Global dynamics in models of fluctuating growth Part I: Two dimensional systems

We consider a modified version of Goodwin's celebrated non-linear model of fluctuating growth, where the incomeY is a quadratic function of the capital stockk, in order to take into account the possibility of increasing or decreasing returns. The dynamics of the model is then defined by a non-autonomous system of two differential equations. Assuming the labour supply,N, and the productivity,a, to be constant in the time, the model becomes autonomous and can be embedded in a stable family of planar dynamical systems whose flows and bifurcations are globally described

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Riassunto Si considera una versione modificata del modello di crescita non-lineare di Goodwin, in cui il reddito,Y, è una funzione quadratica dello stock di capitale,k, così da permettere la possibilità di rendimenti crescenti o decrescenti. La dinamica del modello viene allora rappresentata da un sistema non autonomo di due equazioni differenziali. Con l'ipotesi che l'offerta di lavoro,N, e la produttività,a, siano costanti nel tempo, il modello diventa autonomo e può essere immerso in una famiglia stabile di sistemi dinamici piani, di cui vengono descritti i flussi globali e le biforcazioni.

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This paper relates to the activities of the M.P.I. Group Dinamiche Non-Lineari nelle Scienze Economiche e Sociali.     

Canonical forms and tests of hypotheses Part II: Multivariate mixed linear models

Abstract  In the literature on multivariate analysis of variance, exact test procedures are restricted to linear models with fixed effects only. In this paper tests are presented for multivarite linear hypotheses with respect to mixed models, which constitude a generalization of (univariate) regular models described by R oebruck (1982). Furthermore it is shown, that the matrices, which are used to compute the test statistics, can be derived from the univariate "sums of squares" in the same manner as in the case of fixed models. The applicability of this theory is demonstrated by two examples.     

Computational techniques for analysis of system dynamics models of social systems

This paper presents a methodology for analysis of system dynamics models of social systems. The methodology consists of computational algorithms Specifically, the computational techniques of sensitivity analysis as extended to system dynamics models are shown to enhance an understanding of model behavior and to contribute to considerations of model validity, whereas optimization analyses are shown to contribute to model utility and policy formulation.     

Equilibrium dynamics in a class of one-sector endogenous growth models with external habits: An application of special functions

This paper analyzes the equilibrium dynamics in a class of one-sector endogenous growth models with external habits. Using an explicit solution expressed in terms of the Gauss hypergeometric function, we show that the levels of consumption, habits and capital may exhibit non-monotonic transition dynamics, even though their ratios converge monotonically. A numerical simulation illustrates this result.     

Analysis of high dimensional multivariate stochastic volatility models

This paper is concerned with the Bayesian estimation and comparison of flexible, high dimensional multivariate time series models with time varying correlations. The model proposed and considered here combines features of the classical factor model with that of the heavy tailed univariate stochastic volatility model. A unified analysis of the model, and its special cases, is developed that encompasses estimation, filtering and model choice. The centerpieces of the estimation algorithm (which relies on MCMC methods) are: (1) a reduced blocking scheme for sampling the free elements of the loading matrix and the factors and (2) a special method for sampling the parameters of the univariate SV process. The resulting algorithm is scalable in terms of series and factors and simulation-efficient. Methods for estimating the log-likelihood function and the filtered values of the time-varying volatilities and correlations are also provided. The performance and effectiveness of the inferential methods are extensively tested using simulated data where models up to 50 dimensions and 688 parameters are fit and studied. The performance of our model, in relation to various multivariate GARCH models, is also evaluated using a real data set of weekly returns on a set of 10 international stock indices. We consider the performance along two dimensions: the ability to correctly estimate the conditional covariance matrix of future returns and the unconditional and conditional coverage of the 5% and 1% value-at-risk (VaR) measures of four pre-defined portfolios.     

Bourdieu Comes to Town: Part II

This essay introduces the second selection of essays associated with the Interventions forum ‘Bourdieu Comes to Town’, the first of which appeared in 2018. There seems to be a tendency to conflate the relevance of Bourdieu for urban studies by focusing specifically on particular contentious concepts that have been fashioned from Bourdieu's own tools. I briefly discuss this point with respect to the concepts of ‘elective belonging', which I helped introduce, and ‘territorial stigmatization’, which Loïc Wacquant himself has popularized. I argue that whatever the virtues or otherwise of these concepts, Bourdieu offers substantially more to urban studies, namely the capacity to synthesize across sites, to link micro and macro, to engage pragmatist concerns with daily life to a wider political economy, and to foreground the role of accumulation. I briefly show how the four essays in this selection exemplify these qualities.     

