This thesis focuses on the analysis of heavy-tailed distributions, which are widely applied to model phenomena in many disciplines. The definition of heavy tails based on the theory of regular variation highlights the importance of the tail index, which indicates the existence of moments and characterises the rate at which the tail decays. Two new approaches to make inference for the tail index are proposed. The first approach employs a regression technique and constructs an estimator of the tail index. It exploits the fact that the behaviour of the characteristic function near the origin reflects the behaviour of the distribution function at infinity. The main advantage of this approach is that it utilises all observations to constitute each point in the regression, not just extreme values. Moreover, the approach does not rely on prior information on the starting point of the tail behaviour of the underlying distribution and shows excellent performance in a wide range of cases: Pareto distributions, heavy-tailed distributions with a non-constant slowly varying factor, and composite distributions with heavy tails. The second approach is motivated by the asymptotic properties of a special moment statistic, the so-called partition function. This statistic considers blocks of data and is generally used in the context of multifractality. Due to the interplay between the weak law of large numbers and the generalised central limit theorem, the asymptotic behaviour of the partition function is strongly affected by the existence of moments even for weakly dependent samples. Via a quantity, the scaling function, a graphical method to identify the existence of heavy tails is proposed. Moreover, the plot of the scaling function allows one to make inference for the underlying distribution: with infinite variance, finite variance with tail index larger than two, or all moments finite. Furthermore, since the tail index is reflected at the breakpoint of the plot of the scaling function, this gives the possibility to estimate the tail index. Both these two approaches use the entire distribution, not just the tail, to analyse the tail behaviour. This sheds a new light on the analysis of heavy-tailed distributions. At the end of this thesis, these two approaches are used to detect power laws in empirical data sets from a variety of fields and contribute to the debate on whether city sizes are better approximated by a power law or a log-normal distribution.

The present work is organized in five chapters and it proposes and applies alternative measures of productivity constructed using input-output tables and based mainly on the Sraffian scheme. The first three chapters of the thesis are devoted to the development and the empirical application of new productivity measures. These chapters form the main part of the work. The last two chapters are devoted to sensitivity analysis. In the first chapter, entitled ‘Productivity accounting based on production prices’ an alternative method of productivity accounting is proposed. By using input–output tables from four major OECD countries between 1970 and 2000, we compute the associated wage-profit frontiers and the net national products curves, and from these we derive two measures of productivity growth based on production prices and a chosen numeraire. The findings support the general conclusions in the existing literature on the productivity slowdown and later rebound, and supply new important insights to the extent and timing of these events. The second chapter is entitled ‘New measures of sectoral productivity’. The objective of this chapter is to propose alternative methods of sectoral productivity accounting based the theoretical work of Goodwin (1976), Gossling (1972), Pasinetti (1973), and Sraffa (1960). The indexes developed in this study differ from the standard indexes of productivity because they are designed on the basis of some of the following desiderable features: take into account the interconnections among economic sectors, aggregate heterogeneous goods by using production prices, and compute productivity by using quantity of goods instead of their values. These indexes are then be tested empirically by computing productivity of four major OECD countries. The third chapter is entitled ‘Productivity in the Italian regions: development of Alternative Indicators based on input-output tables’. This chapter calculates indices of aggregate productivity, sectoral productivity, and technological progress for a selected sample of Italian regions. Besides these indices, two different versions of the so-called technological frontier were calculated. The contemporary frontiers that are constructed from all the production techniques extracted from the regional input-output tables in a given year and the intertemporal frontier that is computed for the full set of techniques available over time and across regions. The availability of the technological frontiers allows the calculation of the recently developed Velupillai-Fredholm-Zambelli indices of convergence (Fredholm and Zambelli, 2009) that are based on the distance between the region-specific wage-profit frontiers and the technological frontiers. Given the important role played by the production prices, this chapter also examines the price curves for each region and industry and it identifies remarkable regularities. Not surprisingly, analyses of the findings reveal that there is a productivity gap between the regions of North and South. However, the analysis of sectoral productivity reveals two important facts. The first is that the techniques of some industries are more productive in the South than in the North. The second, who follows from the first, is that all regions could therefore improve productivity through greater integration. Chapter four is entitled ‘An Inquiry into the choice of Numeraire’. This chapter has several objectives. The main aim is to examine the robustness of the results obtained by applying the new approach to measuring productivity if we change the numeraire chosen. However, it should be mentioned that the problem of the choice of numeraire is a general one and for this reason, the chapter also proposes universal guidelines to be followed in choosing the numeraire and in testing the robustness of the results to changes in the numeraire. Finally, chapter five is entitled ‘An Inquiry into the effect of aggregation of input-output tables’. The aim of this chapter is to test the robustness of the results from a progressive aggregation of the input-output tables.