rational versus adaptive expectations in present value models using data on stock price and dividends and on long term and short term interest rates we test an important implication of present value models that current value is a linear function of the conditional expectations of the next period value and the current determining variable this implication combined with rational expectations re is strongly rejected combined with adaptive expectations ae it is accepted the latter model can also explain the observed negative relation between the rate of return and stock price thus the re assumption should be used with caution the ae assumption may be useful in econometric practice

the phillips curve macroeconomic policy and the welfare of canadians a review of the two competing paradigms explaining inflation and unemployment fluctuations singles out the keynesian phillips curve as the clear empirical winner over its classic competitors reestimation of the canadian phillips curve for 1957 90 identifies a sharp structural shift toward a high degree of unemployment hysteresis after 1972 the recent attempt of macropolicy to flatten the aggregate demand curve and limit supply side shock accommodation which aims at lower and more stable inflation is then shown to make unemployment higher and more unstable on average to an extent that is an increasing function of the degree of hysteresis understanding and reducing hysteresis and developing a consensus based incomes policy that has a chance of alleviating the dismal trade off should therefore to top research and policy priorities

effectiveness of developed and emerging market fx options in active currency risk management abstract we analyze the effectiveness of developed and emerging market foreign exchange options in international portfolios as a complement to forwards for actively managing portfolio currency risks under the behavioral framework although prior research finds forwards dominate options using the mean variance framework measures using other objectives may prove more insightful we find that foreign exchange options can be useful behavioral complements to forwards for currency risk management from a perspective of regret risk mean skewness and cross asset lower tail dependence we also draw parallels and contrasts between developed and emerging market foreign exchange options from a behavioral perspective

is international diversification really beneficial abstract previous research claims that low constant correlations among international stock indices create substantial risk reduction from diversification we contend that only using constant correlations is too simplistic an approach we examine international diversification by 1 using conditional correlations 2 evaluating tail risk including the effect of skewness and kurtosis and 3 examining the possible tradeoffs of standard deviation with correlation skewness and kurtosis we show that conclusions concerning diversification based solely on constant correlations across markets can be misleading since the diversification benefits are time varying are affected by non normality and depend on the benchmark country employed finally tradeoffs do exist between standard deviation and the other risk factors

financial portfolio management through the goal programming model current state of the art abstract since markowitz 1952 formulated the portfolio selection problem many researchers have developed models aggregating simultaneously several conflicting attributes such as the return on investment risk and liquidity the portfolio manager generally seeks the best combination of stocks assets that meets his her investment objectives the goal programming gp model is widely applied to finance and portfolio management the aim of this paper is to present the different variants of the gp model that have been applied to the financial portfolio selection problem from the 1970s to nowadays

how good are small firms are predicting employment this paper utilises some data from an interview survey of very small firms in the north of england to examine the relationship between actual and forecast employment in small firms over a twelve month period the paper first provides some summary statistics on actual and forecast employment for the survey firms over the reference period it then looks at how successful the firms are in their short term forecasts and finds that there is systematic over estimation the causes of the systematic forecast error are investigated it is suggested tentatively that the firms may in some way be incorrectly interpreting the information embodied in their own employment figures when making their forecasts the paper concludes with a brief review of the results and possible policy implications avenues for future work are also proposed

pattern based expectations international experimental evidence and applications in financial economics abstract we study how subjects extrapolate simple patterns in financial time series in order to develop a descriptive model of actual agent behavior the laboratory experiment for this analysis was conducted in germany and japan statistical analyses indicate considerable similarity in expectations formation across cultures and document that agents expectations are at variance with the notion of standard trend extrapolation the paper then proposes a method for computing expectations for any economic time series based on the experimental data such pattern based expectations are shown to explain stock prices and the dynamics of the forward discount on the foreign exchange market

learning in expectation formation with applications to cattle and beef exports the paper briefly considers problems associated with rational expectations and formulates a more general model which allows for situations where economic agents do not immediately arrive at a fully rational solution it incorporates a learning mechanism whereby agents can provisionally adopt hypothetically derived expectations as a basis for comparison with the actual outturns utilizing the resultant past expectational errors as indicators of the likelihood of prospective future outcomes agents make explicit allowance a rational solution thus in situations where complete information is not freely available rationality would be approximated over time by means of a dynamic learning process which is founded on a firm empirical approach this essential empiricism requires that the problem be examined on the basis of direct observation of applied situations therefore the method is implemented and analysed with reference to irish foreign trade in fat cattle carcase and processed beef simultaneous equati

