A characterization of the distributions that imply mean—Variance utility functions

If there is a riskless asset, then the distribution of every portfolio is determined by its mean and variance if and only if the random returns are a linear transformation of a spherically distributed random vector. If there is no riskless asset, then the spherically distributed random vector is replaced by a random vector in which the last n ? 1 components are spherically distributed conditional on the first component, which has an arbitrary distribution. If the number of assets is infinite, then there must exist random variables m, v, y, where the distribution of y conditional on m and v is standard normal, such that every portfolio is distributed as some linear combination of m and vy. If there is a riskless asset, then m has zero variance. These distributions exhibit two-fund separability even if the utility function is not concave.     

The quartiles of the maximum entropy distribution

The quartile points and interquartile range of the maximum entropy (ME) distribution and sample distribution are compared, using expected values for sampling from a standard normal population. For sample sizes n?20 such that the sample quartile points are uniquely defined, the ME quartile points and interquartile range are found to have lower mean-squared error (MSE).     

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.     

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→∞.     

Development of the extended linear expenditure system from simple saving assumptions

The extended linear expenditure system (ELES) can be developed as an atemporal maximization of a Stone-Geary utility function wherein saving is treated as a good in itself. The key to this development is the a priori specification of the ‘subsistence quantity’ of saving, γ_{n + 1}, to be zero. Thus, the intertemporal maximization approach to the ELES is equivalent to specifying a Klein-Rubin saving function with γ_{n + 1} = 0 for a linear expenditure system (LES) based on permanent income rather than total expenditure. Any income concept - current, normal, or permanent, for example - is acceptable for the ELES developed from the atemporal maximization.     

The information matrix test: Simplified calculation via a score test interpretation

In Chesher (1982) I show that the Information Matrix test introduced by White (1982) is a score test for parameter constancy. In this letter I show that this result leads to a simple computational procedure for calculating the Information Matrix test. The procedure involves computing, for a sample of n observations, n times the R² from the least squares regression of a column of ones on a matrix whose elements are functions of 1st and 2nd derivatives of the log density function.     

Modelling the risk–return relation for the S&P 100: The role of VIX

A significantly positive risk–return relation for the S&P 100 market index is detected if the implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation. This result holds for 4 alternative GARCH specifications, irrespective of the conditional distribution, and regardless of whether the conditional mean equation includes a constant term. This finding is robust to sub-samples, and to using VIX innovations to control for dividend yield and trading volume effects. Monte Carlo evidence suggests that if VIX is not included, the risk–return relation is more likely to be negative or weak, in line with several previous studies. If VIX is included, the distribution of the risk–return parameter has more than 99% of its mass in the area of positive values. We conclude that VIX carries important forward-looking information which improves the precision of the conditional variance estimation and, subsequently, reveals a significantly positive relation.     

The expected probability of Condorcet's paradox

Let P(n,p) be the probability that there is a Condorcet winner on three alternatives for n (odd) voters. The vector p defines the probability that a randomly selected voter will have any of the six linear rankings on three alternatives as his or her preference ranking. It is shown that if all p vectors are equally likely, the expected value of P(n,p) is given by 15(n+3)²/[16(n+2)(n+4)].     

Length of stay and economic consequences with rivaroxaban vs enoxaparin/vitamin K antagonist in patients with DVT and PE: findings from the North American EINSTEIN clinical trial program

Objective:

Venous thromboembolism (VTE) (deep vein thrombosis [DVT] and pulmonary embolism [(PE]) represents a substantial economic burden to the healthcare system. Using data from the randomized EINSTEIN DVT and PE trials, this North American sub-group analysis investigated the potential of rivaroxaban to reduce the length of initial hospitalization in patients with acute symptomatic DVT or PE.

Methods:

A post-hoc analysis of hospitalization and length-of-stay (LOS) data was conducted in the North American sub-set of patients from the randomized, open-label EINSTEIN trial program. Patients received either rivaroxaban (15?mg twice daily for 3 weeks followed by 20?mg once daily; n?=?405) or dose-adjusted subcutaneous enoxaparin overlapping with (guideline-recommended ‘bridging’ therapy) and followed by a vitamin K antagonist (VKA) (international normalized ratio?=?2.0–3.0; n?=?401). The open-label study design allowed for the comparison of LOS between treatment arms under conditions reflecting normal clinical practice. LOS was evaluated using investigator records of dates of admission and discharge. Analyses were carried out in the intention-to-treat population using parametric tests. Costs were applied to the LOS based on weighted mean cost per day for DVT and PE diagnoses obtained from the Healthcare Cost and Utilization Project dataset.

