Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Satisfaction in choice as a function of the number of alternatives: When "goods satiate" but "bads escalate"

Whereas people are typically thought to be better off with more choices, studiesshow that they often prefer to choose from small as opposed to large sets of alternatives.We propose that satisfaction from choice is an inverted U-shaped function of thenumber of alternatives. This proposition is derived theoretically by considering thebenefits and costs of different numbers of alternatives and is supported by fourexperimental studies. We also manipulate the perceptual costs of information processingand demonstrate how this affects the resulting satisfaction function. We furtherindicate that satisfaction when choosing from a given set is diminished if people aremade aware of the existence of other choice sets. The role of individual differences insatisfaction from choice is documented by noting effects due to gender and culture. Weconclude by emphasizing the need to have an explicit rationale for knowing how muchchoice is enough.

Financing local development: Quasi-experimental evidence from municipalities in Brazil, 1980-1991

This paper uses a regression discontinuity design to estimate the impact of additional unrestrictedgrant financing on local public spending, public service provision, schooling, literacy, andincome at the community (municipio) level in Brazil. Additional transfers increased local publicspending per capita by about 20% with no evidence of crowding out own revenue or otherrevenue sources. The additional local spending increased schooling per capita by about 7% andliteracy rates by about 4 percentage points. The implied marginal cost of schooling -accountingfor corruption and other leakages- amounts to about US$ 126, which turns out to be similar tothe average cost of schooling in Brazil in the early 1980s. In line with the effect on human capital,the poverty rate was reduced by about 4 percentage points, while income per capita gains werepositive but not statistically significant. Results also suggest that additional public spending hadstronger effects on schooling and literacy in less developed parts of Brazil, while poverty reductionwas evenly spread across the country.

Cost efficiency in primary care contracting: A stochastic frontier cost function approach

The principal aim of this paper is to estimate a stochastic frontier costfunction and an inefficiency effects model in the analysis of the primaryhealth care services purchased by the public authority and supplied by 180providers in 1996 in Catalonia. The evidence from our sample does not supportthe premise that contracting out has helped improve purchasing costefficiency in primary care. Inefficient purchasing cost was observed in thecomponent of this purchasing cost explicitly included in the contract betweenpurchaser and provider. There are no observable incentives for thecontracted-out primary health care teams to minimise prescription costs, whichare not explicitly included in the present contracting system.

Finance versus costs for teaching hospitals in Spain

In this paper we analyse the observed systematic differences incosts for teaching hospitals (THhenceforth) in Spain. Concernhas been voiced regarding the existence of a bias in thefinancing of TH s has been raised once prospective budgets arein the arena for hospital finance, and claims for adjusting totake into account the legitimate extra costs of teaching onhospital expenditure are well grounded. We focus on theestimation of the impact of teaching status on average cost. Weused a version of a multiproduct hospital cost function takinginto account some relevant factors from which to derive theobserved differences. We assume that the relationship betweenthe explanatory and the dependent variables follows a flexibleform for each of the explanatory variables. We also model theunderlying covariance structure of the data. We assumed twoqualitatively different sources of variation: random effects andserial correlation. Random variation refers to both general levelvariation (through the random intercept) and the variationspecifically related to teaching status. We postulate that theimpact of the random effects is predominant over the impact ofthe serial correlation effects. The model is estimated byrestricted maximum likelihood. Our results show that costs are 9%higher (15% in the case of median costs) in teaching than innon-teaching hospitals. That is, teaching status legitimatelyexplains no more than half of the observed difference in actualcosts. The impact on costs of the teaching factor depends on thenumber of residents, with an increase of 51.11% per resident forhospitals with fewer than 204 residents (third quartile of thenumber of residents) and 41.84% for hospitals with more than 204residents. In addition, the estimated dispersion is higher amongteaching hospitals. As a result, due to the considerable observedheterogeneity, results should be interpreted with caution. From apolicy making point of view, we conclude that since a higherrelative burden for medical training is under public hospitalcommand, an explicit adjustment to the extra costs that theteaching factor imposes on hospital finance is needed, beforehospital competition for inpatient services takes place.

A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

A low dimensional Kalman filter for systems with lagged observables

This note describes how the Kalman filter can be modified to allow for thevector of observables to be a function of lagged variables without increasing the dimensionof the state vector in the filter. This is useful in applications where it is desirable to keepthe dimension of the state vector low. The modified filter and accompanying code (whichnests the standard filter) can be used to compute (i) the steady state Kalman filter (ii) thelog likelihood of a parameterized state space model conditional on a history of observables(iii) a smoothed estimate of latent state variables and (iv) a draw from the distribution oflatent states conditional on a history of observables.

Firm investment in imperfect capital markets: A structural estimation

We set up a dynamic model of firm investment in which liquidity constraintsenter explicity into the firm's maximization problem. The optimal policyrules are incorporated into a maximum likelihood procedure which estimatesthe structural parameters of the model. Investment is positively related tothe firm's internal financial position when the firm is relatively poor. This relationship disappears for wealthy firms, which can reach theirdesired level of investment. Borrowing is an increasing function of financial position for poor firms. This relationship is reversed as a firm's financial position improves, and large firms hold little debt.Liquidity constrained firms may be unused credits lines and the capacity toinvest further if they desire. However the fear that liquidity constraintswill become binding in the future induces them to invest only when internalresources increase.We estimate the structural parameters of the model and use them to quantifythe importance of liquidity constraints on firms' investment. We find thatliquidity constraints matter significantly for the investment decisions of firms. If firms can finance investment by issuing fresh equity, rather than with internal funds or debt, average capital stock is almost 35% higher overa period of 20 years. Transitory shocks to internal funds have a sustained effect on the capital stock. This effect lasts for several periods and ismore persistent for small firms than for large firms. A 10% negative shock to firm fundamentals reduces the capital stock of firms which face liquidityconstraints by almost 8% over a period as opposed to only 3.5% for firms which do not face these constraints.

A non-quasi-competitive Cournot oligopoly with stability

This paper presents a classical Cournot oligopoly model with some peculiar features: it is non--quasi--competitive as price under N-poly is greater than monopoly price; Cournot equilibrium exists and is unique with each new entry; the successive equilibria after new entries are stable under the adjustment mechanism that assumes that actual output of each seller is adjusted proportionally to the difference between actual output and profit maximizing output. Moreover, the model tends to perfect competition as N goes to infinity, reaching the monopoly price again.

Audit quality: Attributes, private safeguards and the role of regulation

This article examines the private mechanisms used to safeguard quality in auditing, with a view to defining rules capable of facilitating the performance of market forces. An outline is given of a general theory of private quality assurance in auditing, based on the use of quasi-rents to self-enforce quality dimensions. Particular attention is paid to the role of fee income diversification as the key ingredient of private incentives for audit quality. The role of public regulation is then situated in the context defined by the presence of these safeguard mechanisms. This helps in defining the content of rules and the function of regulatory bodies in facilitating and strengthening the protective operation of the market. By making sense of the interaction between regulation, quality attributes and private safeguards, the analysis helps to evaluate the relative merits of different regulatory options.

The quasi-judicial role of large retailers: An efficiency hypothesis of their relation with suppliers

The paper explores an efficiency hypothesis regarding the contractual process between large retailers, such as Wal-Mart and Carrefour, and their suppliers. The empirical evidence presented supports the idea that large retailers play a quasi-judicial role, acting as "courts of first instance" in their relationships with suppliers. In this role, large retailers adjust the terms of trade to on-going changes and sanction performance failures, sometimes delaying payments. A potential abuse of their position is limited by the need for re-contracting and preserving their reputations. Suppliers renew their confidence in their retailers on a yearly basis, through writing new contracts. This renovation contradicts the alternative hypothesis that suppliers are expropriated by large retailers as a consequence of specific investments.

When are layoffs acceptable? Evidence from a quasi-experiment

Many authors have discussed a decline in internal labor markets and an apparent shift to a new employment contract, characterized by less commitment between employer and employee and more portable skills. These discussions occur without much evidence on what employment contract employees currently feel is fair. We perfomed quasi-experimental surveys to study when employees in the U.S. andCanada feel that layoffs are fair.Layoffs were perceived as more fair if they were due to lower product demand than if the result of employee suggestions. This result appears to be solely due to norms of reciprocity (companiesshould not punish employees for their efforts), rather than norms of sharing rents, as new technology was also considered a justification for layoffs.Consistent with theories of distributive and procedural equity, layoffs were perceived as more fair if the CEO voluntarily shared the pain. CEO bonuses due to layoffs lowered their reported fairness only slightly.Respondents in Silicon Valley were not more accepting of layoffsthan were those in Canada on average, although the justificationsconsidered valid differed slightly.

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.