wage expectations in the labor market survey evidence on rationality using a new set of directly observed wage expectations among firms this paper finds that in general firms forecasts fail the unbiasedness and efficiency requirements of weak form rational expectations these market participants consistently underestimate the wages they actually end up paying and their expectations do not efficiently utilize the information in past realizations the mean absolute forecast error of two percent compares with an error of only five percent if static expectations were held the major source of wage fore cast error seems to be errors in predicting demand rather than in predicting supply or the general price level wage forecast errors are positively correlated across fields with distinct supply patterns and are positively correlated with quantity forecast error the properties of stochastically weighted expectations and the effectiveness of the wage and price controls of the early 1970 s are also discussed this abstract was borrowed from another version of this item

expectations in an open economy hyperinflation evidence from germany 1921 23 abstract we reconsider the beladi et al 1993 technique to measure expectations in hyperinflation episodes by allowing money to be substitutable with foreign assets as well as goods we determine new correctness conditions for adaptive and rational expectations formation in this context and show that taking into account these conditions the data for the german hyperinflation of the 1920s is consistent with rational expectation formation

a qualitative response analysis of uk firms employment and output decisions this paper investigates firms employment and output decisions and presents some empirical evidence concerning the rationality of firms expectations the dymanic model is based on the assumptions of convex adjustment costs and monopolistic competition in the product market the results are obtained using categorical information on individual firms contained in business surveys collected by the confederation of british industry ordered probit models are used to estimate the employment and output equations we find that expected demand is a critical determinant of firms decisions the effect of changes in cost conditions is not as well determined and the data are not consistent with the rational expectations hypothesis

finance commission of india s assessments a political economy contention between expectations and outcomes abstractwe explore the normative fiscal assessments of the finance commission fc of india and realisation of fiscal policy with regard to central finances over the period 1990 2012 we employ the theil s inequality coefficient to investigate the magnitude of assessment errors and its partitioning in to bias slope and random components furthermore this article also evaluates the efficiency biasedness and persistence of forecast errors the robustness of the efficiency results are confirmed with the application of maximum entropy bootstrap the objective of this study is to examine the structural basis on which fcs make their awards rather than examining the predictability of the forecasts the story of fc s assessments reflects an interesting political economy theatre of contention between aspirations and outcomes our key findings are as follows first source of errors for assessments of tax revenue nontax revenue interest payments defence revenue expenditure plan revenue expenditure and fisca

what price accountability the lucas island model and the politics of monetary policy this paper develops a model of an electoral cycle in inflation and output based on rational inflation expectations and rational retrospective voting voters are heterogeneous and partially informed about aggregate macroeconomic variables they observe precisely how monetary policy stimulates their local economies but their observations of economic activity in other sectors are imprecise voters extract information about the incumbent policymaker s economic competence from cross sectoral spillover effects the incumbent has incentives to generate preelection monetary surprises that stimulate the local economies and generate cross sectoral spillover effects he thereby creates an impression of economic competence and furthers his reelection prospects his policy manipulations are the price of political accountability on a positive note the incumbent is more likely to survive voter scrutiny if he is more competent than the average political candidate

bias in omb s economic forecasts and budget proposals the office of management and budget omb annually submits the president s budget for the u s government to the congress the economic forecasts and revenue and outlay proposals contained in the budget have been criticized as biased especially during the 1980s tests for bias in one year ahead proposals for the 1963 89 period show no bias in economic forecasts and revenue estimates but substantial bias in outlay proposals most outlay proposals are consistently less than actual outcomes accounting for underprediction of the federal deficit omb outlay proposals appear to be influenced by politics republican administrations show more significant proposal biases with defense proposals higher and domestic outlay proposals lower than outcomes the office of management and budget consistently understates the deficits by resorting to the most optimistic economic assumptions it can credibly and now sometimes even incredibly employ senator james sasserwall street journal 25 january 1990

