Optimal scrutiny in multi-period promotion tournaments

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their skills, and intends to promote one of them at the end. In each period the agents choose effort levels that influence their outputs, and are fully informed of the past history of outputs. The principal's major objective is to maximize the expected total output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and promotes the agent who produces more on the sample. This determines an extensive form game Γ(T,n), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n. More precisely, if η(T) is the maximal optimal sample size, then η(T)/T→0 as T→∞.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

Social insurance for the elderly

We study the effects of retirement benefits provided by social insurance programs on consumption, portfolio choice, and retirement in a continuous-time theoretical model. We show that people tend to retire earlier with an increase in retirement social insurance benefits (SIBs), consistent with empirical evidence. We show also that people tend to increase savings before retirement in anticipation of increased retirement benefits, a counter-intuitive result. The response of risky investment with an increase in the SIBs is ambiguous, depending on parameter values. The overall social welfare will increase with an increase in SIBs if the balanced budget constraint is satisfied. We also investigate the effects of changes in the two streams of the SIBs (paid in perishable goods and cash) and the proportion of workers in entire population on social welfare.     

IS-LM stability and economic policy effectiveness: A note

Accepting the findings of Weber (1970) and Yarrow (1975), Cebula finds that conventional fiscal policy has its usual positive effect on the level of income while monetary policy has a negative impact. This paper shows that if a budget constraint of the specific, simplified form G ? T = ΔM is added to the model, the results differ from Cebula's.     

The micro economics of group behavior: General characterization

We study the demand function of a group of S members facing a global budget constraint. Any vector belonging to the budget set can be consumed within the group, with no restriction on the form of individual preferences, the nature of individual consumptions or the form of the decision process beyond efficiency. Moreover, only the group aggregate behavior, summarized by its demand function, is observable. We provide necessary and (locally) sufficient restrictions that fully characterize the group's demand function, with and without distribution factors. We show that the private or public nature of consumption within the group is not testable from aggregate data on group behavior.     

Friedman meets Becker and Mulligan in a monetary neoclassical growth model

We study a neoclassical growth model with the time preference determined by resources spent on imagining future pleasures along the line of Becker and Mulligan (Q J Econ 112:729–758, 1997). We introduce money into the economy via a cash-in-advance constraint and study the effect of higher seignorage taxes or higher monetary growth rates on capital, consumption and welfare in the long run. We find that if the fraction of investment constrained by cash is smaller than a threshold, the negative-monetary-growth Friedman (The Optimum Quantity of Money and Other Essays, 1969) rule does not hold and the optimal inflation rate is positive. Calibrating our model yields a mild optimal inflation rate per annum with a switch from zero inflation to optimal inflation creating a sizable welfare gain in terms of consumption equivalence.     

The sufficiency strategy: Would rich-world frugality lower environmental impact?

One alleged weapon against unsustainable environmental impact is for the wealthy to consume less. This sufficiency strategy is to complement the efficiency strategy of lowering ratios of resource inputs to economic outputs; the former would reduce the affluence factor in I = PAT, the latter the technology factor. That the latter strategy suffers from a consumption rebound is widely recognized. This paper identifies a similar rebound when the affluence factor is autonomously lowered: The lower initial demand lowers prices, which in turn stimulates new demand by others. The strategy moreover addresses only the rich, raising questions of its theoretical maximum efficacy. Its proponents usually conflate frugality with the North-South dichotomy and intragenerational with intergenerational equity. Moreover, there are difficulties with the supporting arguments that frugality is good for one’s own sake as well as for the environment, and that the rich should ‘lead the way’ to living more lightly. Personal behaviour change is furthermore not a substitute for international political efforts. Finally, since all changes in right-side factors of the I = PAT equation change other right-side factors, such indirect attacks on impact should be abandoned in favor of supply and emissions quotas.     

“Overreaction” of Asset Prices in General Equilibrium

We attempt to explain the overreaction of asset prices to movements in short-term interest rates, dividends, and asset supplies. The key element of our explanation is a margin constraint that traders face which limits their leverage to a fraction of the value of their assets. Traders may lever themselves, furthermore, either directly by borrowing short term or indirectly by engaging in futures and options trading, so that the scenario is relevant to contemporary financial markets. When some shock pushes asset prices to a low enough level at which the margin constraint binds, traders are forced to liquidate assets. This drives asset prices below what they would be with frictionless markets. Also, a shock which simply increases the likelihood that the margin constraint will bind can have a very similar effect on asset prices. We construct a general equilibrium model with margin constrained traders and derive some qualitative properties of asset prices. We present an analytical solution for a deterministic version of the model and a simple numerical computation of the stochastic version.Journal of Economic LiteratureClassification Numbers: G1, E0.     

