Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

On alpha stable distribution of wind driven water surface wave slope

We propose a new formulation of the probability distribution function of wind driven water surface slope with an $\alpha$-stable distribution probability. The mathematical formulation of the probability distribution function is given under an integral formulation. Application to represent the probability of time slope data from laboratory experiments is carried out with satisfactory results. We compare also the $\alpha$-stable model of the water surface slopes with the Gram-Charlier development and the non-Gaussian model of Liu et al\cite{Liu}. Discussions and conclusions are conducted on the basis of the data fit results and the model analysis comparison.Comment: final version of the manuscript: 25 page

Technological Progress, Employment and the Lifetime of Capital

We study the impact of technological progress on the level of employment in a vintage capital model where: i) capital and labor are gross complementary; ii) labor supply is endogenous and indivisible; iii) there is full employment, and iv) the rate of labor-saving technological progress is endogenous. We characterize the stationary distributions of vintage capital goods and the corresponding equilibrium values for employment and capital lifetime. It is shown that both variables are non-monotonic functions of technological progress indicators. Technological accelerations are found to increase employment provided innovations are not too radical

The effects of immigration on wages: An application of the structural skill-cell approach

This paper investigates how recent immigration inflows from 2002 to 2008 have affected wages in Switzerland. This period is of particular interest as it marks the time during which the bilateral agreement with the EU on the free cross-border movement of workers has been effective. Since different types of workers are likely to be unevenly affected by recent immigration inflows, we follow the ”structural skill-cell approach” as for example employed by Borjas (2003) and Ottaviano and Peri (2008). This paper provides two main contributions. First, we estimate empirically the elasticities of substitution between different types of workers in Switzerland. Our results suggest that natives and immigrants are imperfect substitutes. Regarding different skill levels, the estimates indicate that workers are imperfect substitutes across broad education groups and across different experience groups. Second, the estimated elasticities of substitution are used to simulate the impact on domestic wages using the actual immigration inflows from 2002 to 2008. For the long run, the simulations produce some notable distributional consequences across different types of workers: While previous immigrants incur wage losses (−1.6%), native workers are not negatively affected on average (+0.4%). In the short run, immigration has a negative macroeconomic effect on the average wage, which, however, gradually dies out in the process of capital adjustment

Priority for the Worse Off and the Social Cost of Carbon

The social cost of carbon (SCC) is a monetary measure of the harms from carbon emission. Specifically, it is the reduction in current consumption that produces a loss in social welfare equivalent to that caused by the emission of a ton of CO2. The standard approach is to calculate the SCC using a discounted-utilitarian social welfare function (SWF)—one that simply adds up the well-being numbers (utilities) of individuals, as discounted by a weighting factor that decreases with time. The discounted-utilitarian SWF has been criticized both for ignoring the distribution of well-being, and for including an arbitrary preference for earlier generations. Here, we use a prioritarian SWF, with no time-discount factor, to calculate the SCC in the integrated assessment model RICE. Prioritarianism is a well-developed concept in ethics and theoretical welfare economics, but has been, thus far, little used in climate scholarship. The core idea is to give greater weight to well-being changes affecting worse off individuals. We find substantial differences between the discounted-utilitarian and non-discounted prioritarian SCC

Inequality, mobility and the financial accumulation process: A computational economic analysis

Our computational economic analysis investigates the relationship between inequality, mobility and the financial accumulation process. Extending the baseline model by Levy et al., we characterise the economic process trough stylised return structures generating alternative evolutions of income and wealth through historical time. First we explore the limited heuristic contribution of one and two factors models comprising one single stock (capital wealth) and one single flow factor (labour) as pure drivers of income and wealth generation and allocation over time. Then we introduce heuristic modes of taxation in line with the baseline approach. Our computational economic analysis corroborates that the financial accumulation process featuring compound returns plays a significant role as source of inequality, while institutional configurations including taxation play a significant role in framing and shaping the aggregate economic process that evolves over socioeconomic space and time

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Fiscal Policy, Private Investment and Economic Growth: Evidence from G-7 Countries

Measuring the effects of fiscal policy on economic growth is difficult, because fiscal policy variables are influenced by changes in income. This paper uses an unbalanced panel data set for G-7 countries for the period 1965-2000 that includes annual estimates of cyclically adjusted government expenditures, capital outlays, income tax revenues, indirect tax revenues, corporate tax revenues and social security tax revenues, based on definitions developed by OECD revenue statistics. The percentage share of these estimates in GDP is used to investigate the effects of fiscal policy on economic growth, and results are compared with regression results that use 5-year averages of cyclically unadjusted variables. The empirical results from both sets of regressions suggest that only taxes on household income and government expenditures have negative effects on per capita income growth. We consolidate our findings by showing that both government expenditures and income taxes have distortionary effects on private investment