optimal sequencing of credible reforms with uncertain outcomes abstract we study a two period representative agent economy in which economic liberalization is modeled as adding a positive random variable to the marginal product of capital we show liberalization always raises the expected utility of agents agents may respond to this by increasing consumption in the first period consequently consumption in the second period is sometimes smaller than the in the first depending on the realization of the random variable this tail may cause the government to reject liberalization of declining gdp enters negatively in the government s objectives we apply these results to the chilean experience of the 1980s

are survey forecasts of macroeconomic variables rational this article examines the rationality of forecasts of 11 macroeconomic variables among the nonstationary series only surveys of housing starts the unemployment rate and the trade balance are rational forecasts among the stationary series survey forecasts for only consumer prices and personal income are consistent with rational expectations lack of rationality in forecasts of durable goods industrial production leading indicators money supply and retail sales suggests that such forecasts do not fully exploit public information indeed survey forecasts for industrial production and retail sales can be improved significantly with past information copyright 1995 by university of chicago press

a dynamic network model of the unsecured interbank lending market abstract we introduce a dynamic network model of interbank lending and estimate the parameters by indirect inference using network statistics of the dutch interbank market from february 2008 to april 2011 we find that credit risk uncertainty and peer monitoring are significant factors in explaining the sparse core periphery structure of the market and the presence of relationship lending shocks to credit risk uncertainty lead to extended periods of low market activity intensified by reduced peer monitoring moreover changes in the central bank s interest rate corridor have both a direct effect on the market as well as an indirect effect by changing banks monitoring efforts

market rationality tests based on cross equation restrictions abstract the information used by researchers in cross equation tests of rational expectations may be a small subset of the information available to the market such tests produce consistent estimates but have low power we develop a mechanism for dealing with this problem and use the procedure to perform cross equation tests on predictions from the football betting market the tests fail to reject rationality we provide evidence that market predictions from betting markets are not formed rationally it appears therefore that cross equation tests have low power even if the information sets used by the researcher and the market are approximately the same

families schools and primary school learning evidence for argentina and colombia in an international perspective this article presents evidence on the associations between family background school characteristics and student performance in primary school in argentina colombia and several comparison countries as a general pattern educational performance is strongly related to family background weakly to some institutional school features and hardly to schools resource endowments in an international perspective family background effects are relatively large in argentina and relatively small in colombia a specific argentine feature is the lack of performance differences between rural and urban areas a specific colombian feature is the lack of significant between gender performance differences nonnative students and students not speaking spanish at home perform particularly weak in both countries in argentina students perform better in schools with a centralized curriculum and ability based class formation

optimal credit swap portfolios this paper formulates and solves the selection problem for a portfolio of credit swaps the problem is cast as a goal program that entails a constrained optimization of preference weighted moments of the portfolio value at the investment horizon the portfolio value takes account of the exact timing of protection premium and default loss payments as well as any mark to market profits and losses realized at the horizon the constraints address collateral and solvency requirements initial capital position limits and other trading constraints that credit swap investors often face in practice the multimoment formulation accommodates the complex distribution of the portfolio value which is a nested expectation under risk neutral and actual probabilities it also generates computational tractability numerical results illustrate the features of optimal portfolios in particular we find that credit swap investment constraints can have a significant impact on optimal portfolios even for simple investment objectives our problem formulation and solution approach extend to corporate bond portfolios and mixed portfolios of corporate bonds and credit derivatives this paper was accepted by wei xiong finance

efficiency and formation of expectations evidence from the european investment survey the european commission conducts an annual survey regarding planned and realized business fixed investment across various manufacturing sectors in euroland in this study we investigate the predictive content of survey based expectations on investment in addition we empirically test the rationality of respondents both in a time series as well as in a panel context according to our results based on pooling the data efficiency is rejected since expectations are biased predictors of actual outcomes furthermore expectations revisions are found to be correlated with components of the information set known at the time of decision making finally our results qualify regressive expectations as the mechanism that more adequately describes the formation of expectations

skewness persistence with optimal portfolio selection abstract existing studies have found that ex post stock returns are positively skewed but such skewness is only persistent for individual stocks not for portfolios this implies that the ex post knowledge of skewness may not be useful in ex ante portfolio selection however the portfolios in these studies are not optimally formed because preferences for skewness are not taken into consideration when forming these portfolios it is more meaningful to see if the positive skewness would persist in optimally formed mean variance skewness efficient portfolios using stocks from both japanese and us markets and a bootstrap method we find that the portfolios optimally formed by using a polynomial goal programming method which considers preference for skewness greatly enhances skewness persistence over time our results are robust across both japanese and us stocks however the skewness persistence is stronger for portfolios formed with monthly data than that with weekly data these findings have practical implications to investors with skewness preferences

