On Mitra's Sufficient Condition for Topological Chaos: Seventeen Years Later
This letter reports an easy extension of Mitra’s “easily verifiable” sufficient condition for topological chaos in unimodal maps, and offers its application to reduced-form representations of two economic models that have figured prominently in the recent literature in economic dynamics: the check- and the M-map pertaining to the 2-sector Robinson–Solow–Srinivasan (RSS) and Matsuyama models respectively. A consideration of the iterates of these maps establishes the complementarity of the useful 2001 condition with the 1982 (LMPY) theorem of Li–Misiurewicz–Pianigiani–Yorke when supplemented by a geometric construction elaborated in Khan–Piazza (2011).
On Growing through Cycles: Matsuyama's M-map and Li-Yorke Chaos
Journal of Mathematical Economics,
Recent work of Gardini et al. (2008), building on earlier work of Mitra (2001) and Mukherji (2005), considers the so-called M-map that generates a dynamical system underlying Matsuyama’s (1999) endogenous growth model. We offer proofs of the fact that there do not exist 3- or 5-period cycles in the M-map, and an example (a numerical proof) of the existence of a 7-period cycle. We use the latter, and a construction in Khan and Piazza (2011), to identify a range of parameter values of the M-map that guarantee the existence of cycles of all periods, except 3 and 5. Our argumentation relies on, and reports, the first four iterations of the M-map that may have independent interest.
Evaluation von Maßnahmen der aktiven Arbeitsmarktpolitik mit Hilfe eines iterativen Matching-Algorithmus - Eine Fallstudie über langzeitarbeitslose Maßnahmeteilnehmer in Sachsen
IWH Discussion Papers,
The paper evaluates the effects of two labor market programs in Germany, namely the Job Creation- /Structural Adjustment Scheme and Vocational Training, on the unemployment duration of long term unemployed persons. The study uses data from the Mikrozensus Sachsen. A two step Nearest-Neighbor-Matching is employed to solve the sample selection problem. The first step is the estimation of the participation tendency to obtain potential pairs and to compute their Mahalanobis distances. For the assignment of pairs in the second step two different procedures are used: a standard technique and a new one - the iterative improvement of an initial assignment. This process is superior to the standard matching algorithms in the sense that it allows for a closer match between participants and non-participants. Including additional information about a person’s employment history enables us to eliminate the bias due to unobservables. The impact of participation in a labor market program is evaluated by comparing the unemployment duration between both groups using the Cox Proportional Hazard Model. Overall we find empirical evidence that both participation in Job Creation- /Structural Adjustment Scheme and Vocational Training result in even longer unemployment.