Optimal Taxation with Risky Human Capital

We study optimal tax policies in a life-cycle economy with permanent ability differences and risky human capital investments that have both an unobservable component, learning effort, and an observable component, schooling. The optimal policies balance redistribution across agents, insurance against human capital shocks, and incentives to learn and work. In the optimum, (i ) high-ability agents face risky consumption while low-ability agents are insured; (ii ) the optimal schooling subsidy is substantial but less than 100 percent; (iii) if utility is separable in labor and learning effort, the inverse labor wedge follows a random walk; and (iv ) if the utility is not separable then the “no distortion at the top” result does not apply. The welfare gains from switching to the optimal tax system are about 1 percent in annual consumption equivalents. (JEL D15, H21, H24, I26, J24)

Non-Parametric Signal Interpolation

This paper considers the problem of interpolation (smoothing) of a partially observable Markov random sequence. For the dynamic observation models, an equation for the interpolation of the posterior probability density is derived. The main goal of this paper is to consider the smoothing problem for the case of unknown distributions of an unobservable component of a random Markov sequence. Successful results were obtained for the strongly stationary Markov processes with mixing and for the conditional density belonging to the exponential family of densities. The resulting method is based on the empirical Bayes approach and kernel nonparametric estimation. The equation for the optimal smoothing estimator is derived in the form independent of unknown distributions of an unobservable process. Such form of the equation allows to use the nonparametric estimates for some conditional functionals in the equation given a set of dependent observations. To compare the nonparametric estimators with optimal mean square smoothing estimators in Kalman scheme, simulation results are given.

Seasonality As An Unobservable Component In South African Agricultural Market Data

The shortcoming of most of the tests for seasonal patterns is that the problem under investigation is formulated in a stringent manner, leading to a test of the null hypothesis of no seasonality against the alternative of deterministic seasonality. These tests would typically involve using models that incorporate deterministic dummy variables that are then used to capture seasonal effects in the data by means of a regression. This implies that the possibility of stochastic seasonality, which is manifested by changing seasonal factors over the sample period (deterministic seasonality implies constant seasonal factors), is ignored. A possible more comprehensive/rigorous approach would thus be to test for the presence of stochastic seasonality versus deterministic seasonality. The aim of this paper is to investigate the possible presence of unobserved seasonal components in South African agricultural market data, with the emphasis to demonstrate the additional insight such an approach can provide to researchers and especially for pairs traders

Anchoring Effects: Evidence from Art Auctions

This paper shows that the price of a painting sold at an art auction and the experts' pre-sale valuations are anchored on the price at which the painting previously sold at auction. We are able to separate anchoring from rational learning by using the identifying strategy that the unobservable component of quality for a particular painting remains constant between the last auction sale and the current auction sale. We interpret these results as anchoring on the part of the buyers, with the sellers and auctioneers either anticipating anchoring on the part of the buyers or exhibiting anchoring effects themselves. (JEL D44, Z11)

ERGODICITY, MIXING, AND EXISTENCE OF MOMENTS OF A CLASS OF MARKOV MODELS WITH APPLICATIONS TO GARCH AND ACD MODELS

This paper studies a class of Markov models that consist of two components. Typically, one of the components is observable and the other is unobservable or “hidden.” Conditions under which geometric ergodicity of the unobservable component is inherited by the joint process formed of the two components are given. This implies existence of initial values such that the joint process is strictly stationary and β-mixing. In addition to this, conditions for the existence of moments are also obtained, and extensions to the case of nonstationary initial values are provided. All these results are applied to a general model that includes as special cases various first-order generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive conditional duration (ACD) models with possibly complicated nonlinear structures. The results only require mild moment assumptions and in some cases provide necessary and sufficient conditions for geometric ergodicity.