budget deficit and inflation the peruvian experience the purpose of this paper is to investigate the role of huge budget deficits in peru s near hyperinflation during recent years we use the rational expectations macro model of inflation to find out effect of the anticipated budget deficits on inflation rates by using the quartely data of peru for the period 1973 1 to 1988 1 our major finding has been that the budget deficits as well as the rate of growth of money supply do have significant impact on the inflation rates in peru

on estimating skewness in stock returns in recent years skewness has become a much discussed factor in financial research and many studies models involve the skewness of various financial variables this paper i points out the universal neglect in the finance literature of skewness sampling error and its significant consequences ii presents a simple approach for roughly constructing a confidence interval for skewness estimated from lognormal populations iii points out directions of further research for developing a comprehensive approach for estimating skewness reliably

mean variance skewness portfolio performance gauging a general shortage function and dual approach this paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean variance skewness space a shortage function is defined that looks for possible increases in return and skewness and decreases in variance global optimality is guaranteed for the resulting optimal portfolios we also establish a link to a proper indirect mean variance skewness utility function for computational reasons the optimal portfolios resulting from this dual approach are only locally optimal this framework permits to differentiate between portfolio efficiency and allocative efficiency and a convexity efficiency component related to the difference between the primal nonconvex approach and the dual convex approach furthermore in principle information can be retrieved about the revealed risk aversion and prudence of investors an empirical section on a small sample of assets serves as an illustration

us stock prices and recency biased learning in the run up to the global financial crisis and its aftermath abstract this paper presents a consumption based asset pricing model in which fluctuations in stock prices are driven by investors time varying subjective expectations about the dividend process in line with the empirical literature investors display recency bias when revising their beliefs about the actual dividend process and recursively discount the precision of past observations recency biased learning significantly improves the ability of the standard model to replicate the boom and bust episode on the us s p 500 stock market in the run up to the global financial crisis and its aftermath along with features of subjective expectations of stock returns documented in survey data

book reviewinequality poverty and history jeffrey g williamson basil blackwell cambridge ma 1991 isbn 1 55786 118 8 pp vii 151 19 50

switching equilibria the present value model for stock prices revisited abstract this paper analyzes the dynamic features displayed by alternative rational expectations equilibria in the context of the present value model for stock prices with feedback in particular it shows that there exists a unique equilibrium implying cointegration and that equilibrium is characterized by either the fundamental or alternatively the backward solution depending on the size of the feedback parameter it is shown analytically that the existence of switching equilibria induces large stock market swings using us data and structural estimation the hypotheses of feedback and switching equilibria are tested the empirical results provide evidence of both switching equilibria and feedback

toward a service oriented growth strategy abstract this article suggests that the linkage between industrial modernization and significant service sector employment gains has not been adequately considered and that such consideration might lead to a re evaluation of the labour absorption argument which calls for more appropriate technologies with higher labour intensity this paper reviews the literature on labour absorption and appropriate technology it then examines the experience of the service sector in both dcs and ldcs the key relationships between the service sector and the economy are then developed leading up to possible implications for ldc growth strategies

in search of a strictly rational forecast this paper proposes criteria for classifying time series forecasts of inflation as weakly sufficiently strongly and strictly rational forecasts taken from the asa nber surveys some well known one step ahead forecasting techniques and a novel variable length autoregressive moving average model are tested against these criteria none of the forecasts series meets the criteria for strict rationality nor even the less demanding criteria for strong rationality while agents forecast as best they can their forecasts are not likely to meet stringent rationality criteria suggested by econometricians copyright 1991 by mit press

