In a number of econometric models, rules of large-sample inference require a consistent estimate of f(O), where f(A) is the spectral density matrix of Y, = U 0 xt, for covariance stationary vectors it, xt. Typically y, is allowed to have nonparametric autocorrelation, and smoothing is used in the estimation of f(O). We give conditions under which f(O) can be consistently estimated without smoothing. The conditions are relevant to inference on slope parameters in models with an intercept and strictly exogenous regressors, and allow regressors and disturbances to collectively have considerable stationary long memory and to satisfy only mild, in some cases minimal, moment conditions. The estimate of f(O) dominates smoothed ones in the sense that it can have mean squared error of order n -1, where n is sample size. Under standard additional regularity conditions, we extend the estimate of f(O) to studentize asymptotically normal estimates of structural parameters in linear simultaneous equations systems. A small Monte Carlo study of finite sample behavior is included.

The neoclassical theory of demand applies to individuals, yet in empirical work it is usually taken as valid for households with many members. This paper explores what the theory of individuals implies for households that have more than one member. We make minimal assumptions about how the individual members of the household resolve conflicts. All we assume is that however decisions are made, outcomes are efficient. We refer to this as the collective setting. We show that in the collective setting household demands must satisfy a symmetry and rank condition on the Slutsky matrix. We also present some further results on the effects on demands of variables that do not modify preferences but that do affect how decisions are made. We apply our theory to a series of surveys of household expenditures from Canada. The tests of the usual symmetry conditions are rejected for two-person households but not for one-person households. We also show that income pooling is rejected for two-person households. We then test for our collective setting conditions on the couples data. None of the collective setting restrictions are rejected. We conclude that the collective setting is a plausible and tractable next step to take in the analysis of household behavior.