Knowledge that Transforms

The paper by Kiefer, Vogelsang and Bunzel (2000), KVB henceforth, provides an interesting unconventional application of functional limit theory to a conventional problem. In this note, we point out that the limiting distribution of the t^{∗} test proposed by KVB turns out to be equivalent to the asymptotic distribution of one of the statistics analysed by Abadir and Paruolo (1997), AP henceforth. The mixed-Normal random variables studied in AP and KVB are different, but they have identical distributions. The purpose of this note is to prove this equivalence analytically.

Choice models with nonlinear budget sets provide a precise way of accounting for the nonlinear tax structures present in many applications. In this paper we propose a nonparametric approach to estimation of these models. The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set. Then we can do nonparametric regression where the variable in the regression is the budget set. We reduce the dimensionality of this problem by exploiting structure implied by utility maximization with piecewise linear convex budget sets. This structure leads to estimators where the number of segments can differ across observations and does not affect accuracy. We give consistency and asymptotic normality results for these estimators. The usefulness of the estimator is demonstrated in an empirical example, where we find it has a large impact on estimated effects of the Swedish tax reform.

We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log–likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The statistic has a χ2 limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting distribution does not depend on nuisance parameters. The statistic overcomes the deficiencies of the Anderson–Rubin statistic, whose limiting distribution has a degrees of freedom parameter equal to the number of instruments, and the likelihood based, Wald, likelihood ratio, and Lagrange multiplier statistics, whose limiting distributions depend on nuisance parameters. Size and power comparisons reveal that the statistic is a (asymptotic) size–corrected likelihood ratio statistic. We apply the statistic to the Angrist–Krueger (1991) data and find similar results as in Staiger and Stock (1997).

With the cointegration formulation of economic long–run relations the test for cointegrating rank has become a useful econometric tool. The limit distribution of the test is often a poor approximation to the finite sample distribution and it is therefore relevant to derive an approximation to the expectation of the likelihood ratio test for cointegration in the vector autoregressive model in order to improve the finite sample properties. The correction factor depends on moments of functions of the random walk, which are tabulated by simulation, and functions of the parameters, which are estimated. From this approximation we propose a correction factor with the purpose of improving the small sample performance of the test. The correction is found explicitly in a number of simple models and its usefulness is illustrated by some simulation experiments.

The presence of obstinate types in bargaining has been shown to alter dramatically the bargaining equilibrium strategies and outcomes. This paper shows that outside options may cancel out the effect of obstinacy in bargaining. When parties have access to stationary outside options, we show that when opting out is preferable to accepting the inflexible demand of the other party, there is a unique Perfect Bayesian Equilibrium in which each party reveals himself as rational as soon as possible. A similar conclusion holds when outside options may only be available at a later date or when only one party has access to an outside option.

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.