is there a core of practical macroeconomics that we should all believe with emphasis on the adjective practical and the normative verb should my answer to the question of this session is a resounding yes indeed i spent a good deal of time between january 1993 and january 1996 acting on the belief that there is such a core macro model so i certainly hope it exists this believable core model falls well short of perfection leaves many questions unanswered and is subject to substantial stochastic errors nonetheless it is both useful and extensively used in policy analysis where contact with reality is a necessity and you cannot beat something with nothing it also closely resembles but does not quite match the way macroeconomics is taught to beginning and intermediate but not to graduate students in this short presentation i will describe briefly the main practical elements that i think we should agree on without worrying too much about their theoretical underpinnings then i will turn to two critical failings of the standard macro model which cry out for theoretical and empirical repair my organizing principle is the textbook exposition that has been standard though not universal in teaching intermediate macroeconomics for years the question is how does it differ from the core model used in policy analysis

neoliberalism and income distribution in latin america abstract this paper reviews the principal neoliberal policy measures instituted in latin america in the last decade and their impact on equity it first emphasizes the difficulty of separating the impact of liberalization measure from the necessary fiscal adjustments of the 1980s and their transitional vs longrun effects and then places the observed movements in distribution in global and historical context the second part places several innovations of neoliberal regimes in historical perspective and argues that their overall impact is unlikely to be regressive and that previous regimes were probably not especially progressive over the long run developments in factor markets the demand side driven by reoriented industrial growth and the increasing importance of the service sector interacting with the relative supplies of skilled and unskilled labor are likely to be of overriding importance in determining the evolution of the distribution of income

expectation volatility and liquidity in the housing market measuring housing price volatility is fundamental to understanding the dynamics of housing price risk this article aims to explore whether a liquidity factor plays a role in explaining the second moment i e the volatility of housing prices housing price volatility is measured as the conditional variance of a generalized auto regressive conditional heteroscedasticity garch model under the adaptive expectations framework the empirical evidence reveals that volatility transmits from smaller housing units to larger housing units which indirectly supports the trade up effect discussed in the literature in addition less liquid housing classes are more sensitive to unexpected liquidity shocks and the starter housing class is extraordinarily sensitive to negative liquidity shocks consistent with friction search theory pricing errors are alleviated as the trading volume increases because the valuation price tends to be more accurate as more information is available

skewness persistence in common stock returns recent empirical studies have found ex post common stock returns to be consistently positively skewed the frequency of positive skewness in this study is found to be relatively stable over varying time periods from 1961 to 1980 however the skewness of individual stocks and portfolios of stocks does not persist across different time periods positively skewed equity portfolios in one period are not likely to be positively skewed in the next time period past positively skewed returns do not predict future positively skewed returns

on the rationality of us macroeconomic forecasts evidence from a panel of professional forecasters asa nber survey data is used to check the rationality of us macroeconomic forecasts it is found that of 75 forecast series examined 51 are biased 25 are both unbiased and efficient and only two pass the null hypothesis of orthogonality this calls into question the validity of rational expectations hypothesis

the kuznets process and the inequality development relationship abstract in his classic paper on economic growth and income inequality kuznets discussed the process of population shift from traditional to modern activities as the basis for a theory of distributional change during the course of development in this paper we present a formalization of the kuznets process conduct a general analysis of distributional change under this process and derive the functional forms of and conditions for a turning point in the inequality development relationship for six commonly used indices of inequality the functional form appropriate to each index is then estimated using cross section data on 60 developing and developed countries finally some extensions to the initial formalization of the kuznets process are considered

on information and market dynamics the case of the u s beef market abstract the paper investigates the nature of dynamic prices and expectations in a competitive market the approach is applied to the u s beef market which exhibits cyclical patterns and significant biological lags in the production process beef price equations are estimated under different expectation regimes the empirical results indicate the presence of heterogeneous price expectations with a significant number of market participants neglecting information about the existence of a beef cycle

expectations in stability and in viability in realistic overlapping cohorts models abstract in this paper we shall consider the multi cohort generalization of overlapping generations models namely overlapping cohorts olc models each time period consumers of different ages form expectations on future interest rates and conditionally maximize utility arising from their remaining consumption paths under the condition of zero bequest for every time period a coordinator determines the new interest rate to ensure that the total consumption is equal to the total endowment of the society the message of the paper is the following 1 in olc the dynamics generated by rational expectations is frequently not only unstable but unviable 2 in olc the dynamics generated by naive expectations is practically asymptotically stable and viable around the lower steady state

