Redundancy of minimal weight expansions in Pisot bases

Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer $n$ as a sum $n=\sum_k \epsilon_k U_k$, where the digits $\epsilon_k$ are taken from a finite alphabet $\Sigma$ and $(U_k)_k$ is a linear recurrent sequence of Pisot type with $U_0=1$. The most prominent example of a base sequence $(U_k)_k$ is the sequence of Fibonacci numbers. We prove that the representations of minimal weight $\sum_k|\epsilon_k|$ are recognised by a finite automaton and obtain an asymptotic formula for the average number of representations of minimal weight. Furthermore, we relate the maximal order of magnitude of the number of representations of a given integer to the joint spectral radius of a certain set of matrices

Making Work Pay for the Elderly Unemployed: Evaluating Alternative Policy Reforms for Germany

We evaluate three policy reforms targeted at older unemployed people: (i) an hourly wage subsidy, (ii) an in-work credit, and (iii) a subsidy of social security contributions on low wages. The work incentive, labour supply and welfare effects of these hypothetical reforms are analysed on the basis of a detailed micro-simulation model for Germany which includes a structural household labour supply model. We find that the simulated labour supply effects of the three policy reforms would be rather similar and of moderate size, ranging between 20,000 and 30,000 older women and between 10,000 and 20,000 older men. Our results also suggest that the hourly wage subsidy yields the highest welfare gains.in-work support, wage subsidies, unemployment, elderly workers

Reforming Social Welfare as We Know It? A Microsimulation Study for Germany

Social assistance and unemployment assistance, which provide means tested income support (social welfare) without pre-specified time limits, are viewed as one important reason for the persistently high level of unemployment in Germany by many economists. In order to increase work incentives and, at the same time, reduce social expenditures there have been various proposals to reform social welfare in the recent German policy debate. We analyse a specific reform proposal with the following components: (i) an integration of unemployment assistance and social assistance; (ii) a substantial reduction of the social assistance level for ?employable? persons who choose not to work; (iii) improved incentives to take up work by a combination of a reduction of the social assistance withdrawal rate and an earnings-related tax credit. The expected employment and fiscal effects of this welfare reform proposal are simulated on the basis of an econometrically estimated partialequilibrium labour supply/demand model embedded in a detailed tax-benefit microsimulation model. We find that the reductions in net social expenditures may be substantial, although the expected labour supply and employment effects of this reform are much smaller than is typically assumed by contributors to recent discussions on the potential labour market effects of welfare reforms in Germany. Furthermore, these employment gains come at the cost of a substantial expansion of public-works jobs. --

Distributional and Fiscal Effects of the German Tax Reform 2000: A Behavioral Microsimulation Analysis

In the year 2000, the German government passed the most ambitious tax reform in postwar German history aiming at a significant tax relief for households. Drawing on data of the GSOEP, we analyze the distributional and fiscal effects of the tax reform. Our analysis employs microsimulation techniques. Furthermore, we estimate behavioral effects of the tax reform using a discrete choice labor supply model. We find that the tax reform leads to a significant increase of net household income. The relative gains increase with taxable income, thus income inequality is rising. We also find that behavioral effects reduce the revenue loss.Tax reform; Behavioral effects; Distribution and fiscal effects

A Large Deviation Approach to the Measurement of Mobility

We propose an approach to measure the mobility immanent in regular Markov processes. For this purpose, we distinguish between mobility in equilibrium and mobility associated with convergence towards equilibrium. The former aspect is measured as the expectation of a functional, defined on the Cartesian square product of the state space, with respect to the invariant distribution. Based on large deviations techniques, we show how the two aspects of mobility are related and how the second one can be characterized by a certain relative entropy. Finally, we show that some prominent mobility indices can be considered as special cases.mobility index; large deviations; relative entropy

Evaluating Theories of Income Dynamics: A Probabilistic Approach

The paper proposes an approach to evaluate hypotheses about transition dynamics when only the distributions at two points in time are observed. Using principles of statistical mechanics, we show how to adjust in the "most probable" way a hypothesis such that it becomes compatible with the observed distributions. This adjustment procedure also allows to test hypotheses in a statistical sense. The test is based on the relative entropy and is equivalent to a likelihood ratio test. We apply our approach to compare the dynamics of the income distribution between men and women in the U.S. using PSID data.income dynamics; large deviation; relative entropy; misspecification