Modeling Automation

Modeling automation as factor-augmenting technological change has unappealing implications. Instead, modeling it as the process of machines replacing tasks previously performed by labor is both descriptively realistic and leads to distinct and plausible predictions. In contrast to factor-augmenting technological change, the automation of tasks always reduces the labor share and can reduce the equilibrium wage (for realistic parameter values). This approach to automation underscores the role of new tasks, changes in the comparative advantage of labor, the possibility that machines become more productive in automated tasks, and the elasticity of substitution and capital accumulation in the adjustment of the economy.

A toy cosmological model with dynamical backreaction

In this paper, the Buchert averaging of the Dust Shell Universe is explicitly carried out. The dynamical backreaction does not vanish in such a model. Instead, it acts as the possible source of the negative deceleration. However, the parameters of the model allowing negative deceleration lead to mean overdensities with r200 > 10 h -1 Mpc and peculiar velocities as high as the fifth part of the speed of light. With more realistic parameter values the averaged model behavior is close to Friedmannian.

How Large are the Effects of Simultaneity on Testing Granger Causality?

SummaryInterpreting Granger causality as economic causality implies that the underlying VAR model is a structural economic model. This is wrong in the case of simultaneity, and causal conclusions can be misleading. Nevertheless, the empirical relevance of this problem still needs to be determined. Therefore, the magnitude and stability of possible errors are analysed in a simulation study. It is shown that economic misinterpretations of tests of Granger causality can occur with probability one for realistic parameter values. Thus, policy conclusions from Granger causality tests can be wrong with probability one if simultaneity occurs. Furthermore, the power of the test can be rather low even with a sample size of T = 50.

A mathematical model of the defence mechanism of a bombardier beetle

Previous studies of bombardier beetles have shown that some species have a continuous discharge while others exhibit a pulsed discharge. Here, a mathematical model of the defence mechanism of the bombardier beetle is developed and the hypothesis that almost all bombardiers' defences have some sort of cyclic behaviour at frequencies much higher than previously thought is put forward. The observation of pulses arises from secondary lower frequency cycles that appear for some parameter values. For realistic parameter values, the model can exhibit all the characteristics seen in the various species of bombardier. The possibility that all bombardiers have the same underlying defence mechanism gives weight to the theory that all bombardiers' explosive secretory mechanisms have diversified from a common ancestral mechanism.

SOME BIFURCATION DIAGRAMS FOR LIMIT CYCLES OF QUADRATIC DIFFERENTIAL SYSTEMS

Concrete numerical examples of quadratic differential systems having three limit cycles surrounding one singular point are shown. In case another finite singular point also exists, a (3, 1) distribution of limit cycles is also obtained. This is the highest number of limit cycles known to occur in a quadratic differential system so far. Representative bifurcation diagrams are drawn for realistic parameter values.