Quantifying heteroskedasticity metrics

This study proposes a quantification measure for heteroskedasticity in the time series. Two methods are introduced for quantifying heteroskedasticity: Slope of Local Variance Index (SoLVI) and a statistical divergence method using Bhattacharys coefficient. Both measures show reliability in measuring and quantifying heteroskedasticity in comparison to numerical and hypothesis heteroskedasticity tests

Estimating Price Elasticities of Supply for Cotton: A Structural Time-Series Approach

The Kalman Filter is used to estimate a structural time-series model of cotton supply for 30 countries and 16 aggregated regions. Estimated short run supply elasticities with respect to the world price are presented for all 46 countries and regions. While they are broadly within the expected range in light of previous work, they indicate extensive cross-country and regional heterogeneity, as well as considerable parameter uncertainty in some cases. Finally, some proposals are made for incorporating both the core estimates and their sampling distributions into applied equilibrium models.Cotton; price elasticity of supply; structural time-series model; Kalman Filter

A MULTICROP PRODUCTION MODEL OF IRRIGATED AGRICULTURE, APPLIED TO WATER ALLOCATION POLICY OF THE BUREAU OF RECLAMATION

Recipients of irrigation water from the Bureau of Reclamation (BuRec) face a future of water conservation. By formally modeling surface water as a fixed, allocatable input to a multioutput firm, this research captures the institutional constraints governing water allocation and , simultaneously, establishes a cohesive approach to analyzing the production effects of BuRec allocation policy. Econometric results show that BuRec-served irrigators'Â’ crop supply and land allocation decisions are generally inelastic with respect to the water constraint. Using the elasticities, a policy simulation of a 10% reduction in BuRec water allocation indicates that production response to reduced water supply would affect the national price of three of ten major crops produced by BuRec-served farms.Resource /Energy Economics and Policy,

Consumption Risk-sharing within Australia and with New Zealand

quantify how output risks are smoothed within Australia, and between Australia and New Zealand. About 85 percent of shocks were smoothed within Australia through credit and capital markets, with fiscal policy a source of dis-smoothing after 1992. Risk-sharing between Australia and New Zealand was greater than within Europe, occurring mostly through credit markets. With fully integrated financial markets between Australia and New Zealand since 1960, the average welfare gain would be 2.7 percent of certainty-equivalent consumption over 50 years, although these gains favour New Zealand. Australia's gains are from the pooling of PPP risks. These potential gains were largely resolved by the deregulations and CER trade agreement of the early198 0s.Risk-sharing; horizontal fiscal equalization; common currency; welfare gains from integration

Regional Convergence and Aggregate Growth

A striking feature of US states convergence is the link between the spatial speed of convergence and the aggregate growth rate: fast aggregate growth induces a reduction in regional inequalities. This paper uses a neoclassical growth framework with integrated economies in order to capture this phenomena. As it has been stressed by Ventura (1997), the interdependence between regional economies through the access to common markets generates a link between aggregate evolution and spatial convergence dynamics. The paper has two mains results. First, we show how deep parameters of the economy determines quantitatively the magnitude of this link. Second, we propose two directions for testing the model and we provide some empirical evidence using US states data on personal income. These results are mixed, only a part of the convergence pattern is well captured by the model.

Calculating Value-at-Risk

The market risk of a portfolio refers to the possibility of financial loss due to the joint movement of systematic economic variables such as interest and exchange rates. Quantifying market risk is important to regulators in assessing solvency and to risk managers in allocating scarce capital. Moreover, market risk is often the central risk faced by financial institutions. The standard method for measuring market risk places a conservative, one-sided confidence interval on portfolio losses for short forecast horizons. This bound on losses is often called capital-at-risk or value-at-risk (VAR), for obvious reasons. Calculating the VAR or any similar risk metric requires a probability distribution of changes in portfolio value. In most risk management models, this distribution is derived by placing assumptions on (1) how the portfolio function is approximated, and (2) how the state variables are modeled. Using this framework, we first review four methods for measuring market risk. We then develop and illustrate two new market risk measurement models that use a second-order approximation to the portfolio function and a multivariate GARCH(l,1) model for the state variables. We show that when changes in the state variables are modeled as conditional or unconditional multivariate normal, first-order approximations to the portfolio function yield a univariate normal for the change in portfolio value while second-order approximations yield a quadratic normal. Using equity return data and a hypothetical portfolio of options, we then evaluate the performance of all six models by examining how accurately each calculates the VAR on an out-of-sample basis. We find that our most general model is superior to all others in predicting the VAR. In additional empirical tests focusing on the error contribution of each of the two model components, we find that the superior performance of our most general model is largely attributable to the use of the second-order approximation, and that the first-order approximations favored by practitioners perform quite poorly. Empirical evidence on the modeling of the state variables is mixed but supports usage of a model which reflects non-linearities in state variable return distributions. This paper was presented at the Financial Institutions Center's October 1996 conference on "

Methods in functional data analysis and functional genomics

This thesis has two overall themes, both of which involve the word functional, albeit in different contexts. The theme that motivates two of the chapters is the development of methods that enable a deeper understanding of the variability of functional data. The theme of the final chapter is the development of methods that enable a deeper understanding of the landscape of functionality across the human genome in different human tissues. The first chapter of this thesis provides a framework for quantifying the variability of functional data and for analyzing the factors that affect this variability. We extend functional principal components analysis by modeling the variance of principal component scores. We pose a Bayesian model, which we estimate using variational Bayes methods. We illustrate our model with an application to a kinematic dataset of two-dimensional planar reaching motions by healthy subjects, showing the effect of learning on motion variability. The second chapter of this thesis provides an alternative method for decomposing functional data that follows a Poisson distribution. Classical methods pose a latent Gaussian process that is then linked to the observed data via a logarithmic link function. We pose an alternative model that draws on ideas from non-negative matrix factorization, in which we constrain both scores and spline coefficient vectors for the functional prototypes to be non-negative. We impose smoothness on the functional prototypes. We estimate our model using the method of alternating minimization. We illustrate our model with an application to a dataset of accelerometer readings from elderly healthy Americans. The third chapter of this thesis focuses on functional genomics, rather than functional data analysis. Here we pose a method for unsupervised clustering of functional genomics data. Our method is non-parametric, allowing for flexible modeling of the functional genomics data without binarization. We estimate our model using variational Bayes methods, and illustrate it by calculating genome-wide functional scores (based on a partition of our clusters into functional and non-functional clusters) for 127 different human tissues. We show that these genome-wide and tissue-specific functional scores provide state-of-the-art functional prediction