Minimum payments and induced effort in moral hazard problems

Consider a moral hazard problem in which there is a constraint to pay the agent no less than some amount m. This paper studies the effect of changes in m on the effort that the principal chooses to induce from the agent. We present sufficient conditions on the informativeness of the signal observed by the principal and on the agentʼs utility under which when m increases, induced effort (and hence productivity) falls. We also study how the cost minimizing contract for any given effort level varies in m. We present an efficient algorithm for numerically calculating optimal contracts for given parameters and show that induced effort falls when m is increased in many cases even when our sufficient conditions fail.     

The economic impacts of river rehabilitation: A regional Input-Output analysis

We developed a model to predict the impacts of river rehabilitation activities on the local economy. The model is based on the Input-Output analysis technique and was applied to the planned rehabilitation project for the River Thur in northern Switzerland, along the 4 km stretch between the communities of Bürglen and Weinfelden. We estimated changes in local employment and local economic output resulting from government spending on rehabilitation, associated changes in adjacent land use, and increased recreational activity. Accounting for land use changes required a modification of the conventional Input-Output analysis technique which should be of general interest. We accounted for uncertainty in the data and in some of the model assumptions by using a probabilistic formulation and propagating uncertainty through the model equations. As time-consuming local surveys were beyond the scope of this study, we used the Location Quotient non-survey technique to construct the local technical coefficients from national data and local employment data. This implies that the model can be applied quite easily to a different study area in Switzerland as long as local employment data are available. For each CHF 1 million expenditure per year on rehabilitation activities in our study region, we estimate an extra 8 fulltime employment equivalents (standard deviation, σ = 0.4 fte) and an increased output of CHF 1.4 million (σ = CHF 0.05 million). The low uncertainty of these estimates can be partly attributed to the structure of Input-Output analysis and partly to the fact that we estimated changes in the economic output, rather than output itself. In addition to the above impacts, we estimate that increased recreational use of the area will increase output by as much as CHF 0.17 million (σ = CHF 0.12 million) and employment by as much as 1.7 fulltime employment equivalents (σ = 1.3 fte), depending on the specific rehabilitation option selected.     

Quantification of the environmental impacts of road conditions in Brazil

This study evaluates the impacts of Brazilian highway conditions on fuel consumption and, consequently, on carbon dioxide (CO₂) emissions. For the purpose of this study, highway conditions refer to the level of highway maintenance: the incidence of large potholes, large surface cracks, uneven sections, and debris. Primary computer collected data related to the fuel consumption of three types of trucks were analyzed. The data were derived from 88 trips taken over six routes, each route representative of one of two highway conditions: better or worse. Study results are initially presented for each type of truck being monitored. The results are then aggregated to approximate the entire Brazilian highway network. In all cases, results confirmed environmental benefits resulting from travel over the better routes. There was found to be an increase in energy efficiency from traveling better roads, which resulted in lower fuel consumption and lower CO₂ emissions. Statistical analysis of the results suggests that, in general, fuel consumption data were significant at *P < 0.05, rejecting the null hypothesis that average fuel consumption from traveling the better routes is statistically equal to average fuel consumption from traveling the worse routes. Improved Brazilian road conditions would generate economic benefits, reduce dependency on and consumption of fossil fuels (due to the increase in energy efficiency), and reduce CO₂ emissions. These findings may have additional relevancy if Brazil needs to reduce carbon dioxide emissions to reach future Kyoto Protocol's emissions targets, which should take effect in January 2013.     

Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment

We propose a possibilistic portfolio model with VaR constraint and risk-free investment based on the possibilistic mean and variance, while assuming that the expected rate of returns is a fuzzy number. The model shows more clearly that, in the financial market affected by several non-probabilistic factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure that the maximum of their possible future risk is lower than an expected loss. Under the condition that the expected rate of returns is a normal distribution fuzzy variable, we proposed a theorem as the solution, and derive a crisp equivalent form of the possibilistic portfolio under constraints of VaR and risk-free investment. This model is an expansion of the fuzzy possibilistic mean–variance model by Zhang (2007). Finally, an empirical study is carried out using the data concerning some stocks of various industries listed at the Shanghai Stock Exchange. A conclusion is reached that the investors are able to choose a portfolio more suitable to them under the VaR constraint.     

Zero-sum condition: A necessary and sufficient condition for a transitive voting system

A simple and quick way to ascertain whether or not any given majority voting system can always produce a transitive social preference orderings without imposing any restriction on the distribution of diverse individual preference orderings is to examine whether all individual voting (preference) vectors satisfy the Addition Rule or not. This conclusion was obtained by first reformulating the voting mechanism into that of a linear mapping from T^m defined by q = Σp_i. It was found that the subset P of T that can accommodate all possible individual preference ordering profiles and such that every sum vector q = Σ p_i of its member vectors p_i is contained in T can be expressed as P = {p: p∈ T, s(p) = 0}. It was also pointed out that this is equivalent to the requirement that all individual preference (voting) functions must satisfy the Addition Rule. Finally, Borda's Rule and Saposnik's Contributive Rule were shown to be examples of transitive voting rules which satisfy these necessary and sufficient conditions.     

Computation of search duration probabilities and the integral of the normal distribution function

The constraction of likelihood functions for data on individuals assumed to be sampling from a price distribution and operating a reservation price policy involves calculation of the probability that their duration of search exceeds, say, t periods, P( T > t). In this note we show how this calculation can be simply done by (a) working in continuous time, and (b) using a result on the integral of the Normal distribution function. We then use the result to study some properties of the model.     

An Afriat Theorem for the collective model of household consumption

We provide a nonparametric ‘revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex. Our main result is the Collective Afriat Theorem, which parallels the well-known Afriat Theorem for the unitary model. First, it provides a characterization of collectively rational consumption behavior in terms of collective Afriat inequalities. Next, it implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality. Finally, the theorem has some interesting testability implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.     

Minimal conditions for upper-hemicontinuity of the choice correspondence

We denote by ?(M, r) the set of all maximal elements in the constraint set M with respect to a (partial) order r and find the coarsest topologies on the domain of ? such that ? is u.h.c.     

Pareto-optimal Nash equilibria are competitive in a repeated economy

Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in the time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.     

Financial liberalization and short-run housing price dynamics

We develop a continuous time, rational expectations, multi-cohort model of an exchange economy with housing, the purchase of which is subject to a down payment (DP) constraint. The timing of the house purchase decision is a crucial endogenous variable, and four determinants of it are identified – the housing services effect, the interest discounting effect, the consumption smoothing effect, and the rate of price increase effect. Cohort effects, and supply constraints, play crucial roles at the aggregative level. We explore in detail the effects of a discrete financial liberalization, and show that if the liberalization is not announced sufficiently far in advance, housing prices will initially overshoot the new stationary equilibrium, and vice versa. Particular attention is paid to the possibility that for a subset of cohorts along the transition path the DP constraint will not bind. An interesting ‘Prisoners’ Dilemma’ is also identified, and policy implications discussedJEL Classification Numbers: E3, R21Valuable comments and suggestions from Phillip Brock, Ho Kong-Weng, Liu Haoming, David McKenzie, David Miles, Jacques Olivier, Phang Sock-Yong, J. Thampapillai, Ping Wang, Wong Wing-Keung, and Zeng Jinli are gratefully acknowledged. I am also immensely indebted to an anonymous referee, whose incisive, deep and patient comments, on successive drafts, helped greatly to sharpen and improve the paper, as well as to the Editor and the Co-Editor, Professor Mordecai Kurz, for their invaluable advice and encouragement. An earlier version was presented at a Conference in Honour of Ronald McKinnon, held at Stanford University in June 2002     

When expectations become aspirations: reference-dependent preferences and liquidity constraints

A large body of literature suggests that consumers derive utility from gains and losses relative to a reference point. This paper shows that such reference dependence can affect savings in opposite directions depending on whether people face liquidity constraints. Existing models for wealth and intertemporal choice predict that reference dependence reduces savings, but these models abstract from liquidity constraints. Introducing a liquidity constraint, I find that reference dependence can increase optimal savings for people without access to credit. Ex post, after reference points have been formed, liquidity constraints force consumers to take part of an income loss in early periods, inducing those who are reference dependent to concentrate the full loss in early periods and save in order to eliminate future losses. Further, anticipating a liquidity constraint raises the expected level of future consumption and thus the expectations-based reference point for future periods, creating an ex-ante savings motive. These findings underscore that it is important to account for financial market imperfections when applying or testing reference-dependent models in low-income settings, and potentially explain heterogeneity in how much the poor save when facing binding liquidity constraints.     

Time Delay and the Extraction of Information Rent in Regulation

A crucial idea in Laffont and Tirole (1993) is the extraction of costly information rent through production distortion. In this paper we augment the Laffont-Tirole model with time delay, highlighting the possibility of further rent extraction through consumption distortion due to the delayed implementation of a public project. This consumption distortion through delay in essence relaxes the incentive constraint in the presence of asymmetric information. We show that a positive but finite delay can be optimal in regulation, and provide a condition differentiating welfare-improving delays from welfare-worsening ones. This condition generalizes the shutdown condition of an inefficient firm in the Laffont-Tirole model.