Do firms share the same functional form of their growth rate distribution? A new statistical test

We introduce a new statistical test of the hypothesis that a balanced panel of firms have the same growth rate distribution or, more generally, that they share the same functional form of growth rate distribution. We applied the test to European Union and US publicly quoted manufacturing firms data, considering functional forms belonging to the Subbotin family of distributions. While our hypotheses are rejected for the vast majority of sets at the sector level, we cannot rejected them at the subsector level, indicating that homogenous panels of firms could be described by a common functional form of growth rate distribution.Comment: 17 pages, 3 figures, 2 table

Glimpses of an urbanism to come

First exhaustive research paper to provide a comprehensive spatial analysis of the 2001 G8 summit in Genoa, Italy. The paper argues that the 2001 G8 Summit saw the emergence of spatial techniques to control public spaces that would become paradigmatic of the urbanism of the XXIst century. Through maps and diagrams the events that took place during the summit are analysed and then compared to planning techniques utilised in other political rallies (2007 APEC, Sydney) or new cities (Dubai). By highlighting what tools and concepts underpin this emergent urbanism, the paper calls for a kind of architect that understands his role beyond the mere invention of new forms

Time and Islands: the spatial politics of football’

This paper was originally delivered at the eass (European Association for Sociology of Sport) Conference in Münster, Germany (2007), and is the first to examine the territoriality of football clubs as an alternative way of understanding European political boundaries. Bottazzi focuses on European football’s ‘G14’, a group of clubs modelled on the G8 group of economies. An examination of G14’s rules for membership, together with bibliographical research and a series of interviews with the spatial sociologist and sports journalist Pippo Russo, helped in the development of a new kind of territorial analysis. This contrasts two spatial notions: the island, an almost primitive spatial figure, and on the other, the rhetoric of flows and connections which informs most contemporary theoretical discussion on territories. Bottazzi’s paper is a polemical comparison between a definition of the European territory as imagined by theoreticians versus an empirical analysis of what is really happening. The research fills a gap in the work of Bottazzi’s contemporaries: Stefano Boeri, who, through the architectural research group Multiplicity, explores issues of identity, politics, and geography in Europe; Giorgio Agamben, who has examined the concept of the paradigm in his book on method, The Signature of All Things (2009), and Professor Keller Easterling, who, in writings such as Enduring Innocence: Global Architecture and Its Political Masquerades (2005), researches familiar spatial types in precarious political situations around the world. From Bottazzi’s original publication came an invitation to submit the paper to a website hosted by the Network Architecture Lab, Columbia University in a joint venture with Domus Web. It was published online in 2010 (http://testbed2.audc.org/projects/publish/islands_spatial_politics_soccer), and has formed the basis of subsequent research in a project called ‘Molecular City’ (2010–12)

On the Irreconcilability of Pareto and Gibrat Laws

If business firms face a multiplicative growth process in which their growth rates are independent from their sizes, then these sizes cannot be distributed according to a stationary Pareto distribution. At the same time , the Laplace distribution of growth rates cannot be easily reconciled with a Pareto distribution of firm sizes. Recent contributions, using formal arguments, seems to contrast these statements. We prove that the proposed formal results are wrong.Firm Growth, Gibrat's Law, Power law distribution, Laplace distribution.

A comment on the relationship between firms' size and growth rate

Since the seminal work of Pareto, many empirical analyses suggested that the distribution of firms size is characterized by an asymptotic power like behavior. At the same time, recent investigations show that the distribution of annual growth rates of business firms displays a remarkable double-exponential shape. A recent letter propose a possible connection between these two empirical regularities. By assuming a bivariate Marshall-Olkin power-like distribution for the size of firms in subsequent time steps, and performing a qualitative asymptotic analysis, it is suggested that the implied growth rates distribution takes a Laplace shape. By performing a complete analytical investigation, I show that this statement is not correct. The implied distribution does in general possess a non-continuous component and becomes degenerate when perfect correlation is assumed between size levels at different time steps. Essentially, the approach is faulty as it treats firm size levels as stationary stochastic variables and neglects the integrated nature of the growth process.Firm Growth, Size distribution, Power law, Laplace distribution.

Subbotools User's Manual

The SUBBOTOOLS package is intended as an help to the use of the Subbotin family of probability densities in a statistical analysis environment. The package contains various programs for the maximum likelihood estimation of an unknown distribution and for the generation of pseudo random variables. The last version of SUBBOTOOLS can be found at http://bottazzi.sssup.it/~giulio. Comments and bug reports are welcome. E-write to [email protected].

On the Pareto Type III distribution

This short note analyzes the distributional properties of Pareto Type III random variables. We introduce a three parameters version of the orignal two parameters distribution proposed by Pareto and derive both the density and the characteristic function. The analytic expression of the inverse distribution function is also obtained, together with a simple series expansion of its moments of any order. Finally, we propose a simple statistical exercise designed to show the increased reliability of the Pareto Type III distribution in describing asymptotically dumped power-like behaviors.Pareto Distribution, Fat Tails, Power Law Distribution, Zipf Law