the bootstrap approach for testing skewness persistence this study presents a new methodology for testing changes in skewness between time periods or samples using the bootstrap method a monte carlo simulation experiment was conducted to compare the effectiveness of the bootstrap method with the method suggested by lau wingender and lau 1989 to test skewness persistence the results show the bootstrap method to be more powerful than the other method the bootstrap method was also used to determine the persistence of skewness in stock returns the results show that in a large percentage of stocks skewness persists over time

interpreting pre trends as anticipation impact on estimated treatment effects from tort reform abstract while conducting empirical work researchers sometimes observe changes in outcomes before adoption of a new policy the conventional diagnosis is that treatment is endogenous this observation is also consistent however with anticipation effects that arise naturally out of many theoretical models this paper illustrates that distinguishing endogeneity from anticipation matters greatly when estimating treatment effects it provides a framework for comparing different methods for estimating anticipation effects and proposes a new set of instrumental variables to address the problem that subjects expectations are unobservable finally this paper examines a specific set of tort reforms that was not targeted at physicians but was likely anticipated by them interpreting pre trends as evidence of anticipation increases the estimated effect of these reforms by a factor of two compared to a model that ignores anticipation

portfolio selection and skewness evidence from international stock markets abstract this paper finds that the returns of the world s 14 major stock markets are not normally distributed and that the correlation matrix of these stock markets was stable during the january 1988 december 1993 time period polynomial goal programming in which investor preferences for skewness can be incorporated is utilized to determine the optimal portfolio consisting of the choices of 14 international stock indexes the empirical findings suggest that the incorporation of skewness into an investor s portfolio decision causes a major change in the construction of the optimal portfolio the evidence also indicate that investors trade expected return of the portfolio for skewness

beyond demand and supply curves in macroeconomics this paper surveys recent issues in macroeconomics from the viewpoint of dynamic economic theory the need to look beyond demand and supply curves and the insights that come from doing so are emphasized examples of issues in debt management and fiscal policy are analyzed

tests of the rational expectations hypothesis this paper reviews evidence on the structure of anticipation from a number of empirical studies jack muth s rational expectations hypothesis is compared with a variety of alternative models including ferber s law the implicit expectations model of edwin mills and muth s new errors in the variables model the cumulative evidence is of such strength as to compel the suspension of belief in the concept of rational expectations this implies that it is a mistake to proceed under the maintained hypothesis that expectations are rational instead it is necessary to test the sensitivity of empirical and theoretical results to alternative assumptions about the structure by which anticipations are generated copyright 1986 by american economic association

the monetary dynamics of sustained high inflation taiwan 1945 1949 taiwan experienced a sustained period of very high price inflation in the period 1945 1949 which led to an eventual rise in prices even greater than that experienced during some of the classic european hyperinflations analyzed by cagan 3 and others makinen and woodward 22 90 note that on the list of recognized hyperinflations one will not find taiwan but nevertheless argue that this episode should be classed as such although the average rate of taiwanese inflation during this period was not as high as in the episodes examined by cagan the very length of the period during which inflation remained high singles the taiwanese experience out as an extremely interesting period for analysis by monetary economists in this paper a primary aim is to examine whether the salient features of the demand for money during this period can be adequately characterized by an application of cagan s model of money demand under conditions of hyperinflation in particular we apply a test of cagan s model which is not contingent on any particular assumption concerning expectations formation except that agents errors in forecasting inflation are stationary using these first stage estimates we then examine subject only to the same weak assumption of stationary forecasting errors the hypothesis that the monetary authorities expanded the money supply in such a way as to maximize the inflation tax revenue ensuing from money creation finally we test the rational expectations version of the hyperinflation model of money demand the remainder of the paper is set out as follows in section ii we discuss the background to the taiwanese hyperinflation of 1945 1949

geometric representation of the mean variance skewness portfolio frontier based upon the shortage function the literature suggests that investors prefer portfolios based on mean variance and skewness rather than portfolios based on mean variance mv criteria solely furthermore a small variety of methods have been proposed to determine meanvariance skewness mvs optimal portfolios recently the shortage function has been introduced as a measure of e ciency allowing to characterize mvs optimal portfolios using non parametric mathematical programming tools while tracing the mv portfolio frontier has become trivial the geometric representation of the mvs frontier is an open challenge a hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the mvs portfolio frontier the purpose of this contribution is to systematically develop geometric representations of the mvs portfolio frontier using the shortage function and related approaches