Publications

Summary

One of the most famous ranking methods for digraphs is the ranking by Copeland score. The Copeland score of a node in a digraph is the difference between its outdegree (i.e. its number of outgoing arcs) and its indegree (i.e. its number of ingoing arcs). In the ranking by Copeland score, a node is ranked higher, the higher is its Copeland score. In this paper, we deal with an alternative method to rank nodes according to their out- and indegree, namely ranking the nodes according to their degree ratio, i.e. the outdegree divided by the indegree. To avoid dividing by zero, we add 1 to both the out- as well as indegree of every node. We provide an axiomatization of the ranking by degree ratio using a clone property, which says that the entrance of a clone or a copy (i.e. a node that is in some sense similar to the original node) does not change the ranking among the original nodes. We also provide a new axiomatization of the ranking by Copeland score using the same axioms except that this method satisfies a different clone property. Finally, we modify the ranking by degree ratio by taking only the out- and indegree, but by definition assume nodes with indegree zero to be ranked higher than nodes with positive indegree. We provide an axiomatization of this ranking method using yet another clone property and a maximal property. In this way, we can compare the three ranking methods by their clone property.

Summary

The speed and extent of diffusion of behaviors in social networks depends on network structure and individual preferences. The contribution of the present study is twofold. First, we introduce weighted interactions between potential adopters that depend on the similarity in their preferences and moderate the strength of social reinforcement. The reason for the extension is the existence of a confirmation bias in the way agents treat information by prioritizing evidence conforming to their opinion. As a result, individuals become less likely to be influenced by peers with relatively different preferences, reducing the overall diffusion rate under clustered networks. Second, we enrich our analysis by also considering a scale free network topology with a high degree asymmetry, motivated by its pervasiveness in online social networks. This network performs consistently well in terms of diffusion for different parameter combinations and clearly outperforms clustered networks under weighted interactions. Our results show that more realistic assumptions regarding agents' interactions shift the focus from clustering to degree distribution in the study of network structures allowing for fast and widespread behavior adoption.

Summary

State-dependent regime switching diffusion processes or hybrid switching diffusion (HSD) processes are hard to simulate with classical methods which leads us to adopt a Markov chain Monte Carlo (MCMC) Bayesian approach very convenient to estimate complicated models such as the HSD one. In the HSD, the diffusion component is dependent on the switching discrete hidden regimes and the transition rates of the regime switching are dependent on the diffusion observations. Since in reality phenomena are only observed in discrete times, data imputation is called for to create more observations so as to have good approximations for the density of the diffusion process. Three categories of entities will be computed in a Bayesian context: The latent imputed observations, the regime switching states, and the parameters of the models. The latent imputed data is updated at random time intervals in block using a Metropolis Hastings algorithm. The switching states are computed by an adaptation of a forward filtering backward smoothing algorithm to the HSD model. The parameters are estimated after prior specifications and conditional posterior densities formulation using Gibbs sampler or Metropolis Hastings algorithm.

Summary

In this article we develop and estimate a behavioral model of inflation dynamics with heterogeneous firms. In our stylized framework there are two groups of price setters, fundamentalists and random walk believers. Fundamentalists are forward-looking in the sense that they believe in a present-value relationship between inflation and real marginal costs, while random walk believers are backward-looking, using the simplest rule of thumb, naive expectations, to forecast inflation. Agents are allowed to switch between these different forecasting strategies conditional on their recent relative forecasting performance. We estimate the switching model using aggregate and survey data. Our results support behavioral heterogeneity and the significance of evolutionary learning mechanism. We show that there is substantial time variation in the weights of forward-looking and backward-looking behavior. Although on average the majority of firms use the simple backward-looking rule, the market has phases in which it is dominated by either the fundamentalists or the random walk believers.

