This paper concerns applications of variational analysis to some local aspects of behavioral science modeling by developing an effective variational rationality approach to these and related issues. Our main attention is paid to local stationary traps, which reflect such local equilibrium and the like positions in behavioral science models that are not worthwhile to quit. We establish constructive linear optimistic evaluations of local stationary traps by using generalized differential tools of variational analysis that involve subgradients and normals for nonsmooth and nonconvex objects as well as variational and extremal principles.
This chapter considers potential games, where agents play, each period, Nash worthwhile moves in alternation, such that their unilateral motivation to change rather than to stay, other players being supposed to stay, are high enough with respect to their resistance to change rather than to stay. This defines a generalized proximal alternating linearized algorithm, where resistance to change plays a major role, perturbation terms of alternating proximal algorithms being seen as the disutilities of net costs of moving.
Efficient biodiversity management strategies aim to allocate conservation efforts so as to maximize diversity in ecological systems. Toward this end, defining a diversity criterion is an important but challenging task, as several different indices can be used as biodiversity measures. This paper elicits and compares two criteria for biodiversity conservation based on indices stemming from different disciplines: Weitzman's index in economics and Rao's index in ecology. These indices use different approaches to combine information about measures of (1) the probability distributions of the species that are present in an ecosystem (i.e. survival probabilities) and (2) the degree of dissimilarity between these species. As an important step toward in situ conservation criteria, we add to these elements information about (3) the ecological interactions that take place between species. Considering a simple three-species ecosystem, we show that criterion choice has palpable policy implications, as it can sometimes lead to divergent management recommendations. We disentangle the roles played by elements (1), (2) and (3) in the ranking of outcomes, which allows us to highlight several specificities of the two criteria. An important result is that, other things being equal, Weitzman's in situ ranking tends to favor robust species that are least concerned with extinction, while Rao's in situ ranking generally gives priority to more vulnerable species that are closer to extinction.
What would be the analogue of the Lorenz quasi-ordering when the variable of interest is continuous and of a purely ordinal nature? We argue that it is possible to derive such a criterion by substituting for the Pigou-Dalton transfer used in the standard inequality literature what we refer to as a Hammond progressive transfer. According to this criterion, one distribution of utilities is considered to be less unequal than another if it is judged better by both the lexicographic extensions of the maximin and the minimax, henceforth referred to as the leximin and the antileximax, respectively. If one imposes in addition that an increase in someone’s utility makes the society better off, then one is left with the leximin, while the requirement that society welfare increases as the result of a decrease of one person’s utility gives the antileximax criterion. Incidentally, the paper provides an alternative and simple characterisation of the leximin principle widely used in the social choice and welfare literature.
The interplay between growth and public debt is addressed considering a Barro-type (1990) endogenous growth model where public spendings are financed through taxes on income and public debt. The government has a target level of public debt relative to GDP, and the long-run debt-to-GDP ratio is used as a policy parameter. We show that when debt is a large enough proportion of GDP, two distinct balanced-growth paths (BGPs) may coexist, one being indeterminate. We exhibit two types of important trade-offs associated with self-fulfilling expectations. First, we show that the lowest BGP is always decreasing with respect to the debt-to-GDP ratio while the highest one is increasing. Second, we show that the highest BGP, which provides the highest welfare, is always locally indeterminate while the lowest is always locally determinate. Therefore, local and global indeterminacy may arise and self-fulfilling expectations appear as a crucial ingredient to understand the impact of debt on growth, welfare, and macroeconomic fluctuations. Finally, a simple calibration exercise allows to provide an understanding of the recent experiences of many OECD countries.
We consider the link between birthplace and wages. Using a unique panel dataset, we estimate a raw elasticity of wages with respect to birthplace size of 4.2%, two thirds of the 6.8% raw elasticity with respect to city size. Part of this effect simply reflects intergenerational transmission and the spatial sorting of parents, part is explained by the role that birthplace size plays in determining current city size. Lifetime immobility explains a lot of the correlation between birthplace and current city size: we show that 43.7% of individuals only ever work while living in the place they were born. Our results highlight the importance of intergenerational and individual sorting in helping explain the persistence of spatial disparities.
We consider different approaches for assessing variable importance in clustering. We focus on clustering using binary decision trees (CUBT), which is a non-parametric top-down hierarchical clustering method designed for both continuous and nominal data. We suggest a measure of variable importance for this method similar to the one used in Breiman’s classification and regression trees. This score is useful to rank the variables in a dataset, to determine which variables are the most important or to detect the irrelevant ones. We analyze both stability and efficiency of this score on different data simulation models in the presence of noise, and compare it to other classical variable importance measures. Our experiments show that variable importance based on CUBT is much more efficient than other approaches in a large variety of situations.
Why do some OECD countries have high levels of procedural formalism (PF) in the housing market? We provide an explanation based upon complementarities between the strength of social networks and the stringency of procedural formalism. The interest of social networks is that conflict resolution is independent from the law. When local agents belong to social networks whereas non-local agents do not, PF may facilitate housing search for locals at the expense of non-locals. To illustrate this mechanism we build a search-theoretic model of the housing market. The model emphasizes that the demand for PF occurs when the size of social networks is large. By simulations, we show that the support for PF increases with the size of social networks, the default probability on the rent and the proportion of non-local agents.
This paper stresses a new channel through which global financial linkages contribute to the co‐movement in economic activity across countries. We show in a two‐country setting with borrowing constraints that international credit markets are subject to self‐fulfilling variations in the world real interest rate. Those expectation‐driven changes in the borrowing cost in turn act as global shocks that induce strong cross‐country co‐movements in both financial and real variables (such as asset prices, gross domestic product, consumption, investment, and employment). When firms around the world benefit from unexpectedly low debt repayments, they borrow and invest more, which leads to excessive supply of collateral and of loanable funds at a low interest rate, thus fueling a boom both at home and abroad. As a consequence, business cycles are synchronized internationally. Such a stylized model thus offers one way to rationalize both the existence of a world business‐cycle component, documented by recent empirical studies through dynamic factor analysis, and the factor's intimate link to global financial markets.
This article shows how the increase of information availability due to new technologies positively affects aggregate entrepreneurship in national economies. We rely on an “occupational choice” model of managerial production, extended to include the managerial use of information, to explain variations in the number of entrepreneurs, and thus of firms, as measured by the aggregate new business creation data. We present evidence that supports such a theory of industrial organization dynamics for a sample of 78 economies over the period 2004–2012 using panel data instrumental variable regressions.