A unified approach to bivariate discrete distributions

Here we introduce a bivariate generalized hypergeometric factorial moment distribution (BGHFMD) through its probability generating function (p.g.f.) whose marginal distributions are the generalized hypergeometric factorial moment distributions introduced by Kemp and Kemp (Bull Int Stat Inst 43:336–338,1969). Well-known bivariate versions of distributions such as binomial, negative binomial and Poisson are special cases of this distribution. A genesis of the distribution and explicit closed form expressions for the probability mass function of the BGHFMD, its factorial moments and the p.g.f.’s of its conditional distributions are derived here. Certain recurrence relations for probabilities, moments and factorial moments of the bivariate distribution are also established.     

Total Response Measures in Systems of Nonlinear Equations: An Application to a Model of the U.S. Dairy Sector

This paper develops total elasticity and flexibility results for general nonlinear, dynamic systems of equations. Unlike procedures for obtaining total response measures in linear systems, analytical procedures are difficult to obtain for nonlinear models; comparable results, however, may be obtained by using numerical simulations. The potential for obtaining total elasticity measures in nonlinear dynamic models is illustrated with an annual model of the U.S. dairy sector. Results show substantial evidence of asymmetric price and quantity adjustments, as well as limit cycles. Such complexities could not be uncovered by using linear models or a partial-equilibrium framework.     

A multiobjective optimization model for project selection with probabilistic considerations

When faced with limited resources, project managers must determine which projects to fund at what levels from a pool of potential ones. This problem of project selection is inherently multiobjective since various factors, such as the available budget, the chance of success, and the efficient allocation of the project team, must be considered simultaneously. The uncertainty of the data at the time decisions are made further complicates project selection. In this paper, a multiobjective, integer-constrained optimization model with competing objectives for project selection is formulated using probability distributions to describe costs. The objectives correspond to important project criteria, such as: rank (value), managerial labor needed, and average cost. The subjective rank is determined via the Analytic Hierarchy Process. The model is applied to a data set from a US government agency that involves 84 separate projects. The results indicate improved budgetary efficiency compared to the actual project selection, thus supporting use of the model for public sector project selection. The model is unique since it integrates multiobjective optimization, Monte Carlo simulation, and the Analytic Hierarchy Process.     

Does Tourism Promote Cross-Border Trade?

We estimate a simultaneous bivariate qualitative choice model of Arizona agribusiness firms' propensity to trade and visit as a tourist the cross-border state of Sonora, Mexico. Venture business visits, quantified through the tourism equation, were found to have the largest impact on a firm's propensity to trade. Tourist visits have a greater impact on trade when combined with other firm attributes such as age, perceived need for geographic diversity, foreign language fluency, and firm size, than if considered alone. Our results suggest that there is a role for government agencies to play in overcoming imperfect information related to trade opportunities through facilitating exploratory business venture and tourist visits.     

Modeling regime‐dependent agricultural commodity price volatilities

In stark contrast to financial markets, relatively little attention has been given to modeling agricultural commodity price volatility. In recent years, numerous methodologies with various strengths have been proposed for modeling price volatility in financial markets. We propose using a mixture of normals with unique GARCH processes in each component for modeling agricultural commodity prices. While a normal mixture model is quite flexible and allows for time varying skewness and kurtosis, its biggest strength is that each component can be viewed as a different market regime and thus estimated parameters are more readily interpreted. We apply the proposed model to ten different agricultural commodity weekly cash prices. Both in‐sample fit and out‐of‐sample forecasting tests confirm that the two‐state NM‐GARCH approach performs better than the traditional normal GARCH model. A significant and state‐dependent inverse leverage effect is detected only for pork in the regime where the price is expected to drop, indicating the volatility in this regime tends to increase more following a realized price rise than a realized price drop.