Summary

In this paper, we propose an artificial market to model high-frequency trading where fast traders use threshold rules strategically to issue orders based on a signal reflecting the level of stochastic liquidity prevailing on the market. A market maker is in charge of adjusting prices (on a fast scale) and of setting closing prices and transaction costs on a daily basis, controlling for the volatility of returns and market activity. We first show that a baseline version of the model with no frictions is able to generate returns endowed with several stylized facts. This achievement suggests that the two time scales used in the model are one (possibly novel) way to obtain realistic market outcomes and that high-frequency trading can amplify liquidity shocks. We then explore whether transaction costs can be used to control excess volatility and improve market quality. While properly implemented taxation schemes may help in reducing volatility, care is needed to avoid excessively curbing activity in the market and intensifying the occurrence of abnormal peaks in returns.

Summary

Policy implications are derived for an inflation-targeting central bank, whose credibility is endogenous and depends on its past ability to achieve its targets. This is done in a New Keynesian framework with heterogeneous and boundedly rational expectations. We find that the region of allowed policy parameters is strictly larger than under rational expectations. However, when the zero lower bound on the nominal interest rate is accounted for, self-fulfilling deflationary spirals can occur, depending on the credibility of the central bank. Deflationary spirals can be prevented with a high inflation target and aggressive monetary easing.

Summary

We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random effects and non-random diffusion. We build ordinary kernel estimators and histogram estimators and study their risk (), when . Asymptotic results are evaluated as both and N tend to infinity.

Summary

Tracking the chain of events generated by an aggregate shock in an Agent Based Model (ABM) is apparently an impossible mission. Employing the methodology described in Assenza and Delli Gatti (J Econ Dyn Control 37(8):1659–1682 2013) (AD2013 hereafter), in the present paper we show that such a task can be carried out in a straightforward way by using a hybrid macro ABM consisting of a IS curve, an Aggregate Supply (AS) curve and a Taylor Rule (TR) in that aggregate investment is a function of the moments of the distribution of firms’ net worth. For each shock (fiscal expansion, monetary tightening, financial shock) we can decompose the change of the aggregate scale of activity (measured by the employment rate) in a first round effect – i.e., the change generated by the shock keeping the moments of the distribution of net worth at the pre-shock level – and a second round effect, i.e., the change brought about by the variation in the moments induced by the aggregate shock. In turn, the second round effect can be decomposed in a term that would show up also in a pure Representative Agent setting (RA component) and a term that is specific to the model with Heterogeneous Agents (HA component). In all the cases considered, the first round effect explains most of the actual change of the output gap. The second round effect is unambiguously negative. The HA component has the same sign of the RA component and explains a sizable fraction of the second round effect.

Summary

The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates of the multi-dimensional process operate on different time scales, standard inference tools are ill conditioned. In this paper, we propose to use a higher order scheme to discretize the process and approximate the likelihood, such that the different time scales are appropriately accounted for. We show consistency and asymptotic normality with non-typical convergence rates. When only partial observations are available, we embed the approximation into a filtering algorithm for the unobserved coordinates, and use this as a building block in a Stochastic Approximation Expectation Maximization algorithm. We illustrate on simulated data from three models; the Harmonic Oscillator, the FitzHugh-Nagumo model used to model the membrane potential evolution in neuroscience, and the Synaptic Inhibition and Excitation model used for determination of neuronal synaptic input.

Summary

We study a stochastic model of anonymous influence with conformist and anti-conformist individuals. Each agent with a ‘yes’ or ‘no’ initial opinion on a certain issue can change his opinion due to social influence. We consider anonymous influence, which depends on the number of agents having a certain opinion, but not on their identity. An individual is conformist/anti-conformist if his probability of saying ‘yes’ increases/decreases with the number of ‘yes’-agents. We focus on three classes of aggregation rules (pure conformism, pure anti-conformism, and mixed aggregation rules) and examine two types of society (without, and with mixed agents). For both types we provide a complete qualitative analysis of convergence, i.e., identify all absorbing classes and conditions for their occurrence. Also the pure case with infinitely many individuals is studied. We show that, as expected, the presence of anti-conformists in a society brings polarization and instability: polarization in two groups, fuzzy polarization (i.e., with blurred frontiers), cycles, periodic classes, as well as more or less chaotic situations where at any time step the set of ‘yes’-agents can be any subset of the society. Surprisingly, the presence of anti-conformists may also lead to opinion reversal: a majority group of conformists with a stable opinion can evolve by a cascade phenomenon towards the opposite opinion, and remains in this state.