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The conflict between economic growth and sustainable development is foregone and there is prodigious literature examining the nature and causes of such trade-off. Keeping with this dispensation, the current chapter examines the dynamics of such trade-off in Ramsey–Cass–Koopmans (R–C–K) optimal growth-theoretic lines. The model developed in the chapter departs from the fundamental feature of R–C–K framework in as much as the capital is considered on a broader spectrum having its marginal productivity being increasing in nature and it considers a centralised economy with the planner maximising discounted utility over per capita consumption (private good) and pollution (public bad) over the infinite horizon of time. The study reveals potential trade-off between consumption and environmental emission quiet emphatically for the developed, developing and less developed countries, in both single equilibrium and multiple equilibrium cases. Besides, the study examines the impact of rise in population growth and fuel price on the steady-state equilibrium with respect to per capita capital, relative intensity of energy usage, emission and consumption using comparative static exercise.

The BEKK GARCH class of models presents a popular set of tools for applied analysis of dynamic conditional covariances. Within this class the analyst faces a range of model choices that trade off flexibility with parameter parsimony. In the most flexible unrestricted BEKK the parameter dimensionality increases quickly with the number of variables. Covariance targeting decreases model dimensionality but induces a set of nonlinear constraints on the underlying parameter space that are difficult to implement. Recently, the rotated BEKK (RBEKK) has been proposed whereby a targeted BEKK model is applied after the spectral decomposition of the conditional covariance matrix. An easily estimable RBEKK implies a full albeit constrained BEKK for the unrotated returns. However, the degree of the implied restrictiveness is currently unknown. In this paper, we suggest a Bayesian approach to estimation of the BEKK model with targeting based on Constrained Hamiltonian Monte Carlo (CHMC). We take advantage of suitable parallelization of the problem within CHMC utilizing the newly available computing power of multi-core CPUs and Graphical Processing Units (GPUs) that enables us to deal effectively with the inherent nonlinear constraints posed by covariance targeting in relatively high dimensions. Using parallel CHMC we perform a model comparison in terms of predictive ability of the targeted BEKK with the RBEKK in the context of an application concerning a multivariate dynamic volatility analysis of a Dow Jones Industrial returns portfolio. Although the RBEKK does improve over a diagonal BEKK restriction, it is clearly dominated by the full targeted BEKK model.

The United States today boasts of a complex and extensive set of public and private institutions and arrangements for managing its water resources. Today's system of watershed management is neither entirely top-down nor bottom-up. It is not entirely planned, nor is it entirely laissez-faire. Rather it is a hybrid. This chapter analyzes through a historical lens how American watershed management evolved to this state. It looks at two driving factors: technological change and trends in American political culture. Technology provided the reason for water resource and watershed management to evolve because of the conflicts provoked by its unintended and negative side effects, such as pollution. American political culture mediated the way that individuals and government reacted to these conflicts and spurred the evolution of new institutions.