A limit theorem to a time-fractional diffusion

We prove a limit theorem for an integral functional of a Markov process. The Markovian dynamics is characterized by a linear Boltzmann equation modeling a one-dimensional test particle of mass $\lambda^{-1}\gg 1$ in an external periodic potential and undergoing collisions with a background gas of particles with mass one. The object of our limit theorem is the time integral of the force exerted on the test particle by the potential, and we consider this quantity in the limit that $\lambda$ tends to zero for time intervals on the scale $\lambda^{-1}$. Under appropriate rescaling, the total drift in momentum generated by the potential converges to a Brownian motion time-changed by the local time at zero of an Ornstein-Uhlenbeck process.Comment: 35 page

The Effect of Historical Entitlements in Cooperative Bargaining Over Evironment Policy: An Experimental Test

Collaborative policy making has been an increasingly popular method of solving use conflicts on public lands. Representatives of interested groups are authorized to negotiate land use policy in the shadow of a government imposed backstop policy. This process can be modeled using cooperative game theory over multiple goods in an Edgeworth Box framework, and its outcomes predicted using axiomatic bargaining theories (e.g. Pareto efficiency or the Nash bargain). A challenge for collaborative policymaking arises when users’ historical land use entitlements differ from the backstop the government will impose if negotiations fail. A challenge for the predictive power of axiomatic bargaining theory arises when the government’s backstop policy (and the Nash bargain it generates) creates substantial inequality of benefits among users. In this paper, we use laboratory experiments to test the effect on bargaining of 1) the divergence of historical entitlements from the prospective backstop and 2) the divergence of the Nash bargain generated by the backstop policy from the outcome that equalizes benefits. We examine the effects of both types of divergence on agreement rates, and on the likelihood that parties settle inside the bargaining lens, on the contract curve, and at the Nash bargain. We find that divergence of historical entitlements from the backstop significantly changes bargaining outcomes when the historical benefits were equally distributed and the benefits at the backstop and Nash are not. At the same time, historical entitlements do not affect outcomes when they were unequal but the backstop and Nash bargain generate equal benefits. We also find the outcomes parties reach are affected by the divergence of equality from the Nash bargain, independent of historical entitlement.Historical entitlements; Collaborative policy making; Land use conflicts

The Effect of Entitlements and Equality on Cooperative Bargaining with Private, Unverifiable Information

In many bargaining situations a third party is authorized to impose a backstop position on the bargainers. Prominent examples include governments who use collaborative policymaking between stakeholders to set public policy, but also compulsory arbitration in labour negotiations. Axiomatic models of cooperative bargaining, such as the Nash bargain, presume that the status quo allocation will have no effect on the outcome parties reach if it differs from the backstop set by the third party. In contrast, experimental findings have suggested that both equality of outcomes and entitlement (where the status quo establishes a focal point) may affect the agreements bargainers reach, at least under full information. This paper extends the investigation of the effect of equality and entitlement on cooperative bargaining to the case where parties have private, unverifiable information concerning the value of outcomes. We use a two-party, two-attribute experimental design in which subjects take part in unstructured, face-to-face bargaining to jointly select from among approximately 200 potential outcomes. We find that, relative to full information, parties who bargain under private information are almost as likely to reach agreements as those under full information, and that these agreements are still approximately Pareto efficient. Further, the effect of the status quo (rather than backstop) allocation seems amplified under private information, while the effect of equality is dampened, but not eliminated.cooperative bargaining; private information; Nash bargain; egalitarian; entitlement; fairness; focal points

Differential Time and Money Pricing as a Mechanism for In-kind Redistribution

We propose a mechanism to implement the distributional goal of "specific egalitarianism", or that allocation of a good be independent of income, but increasing in relative strength of preference or need. Governments could offer the good at multiple "outlets" that charge different money and time prices. Individuals would self-select between outlets based on time opportunity cost. We show conditions under which differential pricing achieves specific egalitarianism more efficiently than uniform public provision funded from income tax, with or without optional private purchase. Differential pricing becomes more efficient than uniform provision as 1) the relative importance of the good rises, 2) the elasticity of substitution between goods falls, 3) variation in preferences increases and 4) income inequality rises or the proportion of the poor falls.In-kind provision; specific egalitarianism; differential pricing

Does Higher Social Diversity Affect People’s Contributions to Local Schools? Evidence from New Zealand

New Zealand is becoming more socially diverse, in common with other Western countries. Primarily U.S. based-evidence suggests that growing diversity may lower people’s participation in society, and their contributions towards public goods. We test whether there is evidence of a similar relationship in New Zealand, specifically between social diversity and voluntary contributions towards local schools. We use data from the New Zealand Ministry of Education and the Census for the years 2001 and 2006 to estimate whether social heterogeneity affects a school’s ability to raise funds locally. Individual school revenue data is matched with measures of the heterogeneity of the neighbourhood in which the school is located. We consider heterogeneity by language, ethnicity, religion and income. After running cross-section and fixed effects regressions which control for other factors, we find only limited evidence that diversity affects the financial support schools receive from their local communities. We do find that higher nominal household income inequality lowers the revenues schools collect from fundraising, but not the revenues they receive from parental contributions or donations.heterogeneity; social capital; school contributions; fundraising

The Causes of Order Effects in Contingent Valuation Surveys: An Experimental Investigation

CV researchers have found that the hypothetical values respondents place on a nested sequence of environmental goods are sensitive to the order in which the goods are presented. Typically, the smallest bundle of goods is valued more highly if presented first than if following more comprehensive bundles. Such effects appear even when each bundle is valued from an "exclusive" list, or as an alternative to any other, so that income and substitution effects are controlled. Order of presentation has also affected the degree to which values are sensitive to scope. We conduct lab experiments where participants are asked to value sequences of nested goods for actual purchase from an exclusive list using the incentive compatible BDM mechanism. We test whether order effects occur in valuation for a) induced value goods, b) actual private goods, and c) identical private goods that are to be donated to charities. We find significant order effects when the goods are valued for own use, but not when they are valued for donation.Order effects; exclusive list; warm glow; contingent valuation

Paying Vs. Waiting in the Pursuit of Specific Egalitarianism

We propose an allocation mechanism for publicly providing a private good such that the final allocation is simultaneously independent of income and increasing in strength of preference or need. The "pay or wait" mechanism consists of offering the good for sale at two outlets. The 'queuing' outlet would charge a low money price per unit, but high waiting timer per unit. The 'pricing' outlet would charge a relatively high money price with rapid service. High wage individuals will opt for the pricing outlet, and low wage individuals the queuing outlet. If the policy maker stocks the outlets in proportion to the distribution of high and low wage earners in the population, consumers of both wages will purchase the same amount on average, while those who value the good more relative to other goods will receive more of it. These outcomes are at risk if the good can be privately resold, but may be preserved if the policy maker can create transactions costs associated with resale.In-kind provision; redistribution; specific egalitarianism