Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

Traditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by nding evidence of Zipf's Law. Recent studies question this nding, highlighting that, while the Pareto distribution may t reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results con rm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data con rms the di culty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.

The Distribution Dynamics of Output Multipliers in Scotland 1998–2007

In an input-output context the impact of any particular industrial sector is commonly measured in terms of the output multiplier for that industry. Although such measures are routinely calculated and often used to guide regional industrial policy the behaviour of such measures over time is an area that has attracted little academic study. The output multipliers derived from any one table will have a distribution; for some industries the multiplier will be relatively high, for some it will be relatively low. The recentpublication of consistent input-output tables for the Scottish economy makes it possible to examine trends in this mdistribution over the ten year period 1998-2007. This is done by comparing the means and other summary measures of the distributions, the histograms and the cumulative densities. The results indicate a tendency for the multipliers to increase over the period. A Markov chain modelling approach suggests that this drift is a slow but long term phenomenon which appears not to tend to an equilibrium state. The prime reason for the increase in the output multipliers is traced to a decline in the relative importance of imported (both from the rest of the UK and the rest of the world) intermediate inputs used by Scottish industries. This suggests that models calibrated on the set of tables might have to be interpreted with caution.

Intergenerational Mobility and the Informative Content of Surnames

We propose a new methodology for measuring intergenerational mobility in economic wellbeing. Our method is based on the joint distribution of surnames and economic outcomes. It circumvents the need for intergenerational panel data, a long-standing stumbling block for understanding mobility. A single cross-sectional dataset is su cient. Our main idea is simple. If `inheritance' is important for economic outcomes, then rare surnames should predict economic outcomes in the cross-section. This is because rare surnames are indicative of familial linkages. Of course, if the number of rare surnames is small, this won't work. But rare surnames are abundant in the highly-skewed nature of surname distributions from most Western societies. We develop a model that articulates this idea and shows that the more important is inheritance, the more informative will be surnames. This result is robust to a variety of di erent assumptions about fertility and mating. We apply our method using the 2001 census from Catalonia, a large region of Spain. We use educational attainment as a proxy for overall economic well-being. Our main nding is that mobility has decreased among the di erent generations of the 20th century. A complementary analysis based on sibling correlations con rms our results and provides a robustness check on our method. Our model and our data allow us to examine one possible explanation for the observed decrease in mobility. We nd that the degree of assortative mating has increased over time. Overall, we argue that our method has promise because it can tap the vast mines of census data that are available in a heretofore unexploited manner.

The Optimal Distribution of the Tax Burden over the Business Cycle

This paper analyses optimal income taxes over the business cycle under a balanced-budget restriction, for low, middle and high income households. A model incorporating capital-skill complementarity in production and differential access to capital and labour markets is developed to capture the cyclical characteristics of the US economy, as well as the empirical observations on wage (skill premium) and wealth inequality. We .nd that the tax rate for high income agents is optimally the least volatile and the tax rate for low income agents the least countercyclical. In contrast, the path of optimal taxes for the middle income group is found to be very volatile and counter-cyclical. We further find that the optimal response to output-enhancing capital equipment technology and spending cuts is to increase the progressivity of income taxes. Finally, in response to positive TFP shocks, taxation becomes more progressive after about two years.