Results:

Of 382 patients hospitalized, 321 (84%), had acute symptomatic PE; few DVT patients required hospitalization. Similar rates of VTE patients were hospitalized in the rivaroxaban and enoxaparin/VKA treatment groups, 189/405 (47%) and 193/401 (48%), respectively. In hospitalized VTE patients, rivaroxaban treatment produced a 1.6-day mean reduction in LOS (median?=?1 day) compared with enoxaparin/VKA (mean?=?4.5 vs 6.1; median?=?3 vs 4), translating to total costs that were $3419 lower in rivaroxaban-treated patients.

Conclusion:

In hospitalized North American patients with VTE, treatment with rivaroxaban produced a statistically significant reduction in LOS. When treating DVT and PE patients, clinicians should consider newer anti-coagulants with less complex treatment regimens.     

Bonus pay for teachers,spatial sorting,and student achievement

Bonus pay policy for teachers in the U.S. is analyzed in this paper. We quantitatively argue that, because of the decentralized education finance system in the U.S., this policy may lead to higher teacher and household sorting across school districts. This then may lead to higher variance of achievement and lower mean achievement. Formally, we use an equilibrium political economy model of education at which households, heterogeneous in exogenously set income, and teachers, heterogeneous in exogenously set quality, are endogenously allocated across two school districts. Public education expenditures, which includes teachers’ wage payment and non-teacher related education spending, are financed through local income taxation. Income tax rate in each district is determined via majority voting. Achievement depends on the efforts chosen by teachers and non-teacher related education spending. Teacher efficiency wage per unit of quality is determined at the national teacher labor market. We first calibrate our benchmark model by matching certain statistics from the U.S. data. Then in a computational experiment, we introduce bonus pay for teachers which rises with average achievement. We find that for the recently observed level of average bonus pay (6.59% of average base salary), variance of achievement is 2.46% higher and mean achievement is 1.79% lower than the benchmark. Variance of achievement reaches its peak when average bonus pay is 14.06% and then it starts falling. Also, mean achievement always falls as average bonus pay rises.     

Resource use in patients hospitalized with complicated skin and soft tissue infections in Europe and analysis of vulnerable groups: the REACH study

Background:

Hospitalized patients with complicated skin and soft tissue infections (cSSTI) present a substantial economic burden, and resource use can vary according to the presence of comorbidities, choice of antibiotic agent, and the requirement for initial treatment modification. REACH (NCT01293435) was a retrospective, observational study aimed at collecting empirical data on current (year 2010–2011) management strategies of cSSTI in 10 European countries.

Methods:

Patients (n?=?1995) were aged ≥18 years, hospitalized with a cSSTI and receiving intravenous antibiotics. Data, collected via electronic Case Report Forms, detailed patient characteristics, medical history, disease characteristics, microbiological diagnosis, disease course and outcomes, treatments before and during hospitalization, and health resource consumption.

Results:

For the analysis population, mean length of hospital stay (including duration of hospitalizations for patients with recurrences) was 18.5 days (median 12.0). Increased length of hospital stay was found for patients with comorbidities vs those without (mean?=?19.9; [median?=?14.0] days vs 13.3 [median?=?8.0] days), for patients with methicillin-resistant Staphylococcus aureus compared with patients with methicillin-sensitive S. aureus (mean?=?27.7 [median?=?19.5] days vs 18.4 [median?=?13.0] days) and for patients requiring surgery (mean?=?24.4 [median?=?16.0] days vs 15.0 [median?=?11.0] days). Patients requiring modification of their initial antibiotic treatment had an associated increase in mean length of hospital stay of 10.9 days (median?=?6.5) and additional associated hospital resource use. A multivariate analysis confirmed the association of nosocomial infections, comorbidities, directed treatment, recurrent infections, diabetes, recent surgery, and older age (≥65 years), with longer hospital stay.

Conclusions:

This study provides real-life data on factors that are expected to impact length of hospital stay, to guide clinical decision-making to improve outcomes, and reduce resource use in patients with cSSTI.     

