In marine environments, the open system (OS) theory, whereby populations are assumed to be well connected through large-scale dispersal, is currently being challenged by studies demonstrating limited dispersal. Using a novel metapopulation framework featuring nonequilibrium within-site disturbance cycles and limited dispersal, I investigate the large-scale response of marine mussel populations to changes in oceanographic productivity. By altering the fecundity parameter, I am able to shift from open to dynamically-coupled systems (DCS), thereby generating predictions that can be used to test the connectivity of marine populations. Within-site disturbance cycles scale-up and drive regional dynamics in both OS and DCS. Fast disturbance cycles induce synchronized oscillations that promote regional extinction risk in response to changes in oceanographic productivity for DCS but not OS. Slow disturbance cycles maintain spatial variability and temporal stability in both OS and DCS. These predictions can be used to test the applicability of OS theories to natural coastal ecosystems.

We present a tree algorithm, called the willow tree, for financial derivative pricing. The setup of the tree uses a fixed number of spatial nodes at each time step. The transition probabilities are determine by solving linear programming problems. The willow tree method is radically superior in numerical performance when compared to the binomial tree method.

The present thesis provides a definite answer to the question of how comparisons of certain aggregate quantities and price levels should be made across two or more geographic regions. It does so from the viewpoint of both economic theory and the “test” (or “axiomatic”) approach to index-number theory. Chapter 1 gives an overview of the problem of multilateral interspatial comparisons and introduces the rest of the thesis. Chapter 2 focuses on a particular domain of comparison involving consumer goods and services, countries and households in developing a theory of international comparisons in terms of the the (Kontis-type) cost-of-living index. To this end, two new classes of purchasing power parity measures are set out and the relationship between them is explored. The first is the many-household analogue of the (single-household) cost-of-living index and, as such, is rooted in the theory of group cost-of-living indexes. The second Consists of sets of (nominal) expenditure-share deflators, each corresponding to a system of (real) consumption shares for a group of countries. Using this framework, a rigorous exact index- number interpretation for Diewert’s “own-share” system of multilateral quantity indexes is provided. Chapter 3 develops a novel multilateral test approach to the problem at hand by generalizing Eichhorn and Voeller’s bilateral counterpart in a sensible manner. The equivalence of this approach to an extended version of Diewert’s multilateral test approach is exploited in an assessment of the relative merits of several alternative multilateral comparison formulae motivated outside the test-approach framework. Chapter 4 undertakes an empirical comparison of the formulae examined on theoretical grounds in Chapter 3 using an appropriate cross-sectional data set constructed by the Eurostat—OECD Purchasing Power Parity Programme. The principal aim of this comparison is to ascertain the magnitude of the effect of choosing one formula over another. In aid of this, a new indicator is proposed which facilitates the measurement of the difference between two sets of purchasing power parities, each computed using a different multilateral index-number formula.

This thesis includes three essays which examine the implications of incorporating parameter heterogeneity, consideration set heterogeneity, and decision rule heterogeneity, respectively, in brand choice models. In the first essay, we identify the conditions under which unaccounted for price response heterogeneity results in a spurious sticker shock effect. We show, using an analytical derivation, a simulation study and an empirical application to scanner panel data, that estimates of the sticker shock effect may be biased if households that are price sensitive in their brand choice decision are also more likely to respond to category marketing activity in their purchase timing decision. The empirical results, from two product categories, show that the sticker shock coefficient from a Hierarchical Bayes model (which continuously accounts for price response heterogeneity) is statistically insignificant, providing no evidence of the existence of a sticker shock effect. In contrast, the corresponding coefficient from the standard model, which ignores this heterogeneity, is highly significant and supports the existence of a sticker shock effect. A posterior analysis of household parameters confirms the hypothesized relationship between price sensitivity in brand choice and responsiveness to promotional activity in purchase incidence, and is consistent with our explanation of the underlying cause of the bias in the standard model. The second essay develops a new consideration set model that can be estimated with scanner panel data. In contrast to many previous approaches, which require enumeration of all possible consideration sets, we directly model uncertainty about including a brand in the consideration set. The resulting inclusion probabilities for brands reflect a "fuzzy" consideration set in the sense that a brand belongs to the consideration set only probabilistically. The proposed fuzzy set model outperforms several previous consideration set models in two product categories (yogurt and ketchup). We then apply the fuzzy set approach to examine the role of the consideration set in moderating the impact of advertising on price sensitivity. In contrast to the experimental findings of Mitra and Lynch (1995), we find no positive relationship between consideration set size and price sensitivity. Further empirical test may be necessary to confirm the hypothesized relationship. In the third essay, we investigate the role of decision rule heterogeneity in brand choice behavior. We develop a flexible model, which allows for the uncertainty in decision rules used by the consumer. Specifically, we develop a Hierarchical Bayes model of reference price effects that accommodates both the sticker shock and reference-dependent formulations. In addition, we also incorporate the possibility that consumers may mix the two decision rules probabilistically. Therefore, the proposed model allows for three different decision hierarchies which incorporate sticker shock, reference-dependent and mixed rules respectively. The empirical results show that consumers differ not only in their preference and response but also in their decision rules. On average, half the sample households appear to show loss aversion, i.e., follow a reference-dependent decision rule, while the remaining households do not seem to respond to reference prices. The proposed model provides a richer description of consumer choice processes than the comparison models that allow for only one model structure and ignore model uncertainty.

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