Global imbalances and dynamics of international financial markets

We provide an overview of the special issue “Global Imbalances and dynamics of international financial markets”. This special issue, which is associated with the 7th International Finance Conference, features research papers dealing with the impact of global imbalances, market complexity, and the impact of the recent global financial crisis on the conduct of monetary policies, financial market dynamics, financial stability, and risk management models.     

Achieving voluntary data sharing in cross sector partnerships: Three partnership models

The complex societal problems that we face today require unprecedented collaboration and evidence-based decisions. These collaboration processes are further propelled by the datafication of virtually all spheres of public life. To benefit from this, the data needs to be made available to allow for data analytics. Thus, data sharing becomes a crucial aspect of cross-sector collaborations that aim to create and capture value from information. Compared to collaborations where data sharing is not the main goal, data sharing partnerships face a number of novel challenges, such as mitigating data risks, complying with data protection legislation, and ensuring responsible data use. Navigating these waters and achieving data sharing can be challenging for both governments and businesses, as well as other actors. How do organizations from different sectors manage to achieve data sharing for addressing societal challenges? To address this research question, we apply a framework of three models of cross sector social partnerships developed in the field of organization studies to structure the analysis of six cases. Our analysis suggests that to a certain extent the partnership model determines the types of drivers and challenges to sharing data in a partnership. Leveraging the drivers and anticipating these challenges can help organizations be more aware of key terms of the collaboration and the mechanisms that can be used to succeed in their partnership goals.     

Computational suite of models with heterogeneous agents II: Multi-country real business cycle models

This paper describes the second model considered in the computational suite project that compares the performance of different numerical algorithms. It is a multi-country model in which countries face different productivity shocks. Solving such models is a challenging numerical problem unless the number of countries is small. The solutions are functions of a large set of arguments and the functional forms are unknown. Moreover, the solution procedures have to deal with high-dimensional integration problems.     

Individual effects and dynamics in count data models

In this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables. Use of a linear feedback model is proposed. A quasi-differenced GMM estimator is consistent for the parameters in the dynamic model, but when series are highly persistent, there is a problem of weak instrument bias. An estimator is proposed that utilises pre-sample information of the dependent count variable, which is shown in Monte Carlo simulations to possess desirable small sample properties. The models and estimators are applied to data on US patents and R&D expenditure.     

Perfect simulation for models of industry dynamics

In this paper we introduce a technique for perfect simulation from the stationary distribution of a standard model of industry dynamics. The method can be adapted to other, possibly non-monotone, regenerative processes found in industrial organization and other fields of economics. The algorithm we propose is a version of coupling from the past. It is straightforward to implement and exploit the regenerative property of the process in order to achieve rapid coupling.     

Patterns and dynamics of population heterogeneity in mixtures models

Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.     

Asymptotic consequences of neglected dynamics in individual effects models*

We assess the asymptotic consequences of estimating static models based on cross-section or panel data, when in reality the data are generated by a dynamic relationship, involving lagged dependent and current and lagged exogenous variables as well as individual effects. If the exogenous variable follows a stationary process, then the static estimators usually underestimate its long-run effect. This inconsistency is less severe, the higher the autocorrelation of the exogenous variable. If the exogenous variable follows a random walk with or without individual-specific drift, then the estimators are found to be consistent for the long-run effect.     

Hierarchical system identification of models for urban dynamics

A critical problem in urban modeling is the validation of system models and identification of system parameters within an assumed structure. This paper applies recent developments in system identification in hierarchical structure to identification of system parameters for two models of urban dynamics.     

Variable markups in the long-run: A generalization of preferences in growth models

This paper introduces variable markups in a horizontal-differentiation growth model by considering a larger class of preferences that nests the classic “CES” specification usually present in the workhorse love-for-variety models. Our first result is to obtain a generalized characterization of the Euler condition for this broader class of utility functions: in our model, the Euler rule features a supplementary term aiming at compensating the consumer for variations in the preference for variety along the consumption level. We are then also able to demonstrate that in our generalized framework, the economy’s balanced growth path displays both endogenous markups and a strictly positive growth rate of the number of available varieties (being the engine of growth). Finally, we show that under endogenous markups, the economy’s growth rate and firms’ market power can display a negative correlation, as opposed to the standard result obtained in the CES framework.