Limit Distribution of Evolving Strategies in Financial Markets

In this paper we model a financial market composed of agents with heterogeneous beliefs who change their strategy over time. We propose two different solution methods which lead to two different types of endogenous dynamics. The first makes use of the maximum entropy approach to obtain an exponential type probability function for strategies, analogous to the well known Brock and Hommes (1997) model, but with the endogenous specification for the intensity of choice parameter, which varies over time as a consequence of the relative performances of each strategy. The second type of dynamics is obtained by setting up a master equation and solving it using recently developed asymptotic solution techniques, which yield a system of differential equations describing the evolution of the share of each strategy in the market. The performance sof the two solutions are then compared and contrasted with the empirical evidence.

Power Law Scaling in the World Income Distribution

We show that over the period 1960-1997, the range comprised between the 30th and the 85th percentiles of the world income distribution expressed in terms of GDP per capita invariably scales down as a Pareto distribution. Furthermore, the time path of the power law exponent displays a negatively sloped trend. Our findings suggest that the cross-country average growth process appears to be scale invariant but for countries in the tails of the world income distribution, and that the relative volatility of smaller countries' growth processes have increased over time.Growth

Uncertainty, rationality and complexity in a multi-sectoral dynamic model: The dynamic stochastic generalized aggregation approach

The paper proposes an innovative approach for the analytical solution of agent-based models. The approach is termed dynamic stochastic generalized aggregation (DSGA) and is tested on a macroeconomic model articulated in a job and in a goods markets with a large number of heterogeneous and interacting agents (namely firms and workers). The agents heuristically adapt their expectations by interpreting the signals from the market and give rise to macroeconomic regularities. The model is analytically solved in two different scenarios. In the first, the emergent properties of the system are determined uniquely by the myopic behavior of the agents while, in the second, a social planner quantifies the optimal number of agents adopting a particular strategy. The integration of the DSGA approach with intertemporal optimal control allows the identification of multiple equilibria and their qualitative classification

On the mean/variance relationship of the firm size distribution: evidence and some theory

In this paper we make use of firm-level data for a sample of European countries to prove the existence of a positive linear relationship between the mean and the variance of firms’ size, an empirical regularity known in mathematical biology as the Taylor power law. A computerized experiment is used to show that the estimated slope of the linear relationship can be fruitfully employed to discriminate among alternative theories of firms’ growth.Taylor power law; Firm size distribution; Stochastic growth

The effectiveness of Non-Pharmaceutical Interventions in reducing the COVID-19 contagion in the UK, an observational and modelling study

Epidemiological models used to inform government policies aimed to reduce the contagion of COVID-19, assume that the reproduction rate is reduced through Non-Pharmaceutical Interven-tions (NPIs) leading to physical distancing. Available data in the UK show an increase in physical distancing before the NPIs were implemented and a fall soon after implementation. We aimed to estimate the effect of people’s behaviour on the epidemic curve and the effect of NPIs taking into account this behavioural component. We have estimated the effects of confirmed daily cases on physical distancing and we used this insight to design a behavioural SEIR model (BeSEIR), simu-lated different scenaria regarding NPIs and compared the results to the standard SEIR. Taking into account behavioural insights improves the description of the contagion dynamics of the epi-demic significantly. The BeSEIR predictions regarding the number of infections without NPIs were several orders of magnitude less than the SEIR. However, the BeSEIR prediction showed that early measures would still have an important influence in the reduction of infections. The BeSEIR model shows that even with no intervention the percentage of the cumulative infections within a year will not be enough for the epidemic to resolve due to a herd immunity effect. On the other hand, a standard SEIR model significantly overestimates the effectiveness of measures. Without taking into account the behavioural component, the epidemic is predicted to be resolved much sooner than when taking it into account and the effectiveness of measures are significantly overestimated

Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms

By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto-Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically