higher education subsidies and heterogeneity a dynamic analysis abstract in this paper we develop a simple dynamic general equilibrium framework to address the effects of increasing higher education subsidies in the us from their already substantial levels on inequality welfare and efficiency we focus on three policies the first is a tax and subsidy scheme that ensures that the parental decision to send a child to college is independent of income such a policy decreases the efficiency of the utilization of education resources while the welfare gain is minimal the second policy maximizes the fraction of college educated labor this results in a large drop in the above mentioned efficiency with little or no welfare gain the third is the provision of merit based aid to the poor as opposed to purely need based aid this policy can increase education efficiency with little decrease in welfare based on these experiments we conclude that the case for further increases in higher education subsidies might have been overstated

efficient mechanisms for bilateral trading we consider bargaining problems between one buyer and one seller for a single object the seller s valuation and the buyer s valuation for the object are assumed to be independent random variables and each individual s valuation is unknown to the other we characterize the set of allocation mechanisms that are bayesian incentive compatible and individually rational and show the general impossibility of ex post efficient mechanisms without outside subsidies for a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade and mechanisms that can maximize a broker s expected profit journal of economic literature classification number 026

delay and settlement in litigation delay in litigation is a policy concern in many jurisdictions little evidence is available on the causes of such delay however we present a version of spier s 1992 bargaining model of litigation and derive directly a functional form for the conditional probability of case settlement we then estimate this and test predictions about the effects of legal costs and uncertainty over damages and liability on the conditional probability of settlement using data from negligence claims against several nhs trusts our results provide a direct test of the model and shed light on the causes of settlement delay in england

pretrial bargaining with asymmetric information unilateral versus bilateral payoff relevance author affiliation amy farmer amyf walton uark edupaul pecorino ppecorin cba ua edu acknowledgment we would like to thank akram temimi and two anonymous referees for providing helpful comments on the article 1 introductionasymmetric information is a leading explanation for bargaining failure and the role of asymmetric information has been extensively analyzed in the civil litigation literature 1 most of this literature concerns information that has bilateral payoff relevance in the sense that the information in question affects the expected payoff at trial of both the plaintiff and defendant when there is bilateral payoff relevance trials may be predicted in the equilibrium of the bargaining game regardless of whether the informed or uninformed party makes the offer in this article we analyze information that has unilateral payoff relevance meaning that it affects the expected payoff of one of the two parties to the dispute but not the other as an example suppose the plaintiff has private information on her risk preferences this affects her expected payoff at trial but not the defendant s when there is unilateral payoff relevance there are never inefficient trials in the equilibrium of the game where the informed party makes the offer 2 however there may still be costly disputes in the equilibrium of the game in which the uninformed party makes the offer examples of information with bilateral payoff relevance include information on the probability that the plaintiff will prevail at trial and information on the amount of the judgment to be awarded at trial in the event the plaintiff is victorious in both cases the information clearly affects the expected payoff of both the plaintiff and defendant at trial and these are the types of informational asymmetry considered most often in the literature what type of information has only unilateral payoff relevance one example mentioned above is information on risk preferences farmer and pecorino 1994 swanson and mason 1998 and heyes rickman and tzavara 2004 all examine asymmetric information on risk preferences within the context of the screening model in which the uninformed party makes the offer 3 in each case trials are predicted in the equilibrium of these models as long as trials are not too costly for the participants however other types of information also have only unilateral payoff relevance a large literature on the ultimatum game has provided convincing evidence that under certain circumstances individuals will express a preference for being treated fairly 4 this preference may be expressed specifically by the percentage of her own court costs a player is willing to concede to her opponent via his settlement offer 5 since this preference is not observable and presumably differs across individuals the proposer in a screening game must decide how much of the joint surplus of settlement he will attempt to extract without knowledge of how low he can go before triggering a rejection suppose the judgment is 100 000 and the plaintiff s court costs are 30 000 a plaintiff without a taste for fairness will accept an offer of 70 000 rather than proceed to trial a plaintiff with a taste for fairness might as an example accept no less than 90 000 the defendant then must choose between an offer of 90 000 and 70 000 without knowledge of whether the other party has a taste for fairness or not the defendant will make the low offer if he believes it will be accepted with a sufficiently high probability if the plaintiff does indeed have a taste for fairness she will reject the low offer and a trial will result presumably a mechanism along these lines explains the persistence of disputes in ultimatum game experiments another example of information with unilateral payoff relevance is the degree of litigiousness which can be modeled as differences in perceived court costs on the part of the plaintiff eisenberg and farber 1997

household energy prices and inequality evidence from german microdata based on the easi demand system abstract this paper studies the distributional effects of rising energy costs for households in contrast to most of the previous literature our specification differentiates between electricity and heating demand and still models other consumption goods in realistic detail we use a yet unexplored data set on household expenditures in germany and extend the recently developed easi demand system for the analysis of inequality and welfare at the individual and social level the easi system reveals non linearity of engel curves which when neglected can lead to biased estimates of distributional effects we find that increases in heating prices are more regressive than those in electricity furthermore current proposals for social tariffs are found to be less effective than targeted compensation schemes

interest rates and currency prices in a two country world abstract this paper is a theoretical study of the determination of prices interest rates and currency exchange rates set in an infinitely lived two country world which is subject both to stochastic endowment shocks and to monetary instability formulas are obtained for pricing all equity claims nominally denominated bonds and currencies and these formulas are related to earlier closely related results in the theories of money finance international trade

welfare analysis of tax reforms using household data abstract this paper discusses a methodology for calculating the distribution of gains and losses from a policy change using data for a large sample of households estimates are based on the equivalent income function which is money metric utility defined over observable variables this enables calculations to be standardised and a computer program to compute the statistics presented in the paper is available for a general demand system equivalent income is related to measures of deadweight loss and standard errors are computed for each of the welfare measures an application to u k data for 5 895 households is given which simulates a reform that involves eliminating housing subsidies

carbon tax simulations using a household demand model abstract the main objective of this paper is to analyse consumer response and welfare effects due to changes in energy or environmental policy to achieve this objective we formulate and estimate an econometric model for non durable consumer demand in sweden that utilises micro and macro data in the simulations we consider two revenue neutral scenarios that both imply a doubling of the co2 tax one that returns the revenues in the form of a lower vat and one that subsidise public transport one conclusion from the simulations is that the co2 tax has regional distribution effects in the sense that household living in sparsely populated areas carry a larger share of the tax burden

efficient investment in children abstract many would say that children are society s most precious resource so how should we invest in them to gain insight into this question a dynamic general equilibrium model is developed where children differ by ability parents invest time and money in their offspring depending on their altruism this allows their children to grow up as more productive adults first the efficient allocation is characterized next this is compared with the outcome that arises when financial markets are incomplete the situation where child care markets are also lacking is then examined additionally the consequences of impure altruism are analyzed journal of economic literature classification numbers d1 d31 d58 i2

property rights and efficiency in olg models with endogenous fertility is there an economic rationale for pronatalist policies we propose and analyze a particular market failure that leads to inefficiently low fertility in equilibrium the friction is caused by the lack of ownership of children if parents have no claim on their children s income the private benefit from producing a child can be smaller than the social benefit we analyze an overlapping generations model with fertility choice and parental altruism ownership is modeled as a minimum constraint on transfers from parents to children using the efficiency concepts proposed in golosov jones and tertilt 2007 we find that whenever the transfer floor is binding fertility choices are inefficient second we show that the usual conditions for efficiency are not sufficient in this context third in contrast to settings with exogenous fertility a payg social security system cannot be used to implement efficient allocations to achieve an efficient outcome government transfers need to be tied to fertility choice

the role of intergenerational transfers and life cycle saving in the accumulation of wealth he purpose of this paper is to review what economists know at present about the following question how large a portion of the existing wealth is the result of a bequest motive that is of accumulation for the specific purpose of leaving bequests i will also endeavor to clarify why an answer to this question is of interest in the early keynesian period when the study of national saving first attracted wide interest relatively little attention was paid to what led people to save though it was generally understood that the main systematic reason was to leave bequests j m keynes in the famous chapter 9 of the general theory of employment interest and money 1936 had listed seven distinct motives for saving besides the leaving of bequests but five of these which include to increase one s future income or to insure one s independence and power implied that all or nearly all the accumulation would finally wind up as bequeathed wealth this in turn meant that most private wealth originated through bequests that is it either had been received through bequests or was destined to be bequeathed and indeed how else could society accumulate wealth however keynes 1936 p 107 also mentioned two further motives precaution that is to build up a reserve against unforeseen contingencies and foresight that is to provide for an anticipated future relation between the income and the needs of the individual or his family different from that which exists in the present as for example in relation to old age family education or the maintenance of dependents these motives in contrast to most of the previous ones have the

litigation and settlement an empirical approach litigants in civil lawsuits involving monetary damages often find an out of court settlement preferable to a trial most theoretical models of settlement choice employ an expected utility maximizing framework that emphasizes the importance of risk preferences litigation costs and the distribution of trial awards an empirical model of settlement choice is used to examine whether the variables prominent in the theoretical literature are statistically useful in explaining the occurrence and monetary value of settlements estimates from a sample of civil filings provide new empirical evidence of how the legal system affects the behavior of litigants during the settlement process copyright 1989 by mit press

equity and efficiency effects of redistributive policies abstract how do various forms of redistribution affect the distributions of earnings and consumption and their intergenerational mobility do redistributive policies enhance efficiency by mitigating market imperfections or do they create a trade off between equity and efficiency to address these issues a dynamic general equilibrium model is constructed and solved numerically the effects of the degrees of targeting of money transfers and educational transfers and the relative performance of the two types of transfers are examined

intergenerational income mobility in the united states social scientists and policy analysts have long expressed concern about the extent of intergenerational income mobility in the united states but remarkably little empirical evidence is available the few existing estimates of the intergenerational correlation in income have been biased downward by measurement error unrepresentative samples or both new estimates based on intergenerational data from the panel study of income dynamics imply that the intergenerational correlation in long run income is at least 0 4 indicating dramatically less mobility than suggested by earlier research copyright 1992 by american economic association

bias in estimating the almost ideal demand system with the stone index approximation this paper shows that the commonly used stone index approximation can bias the parameter estimates of the almost ideal demand system the bias mostly affects the price parameters and can be more serious when the budget share equations are estimated with individual household rather than aggregate data in the absence of strong substitution effects the price parameter bias can be largely corrected through simple reparameterization copyright 1993 by royal economic society

random earnings differences lifetime liquidity constraints and altruistic intergenerational transfers abstract this paper develops a model of private savings behavior in which households care about their descendants cannot have negative net worth and have lifetime earnings depending on random draws from an exogenous distribution of abilities the elements interact very lucky parents are likely to leave large estates constrained children are unusually likely to receive intergenerational transfers the paper proves the existence of a stationary cross sectional distribution of wealth endogenously determines where liquidity constraints will bind and shows that the long term interest rate must be such that ricardian neutrality fails its last section generates several illustrative numerical simulations

the settlement of patent litigation in this article i develop a model to analyze patent licensing that is induced as part of a settlement agreement to avoid litigation of the issue of patent validity the patentee possesses private information about patent validity and makes a take it or leave it settlement offer to a single potential rival an essentially unique sequential equilibrium exists if out of equilibrium beliefs are restricted appropriately the model analyzes the effect of the probability of settlement and litigation

plea bargaining and prosecutorial discretion a model of plea bargaining with asymmetric information is presented the prosecutor s private information consists of the strength of the case while the defendant s private information consists of h is guilt or innocence in equilibrium a fraction of cases are dismis sed because they are too likely to involve an innocent defendant in the remaining cases the prosecutor s offer of a sentence in exchange for a plea of guilty reveals the strength of the case it is shown t hat unlimited prosecutorial discretion may be socially disadvantageou s since it carries with it the requirement of sequential rationality copyright 1988 by american economic association

the nature of credit constraints and human capital we develop a human capital model with borrowing constraints explicitly derived from government student loan gsl programs and private lending under limited commitment the model helps explain the persistent strong positive correlation between ability and schooling in the u s as well as the rising importance of family income for college attendance it also explains the increasing share of undergraduates borrowing the gsl maximum and the rise in student borrowing from private lenders our framework ofiers new insights regarding the interaction of government and private lending as well as the responsiveness of private credit to economic and policy changes

welfare comparison under exact aggregation new econometric model of aggregate consumer behavior in the united states and to apply this model to the analysis of impacts of alternative economic policies on the welfare of individual consuming units the model incorporates time series data on quantities consumed prices the level and distribution of income and demographic characteristics of the population it also incorporates cross section data on the allocation of consumer expenditures for households with different demographic characteristics our econometric model is based on the theory of exact aggregation developed by lau 1977a c this theory makes it possible to dispense with the notion of a representative consumer in constructing models of aggregate consumer behavior one of the most remarkable implications of lau s theory of exact aggregation is that systems of demand functions for individuals with common demographic characteristics can be recovered uniquely from the system of aggregate demand functions using the individual demand functions we can analyze the impact of economic policy on consumer welfare

the dynamics of pretrial negotiation it is shown that many cases proceed to court despite ample opportunity for interaction and much of the settlement takes place on the courthouse steps the deadline effect when fixed costs of bargaining are introduced a u shaped pattern of settlement appears with a greater chance of settlement at the beginning and at the end of negotiations than in the middle these characteristics persist even as the time between offers approaches zero the theoretical predictions are consistent with the stylized facts a large proportion of the lawsuits that are settled out of court are settled very close to the trial date or in the first several days of the trial 3 although the deadline effect appears in many other settings as well it has little theoretical support 4

a sequential concession game with asymmetric information the essence of the situation to be studied here is this two players are involved in a conflict that can be resolved in only two possible ways each player favors a different outcome during the bargaining phase which lasts until some finite time to each player has the option to concede if none concedes the game ends at time t in a way that is known to one of the players from the beginning of the game the other player is uncertain about the outcome time is valuable but each player prefers to receive his favored outcome at m than to concede immediately thus the game analyzed here is characterized by the asymmetric information about the outcome at the end point i e at time to whereas one player is perfectly informed about the possible outcome the other is compelled to deduce the information from the actions of his informed opponent the latter in turn can try to exploit his initial advantage by manipulating the flow of information for example the informed player may adopt a tough stance in order to create the impression that he is not afraid of forcing the resolution of the conflict at to and thereby builds his reputation at the same time the uninformed player by not conceding can test the opponent s resolve this brief description suggests that the problem analyzed here is a variant of the game of attrition 2 however our problem differs from the standard game of attrition in two respects first we formulate the game in discrete time which has important analytic consequences these are fully developed in hendricks and wilson 1985 second and more important perhaps we study

early settlement in european merger control we analyse the determinants of early settlement between merging parties and the european commission over remedies that remove concerns of anticompetitive effects this extends the previously narrow range of econometric literature on early settlement consistent with the theory of early settlement our results confirm the importance of delay costs and of uncertainty measured by the complexity of the economic analysis required for each merger we also find a non monotonic effect of agency resourcing which raises questions about the commission s efficiency in times of high case load econometrically we select a sample of merger decisions in which the european commission intervened due to concerns of anticompetitive effects and our selection model provides estimates of the factors determining intervention by the commission conclusions are drawn for public policy

litigation liability and incentives for care abstract in this paper potential injurers are subject to a negligence standard and differ in cost of taking care in the event of accident the injurer s degree of care is private information in litigation that follows award of damages for pain and suffering will lead to a general increase in care and hence reduce the likehood of accident a tighter negligence standard will lead some potential injurers to take more care and others to take less adoption of a rule under which the loser at trial must pay the litigation costs of the winner will reduce the pressure for punitive damages

intergenerational persistence of earnings the role of early and college education recent empirical evidence from the united states indicates a high degree of persistence in earnings across generations designing effective public policies to increase social mobility requires identifying and measuring the major sources of persistence and inequality in earnings we provide a quantitative model of intergenerational human capital transmission that focuses on three sources innate ability early education and college education we find that approximately one half of the intergenerational correlation in earnings is accounted for by parental investment in education in particular early education we show that these results have important implications for education policy

the effects of a fat tax on french households purchases a nutritional approach this article assesses the effects of a fat tax on the nutrients purchased by french households across different income groups this is done by making a preliminary estimation of price elasticities using a complete demand system on household scanner data and by calculating nutrient elasticities using estimated price elasticities we find that a fat tax has small and ambiguous effects on nutrients purchased by french households and a slight effect on body weight in the short run with a greater effect in the long run such a tax generates substantial tax revenue but is highly regressive

simulation of indirect tax reforms using pooled micro and macro french data this paper assesses the consequences of two reforms of the french indirect taxation system a vat harmonization which is close to initial ec proposals and a carbon tax which aims at decreasing the emissions of carbon dioxide we simulate the effects of tax reforms using estimates of a model of household expenditure behaviour estimation is obtained by using the property of perfect aggregation over households of the almost ideal demand system on pooled micro data from the 1978 1979 1984 1985 1989 issues of the french enquete budgets des familles combined with macro data from the quarterly national accounts from 1970 to 1990 simulations are conducted using a subsample of households from the 1989 consumer survey and generate useful results about the behavioural reactions to tax changes the impact on government revenue and the distributional effects of the reforms

litigation and settlement under two sided incomplete information this paper deals with a simple game of litigation and settlement with incomplete information parties are assumed to have the choice between settling their dispute out of court or resorting to costly litigation the set of sequential equilibria is characterized and conditions are given under which an efficient equilibrium does exist efficient equilibria however will be ruled out by various tests of refinement a comparative statics analysis is carried out with respect to the quality of private information which parties are assumed to receive before any moves have to be made

vertical coordination antitrust law and international trade this paper demonstrates that vertically aligned private or public organizations are capable of generating strategic trade advantage similar to that acquired through direct government export subsidization the model considers two forms of vertical coordination that lead to advantageous trade positions in international markets upstream vertical restraint and downstream equity sharing such practices are commonly employed both by state trading agencies and by private firms in nations with lenient antitrust laws the finding has important implications under new world trade organization wto rules intended to reduce government intervention in international transactions recent reforms in the wto favor nations that sanction highly refined vertical linkages between firms while nations with stringent antitrust legislation have an incentive to negotiate for greater harmonization of international laws

delay in contests abstract why is there delay in contests in this paper we follow and extend the line of reasoning of carl von clausewitz to explain delay for a given contest technology delay may occur if there is an asymmetry between defense and attack if the expected change in relative strengths is moderate and if the additional cost of investment in future strength is low

the distributional effects of a carbon tax and its impact on fuel poverty a microsimulation study in the french context abstract this paper studies the distributional effects of france s recently introduced carbon tax using a microsimulation model built on a representative sample of the french population from 2012 it simulates the taxes levied on each household s consumption of energy for housing and transport without revenue recycling the carbon tax is regressive and increases fuel poverty from a policy perspective this finding indicates that the question of fuel poverty cannot be ignored in the quest for a fair ecological transition it proposes that some of the revenues from the carbon tax should be redistributed to households different designs of cash transfer to support households are then compared the results show that the inequities of the carbon tax could be offset at reasonable cost relative to total carbon tax revenues however adjusting the design of cash transfers to criteria other than income level does not diminish the cost of compensating households the benefits of finely adjusting cash transfers may therefore be somewhat limited most notably the results show that targeting revenue recycling at low income households would help to reduce fuel poverty substantially this study therefore indicates that carbon taxation actually provides an opportunity to finance ambitious policies to fight fuel poverty

carbon taxation prices and welfare in new zealand abstract this paper examines the effects on consumer prices arising from imposing a carbon tax in new zealand using information about inter industry transactions and the use of fossil fuels by industries the welfare effects of the carbon tax are examined for a range of different household types finally overall measures of inequality are reported

wealth inequality family background and estate taxation this paper generates two main contributions first it provides a new theory of wealth inequality that merges two empirically relevant forces generating inequality bequest motives and inheritance of ability across generations and an earnings process that allows for more earnings risk for the richest second it uses the resulting calibrated framework to study the effects of changing estate taxation increasing the estate tax reduces the wealth concentration in the hands of the richest few and the economic advantage of being born to a rich and super rich family at the cost of reduced aggregate capital and output however all of these effects are quite small in contrast increasing estate taxation can generate a significant welfare gain to a newborn under the veil of ignorance but this comes at a large welfare cost for the super rich

strategic voting over strategic proposals prior research on strategic voting has reached the conclusion that unanimity rule is uniquely bad it results in destruction of information and hence makes voters worse off we show that this conclusion depends critically on the assumption that the issue being voted on is exogenous that is independent of the voting rule used we depart from the existing literature by endogenizing the proposal that is put to a vote and establish that under many circumstances unanimity rule makes voters better off moreover in some cases unanimity rule also makes the proposer better off even when he has diametrically opposing preferences in this case unanimity is the pareto dominant voting rule voters prefer unanimity rule because it induces the proposing individual to make a more attractive proposal the proposing individual prefers unanimity rule because the acceptance probabilities for moderate proposals are higher we apply our results to jury trials and debt restructuring

early and late human capital investments borrowing constraints and the family we develop a dynastic human capital investment framework to study the importance of family borrowing constraints and uninsured labor market risk as well as the process of intergenerational ability

comparative analysis of litigation systems an auction theoretic approach a simple auction theoretic framework is used to examine symmetric litigation environments where the legal ownership of a disputed asset is unknown to the court the court observes only the quality of the case presented by each party and awards the asset to the party presenting the best case rational litigants influence the quality of their cases by hiring skilful attorneys this framework permits us to compare the equilibrium legal expenditures that arise under a continuum of legal systems the british rule continental rule american rule and some recently proposed legal reforms are special cases of our model

credible pretrial negotiation pretrial negotiation is a structured environment in which to study bargaining with incomplete information when a plaintiff believes that a defendant owes him damages he may first attempt to reach a private settlement before resorting to a costly court imposed judgment a central issue in their negotiations is whether the plaintiff s threat to litigate is credible it is possible for the plaintiff to undermine the credibility of his litigation threat by making a settlement demand that is insufficient as a result the plaintiff must raise his settlement demand to limit the amount of bad news he can learn if his offer is rejected when this credibility constraint is binding traditional comparative static results are reversed in addition even though the defendant is being sued he wants the plaintiff s threat to be credible

price and income elasticities of demand for passenger transport fuels in spain implications for public policies abstract the significant increase in passenger transport activity cars experienced by spain and its associated increase in energy consumption have several associated negative aspects including a greater dependence on foreign energy sources and higher ghg emissions therefore reducing the level of transport activity would bring important socioeconomic and environmental benefits the aim of this paper which focuses on energy consumption in the passenger transport is fourfold 1 to provide a diagnostic of energy consumption in the spanish passenger transport system and the related problems 2 to develop a model to calculate price and income elasticities of demand for transport fuel 3 to apply this model to the spanish passenger transport sector 4 to infer policy recommendations derived from the results of the diagnostic and the model it is claimed that in view of those low price elasticities and high income elasticities and if a reduction in the scale of transport activity is deemed socially desirable a combination of instruments is necessary fuel taxes play an important role within this combination apart from their long term effects the low price elasticity of demand for transport fuel would allow the collection of a significant amount of revenues which could eventually be earmarked to encourage reductions in private transport demand and modal shifts with other instruments

the economics of a centralized judiciary uniformity forum shopping and the federal circuit abstract in 1982 the u s congress established the court of appeals for the federal circuit cafc as the sole appellate court for patent cases this court was created ostensibly to eliminate inconsistencies in the application and interpretation of patent law across federal courts and thereby mitigate the incentives of patentees and alleged infringers to forum shop for a preferred venue we perform the first econometric study of the extent of nonuniformity and forum shopping in the pre cafc era and of the cafc s impact on these phenomena we find that in patentee plaintiff cases the pre cafc era was indeed characterized by significant nonuniformity in patent validity rates across circuits and by forum shopping on the basis of validity rates we find weak evidence that the cafc has increased uniformity of validity rates and strong evidence that forum shopping on the basis of validity rates ceased several years prior to the cafc s establishment

antitrust settlements and trial outcomes risk aversion plays an important role in explaining why antitrust cases settle instead of going to trial using a jointly estimated model of settlement and trial outcome the authors find that a one percent increase in the probability that the plaintiff wins at trial raises the probability of a settlement by 0 13 percent they also find that reputation effects are not a significant factor for defendants so the risk aversion of the defendants does not play a dominant role in determining whether the parties settle plaintiffs are more likely to win in certain jurisdictions which encourages venue shopping by plaintiffs copyright 1996 by mit press

differential demand systems a further look at barten s synthesis barten s synthetic model is attractive to applied researchers since it is useful for testing the adequacy of the competing functional forms of differential demand systems including the popular rotterdam and almost ideal demand systems this article shows that the synthetic model is not a mere artificial composite of the known differential demand systems as it has been considered but rather viewed as a model in its own right it is demonstrated that at the individual consumer level barten s model has the same marginal budget shares as generated by specific forms of engel curves formulated by the box cox transformation