Tax competition,tax exporting and higher-government choice of tax instruments for local governments

This paper presents a theoretical model with tax exporting due to external ownership of a fraction θ of the land in each local jurisdiction. There are n local jurisdictions in a metropolitan area (n≥1) and many metropolitan areas in a world economy. The paper examines the usage of business property taxes and source-based wage taxes by local jurisdictions, first in the presence of and then in the absence of residence-based lump-sum taxes, and how this depends on θ and n. The paper then examines the choice of a world, national or state government as to whether to allow local (metropolitan or sub-metropolitan) governments to use business property taxes, wage taxes or both, assuming that the local governments choose the actual tax rates.     

A proposed convention for measuring the state of the art of products or processes

During 1980, The Futures Group performed a study under contract to the National Science Foundation to devise a convention for describing—in quantitative terms—technological state of the art of essential any technology. In designing this convention we hope that different analysts, working independently, would be able to arrive at a similar conclusion about the state of the art of a technology under study. With such a measure at hand, it would be possible, for example, to evaluate the effectiveness of investment in R&D by evaluating the improvement in the technological state of the art of a given technology, per unit investment.The form of the equation chosen for the state-of-the-art convention was SOA = K₁(P₁/P'₁ + K₂(P₂/P'₂) ? K_n(P_n/P'_n) where SOA = state of the art, K_n = the relative weight associated with each parameter describing the technology, P_n = the value of the particular parameter useful in describing the state of the art, and P'_n = a reference value of the parameter. Various approaches to the selection of the parameters and their weights were described. Of particular interest is a statistical approach which assumes that the state of the art, over time, is an S-shaped curve. In this instance it is possible to compute the value of the weights through an iterative numerical technique.The convention was applied to two technologies: computers and antibiotics, and state-of-the-art measures were developed for each. In the case of antibiotics, selected organism/antibiotic pairs were analyzed to identify the state of the art of a particular antibiotic as applied to the control of a particular microorganism, over time.     

Adaptive behavior and the existence of Weizsäcker's long-run indifference curves

Suppose that past consumptions of the first r commodities (r < n) influence present consumption. Then, the long-run demand function to which demand converges maximizes the equilibrium short-run utility function only under very restrictive conditions. The long-run demand functions can be rationalized by a utility function, different from the equilibrium short-run utility function, if and only if the short-run utility function is such that past consumptions of any good that experience, learning, or taste changes is separable from all other goods. The class of such utility functions has been found.     

A progress report on Kelly's majority conjectures

LetC(m, n) be the proportion of n-voter profiles on m alternatives that have a majority winner. Jerry Kelly conjectured that C(m, n) > C(m + 1, n) for m ? 3 and n = 3 and n ? 5, and C(m, n) > C(m, n + 2) for m ? 3 and n ? 3. We prove these for special cases.     

Nonparametric measures of returns to scale: an application to German water supply

The evaluation of market structures and the quantification of returns to scale in network industries usually are of high interest for researchers and policy makers. Regarding the debate on optimal market structures in German potable water supply, we use a cross-sectional sample of 364 German water utilities observed in 2006 to derive a nonparametric measure of scale elasticity for the water industry. The data sample is validated by applying a super-efficiency approach and a statistical testing procedure for outlier detection. Besides using a standard data envelopment analysis approach, a conditional efficiency approach is applied to account for the water utilities’ operating environments. The results indicate non-decreasing returns to scale for the majority of water utilities and constant or non-increasing returns for larger utilities. Optimal firm size is found to be generally larger than the current sample median firm size. Efficiency improvements could be realized by increases in firm sizes and through a consolidation of the industry.     

A new test for D-stability

A sufficient condition for D-stability of an n × n matrix A is the existence of a positive diagonal matrix P such that PA + A′P is negative definite. The search for P is replaced by solving a convex minimization problem.     

Passing the Buck On the acceptance of responsibility

In the Passing the Buck game, the n members of a group decide in a given order whether or not to incur costs so that they can fix a certain problem for the benefit of the group. Passing the Buck means that one relies on the service of a successor. The decision is influenced by social preferences and by strategic considerations. We derive three main conclusions from experiments with n=3 and n=4. (i) The unique perfect Baysian equilibrium of the Passing the Buck game with incomplete information about the preferences of other players generally fits the data, however with two interesting exceptions. (ii) Backward induction breaks down if it requires more than two steps, i.e., for the first player in the game with n=4. (iii) Making one of the members of the group an “expert” who alone is competent to fix the problem is connected with a change of social preferences.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.