Power law and evolutionary trends in stock markets

Modelling losses and locating the tail with the Pareto Positive Stable distribution

“…Gabaix and Ioannides, 2004). The two most commonly used are the Hill Estimator (Hill, 1975) and the Zipf Regression (Gabaix, 1999a,b;Balakrishnan et al, 2008). Both of them have several problems (see Reiss and Thomas, 1997;Drees et al, 2000;Matthys and Beirlant, 2002;Gabaix and Ioannides, 2004;Melo and Becerra, 2006;Bauke, 2007;Clauset et al, 2009).…”

Market closings and concentration of stock trading: an empirical analysis

“…Balakrishnan et al (2008) model the distribution of the trading volumes of individual firms on the US stock markets on each trading day as a power law distribution. The power law exponent, q t , for each day t is estimated from Equation 3 below.…”

“…In 1960, the average daily volume of trading in all the stocks covered in the Center for Research in Security Prices (CRSP) database was 3 million shares with a value of $112 million; by 2010, the average daily volume of trading was 8.4 billion shares valued at $232 billion. Balakrishnan et al (2008) examine whether this extraordinary growth came from a proportionate increase in the volume of all stocks or whether it was due to a disproportionately large increase in a small subset of stocks. They model the distribution of daily trading volume of US stocks from 1962 to 2005 as a power law function and examine its trajectory over time.…”

The Contribution of Regions to Aggregate Growth in the OECD

“…Common procures to estimate power laws include using Zipf Regressions (Gabaix 1999a, Gabaix 1999b, Balakrishnan et al, 2008) and Hill Estimators (Hill, 1975. At first glance a visual test can detect power laws by sorting the regions with the largest contribution to growth into a sequence and then assigning each region a rank within the sequence and plotting a log-log relation between their rank in the sequence and their contribution to growth.…”