizing and unifying two previous strands of literature. Large portfolios representing unobserved factors are treated as endogenous, and nonlinear 3SLS estimates are shown to differ sharply from estimates that ignore this endogeneity. Using monthly stock returns and six factors, we cannot reject January effects. The following results are invariant with respect to the inclusion of January effects: we reject the CAPM in favor of the APT; however, we cannot reject the APT restrictions on the linear factor model.