Simple random sampling has been assumed in most statistical inference procedures developed to test Lorenz dominance and other partial ordering conditions. This note, using the Bahadur representation, derives the (asymptotic) covariance structures of the Lorenz and generalized Lorenz ordinates for stratified, cluster and multistage samples. The comparison of these covariance structures illustrates the necessity of taking the sampling method into account in inference testing.
We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency–domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non–normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss–Markov efficient with standard convergence rate. Despite the anomalous behavior of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency–domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included.
Models of utility in stochastic continuous–time settings typically assume that beliefs are represented by a probability measure, hence ruling out a priori any concern with ambiguity. This paper formulates a continuous–time intertemporal version of multiple–priors utility, where aversion to ambiguity is admissible. In a representative agent asset market setting, the model delivers restrictions on excess returns that admit interpretations reflecting a premium for risk and a separate premium for ambiguity.
This paper studies the effects of progressive income taxes and education finance in a dynamic heterogeneous-agent economy. Such redistributive policies entail distortions to labor supply and savings, but also serve as partial substitutes for missing credit and insurance markets. The resulting tradeoffs for growth and efficiency are explored, both theoretically and quantitatively, in a model that yields complete analytical solutions. Progressive education finance always leads to higher income growth than taxes and transfers, but at the cost of lower insurance. Overall efficiency is assessed using a new measure that properly reflects aggregate resources and idiosyncratic risks but, unlike a standard social welfare function, does not reward equality per se. Simulations using empirical parameter estimates show that the efficiency costs and benefits of redistribution are generally of the same order of magnitude, resulting in plausible values for the optimal rates. Aggregate income and aggregate welfare provide only crude lower and upper bounds around the true efficiency tradeoff.
This paper proposes new estimators of the latent regression function in nonparametric censored and truncated regression models. Our estimators are computationally convenient, consisting only of two nonparametric regressions and a univariate integral. We establish consistency and asymptotic normality for an implementation based on local linear kernel estimators. An extension permits estimation in the presence of a general form of heteroscedasticity.
We study the problem of identi cation of the long regression E(y j x � z) when the short conditional distributions P (y j x) and P (z j x) are known but the long conditional distribution P (y j x � z) is not known. This problem often arises when a researcher utilizes data from two separate data sets. (A leading example is the ecological inference problem of political science, where voting behavior across electoral districts is observed from administrative records, the demographic composition of voters within a district is observed from census data, and the researcher wants to infer voting behavior conditional on district and demographic attributes.) We isolate an identi cation region containing feasible values of the long regression, and show that this region forms a sharp bound on the long regression. The identi cation region can be calculated precisely when y has nite support. When y has in nite support we characterize two sets, one that contains the identi cation region, and one that is contained by it. Following this completely nonparametric analysis, we examine the identifying power yielded by exclusion restrictions across distinct covariate values. Such restrictions cause the identi cation region to shrink, in many cases to a single point. To illustrate the theory, we pose and address this hypothetical question: What would be the outcome if the 1996 U.S. presidential election were re-enacted in a population of di erent demographic composition, ceteris paribus? We have bene tted from the opportunity to present this research in seminars at Northwestern
In previous work on cheap talk, uncertainty has almost always been modeled using a single–dimensional state variable. In this paper we prove that the dimensionality of the uncertain variable has an important qualitative impact on results and yields interesting insights into the “mechanics” of information transmission. Contrary to the unidimensional case, if there is more than one sender, full revelation of information in all states of nature is generically possible, even when the conflict of interest is arbitrarily large. What really matters in transmission of information is the local behavior of senders’ indifference curves at the ideal point of the receiver, not the proximity of players’ ideal point.
We present an axiomatic model depicting the choice behavior of a self-interest seeking moral individual over random allocation procedures. Individual preferences are decomposed into a self-interest component and a component representing the individual's moral value judgment. Each component has a distinct utility representation, and the preference relation depicting the choice behavior is representable by a real-valued function defined on the components utilities. The utility representing the self-interest component is linear and the utility representing the individual's moral value judgment is quasi-concave. The addition of a hexagon condition implies that the utility representing the individual's preference is additively separable in the components utilities.