Endogenous Separations, Wage Rigidities, and Unemployment Volatility

We show that in microdata, as well as in a search and matching model with flexible wages for new hires, wage rigidities of incumbent workers have substantial effects on separations and unemployment volatility. Allowing for an empirically relevant degree of wage rigidities for incumbent workers drives unemployment volatility as well as the volatility of vacancies and tightness to that in the data. Thus, the degree of wage rigidity for newly hired workers is not a sufficient statistic for determining the effect of wage rigidities on macroeconomic outcomes. This finding affects the interpretation of a large empirical literature on wage rigidities. (JEL E24, J23, J31, J41, J63)

Indirect NRDF for Partially Observable Gauss-Markov Processes with MSE Distortion: Complete Characterizations and Optimal Solutions

In this paper we study the problem of characterizing and computing the nonanticipative rate distortion function (NRDF) for partially observable multivariate Gauss-Markov processes with hard mean squared error (MSE) distortion constraints. For the finite time horizon case, we first derive the complete characterization of this problem and its corresponding optimal realization which is shown to be a linear functional of the current time sufficient statistic of the past and current observations signals. We show that when the problem is strictly feasible, it can be computed via semidefinite programming (SDP) algorithm. For time-varying scalar processes with average total MSE distortion we derive an optimal closed form expression by means of a dynamic reverse-waterfilling solution that we also implement via an iterative scheme that convergences linearly in finite time, and a closed-form solution under pointwise MSE distortion constraint. For the infinite time horizon, we give necessary and sufficient conditions to sure that asymptotically the sufficient statistic process of the observation signals achieves a steady-state solution for the corresponding covariance matrices and impose conditions that allow existence of a time-invariant solution. Then, we show that when a finite solution exists in the asymptotic limit, it can be computed via SDP algorithm. We also give strong structural properties on the characterization of the problem in the asymptotic limit that allow for an optimal solution via a reverse-waterfilling algorithm that we implement via an iterative scheme that converges linearly under a finite number of spatial components. Subsequently, we compare the computational time needed to execute for both SDP and reverse-waterfilling algorithms when these solve the same problem to show that the latter is a scalable optimization technique. Our results are corroborated with various simulation studies and are also compared with existing results in the literature.

Sufficient statistics for the Pareto distribution parameter

The task of estimating the parameters of the Pareto distribution, first of all, of an indicator of this distribution for a given sample, is relevant. This article establishes that for this estimate, it is sufficient to know the product of the sample elements. It is proved that this product is a sufficient statistic for the Pareto distribution parameter. On the basis of the maximum likelihood method the distribution degree indicator is estimated. It is proved that this estimate is biased, and a formula eliminating the bias is justified. For the product of the sample elements considered as a random variable the distribution function and probability density are found; mathematical expectation, higher moments, and differential entropy are calculated. The corresponding graphs are built. In addition, it is noted that any function of this product is a sufficient statistic, in particular, the geometric mean. For the geometric mean also considered as a random variable, the distribution function, probability density, and the mathematical expectation are found; the higher moments, and the differential entropy are also calculated, and the corresponding graphs are plotted. In addition, it is proved that the geometric mean of the sample is a more convenient sufficient statistic from a practical point of view than the product of the sample elements. Also, on the basis of the Rao–Blackwell–Kolmogorov theorem, effective estimates of the Pareto distribution parameter are constructed. In conclusion, as an example, the technique developed here is applied to the exponential distribution. In this case, both the sum and the arithmetic mean of the sample can be used as sufficient statistics.

A Sufficient Statistic for Influence in Structured Multiagent Environments

Making decisions in complex environments is a key challenge in artificial intelligence (AI). Situations involving multiple decision makers are particularly complex, leading to computational intractability of principled solution methods. A body of work in AI has tried to mitigate this problem by trying to distill interaction to its essence: how does the policy of one agent influence another agent? If we can find more compact representations of such influence, this can help us deal with the complexity, for instance by searching the space of influences rather than the space of policies. However, so far these notions of influence have been restricted in their applicability to special cases of interaction. In this paper we formalize influence-based abstraction (IBA), which facilitates the elimination of latent state factors without any loss in value, for a very general class of problems described as factored partially observable stochastic games (fPOSGs). On the one hand, this generalizes existing descriptions of influence, and thus can serve as the foundation for improvements in scalability and other insights in decision making in complex multiagent settings. On the other hand, since the presence of other agents can be seen as a generalization of single agent settings, our formulation of IBA also provides a sufficient statistic for decision making under abstraction for a single agent. We also give a detailed discussion of the relations to such previous works, identifying new insights and interpretations of these approaches. In these ways, this paper deepens our understanding of abstraction in a wide range of sequential decision making settings, providing the basis for new approaches and algorithms for a large class of problems.