unknown wage offer distribution and job search duration abstract if job searchers do not know the wage offer distribution they are facing they might take the wage structure in their last firm as a prior doing so reservation wages will be biased which will also bias unemployment duration using data for austrian workers it is shown that workers seem to have good knowledge of expected mean wages but less so for higher moments of the wage offer distribution

applications of behavioural economics to tax evasion the paper reviews recent models that have applied the techniques of behavioural economics to the analysis of the tax compliance choice of an individual taxpayer the construction of these models is motivated by the failure of the yitzhaki version of the allingham sandmo model to predict correctly the proportion of taxpayers who will evade and the effect of an increase in the tax rate upon the chosen level of evasion recent approaches have applied non expected utility theory to the compliance decision and have addressed social interaction the models we describe are able to match the observed extent of evasion and correctly predict the tax effect but do not have the parsimony or precision of the yitzhaki model

optimism pessimism and financial bubbles this paper shows that it is possible to extend the scope of the existence of rational bubbles when uncertainty is introduced associated with rank dependent expected utility this rdu assumption can be viewed as a transformation of probabilities depending on the pessimism optimism of the agent the results show that pessimism favors the existence of deterministic bubbles when optimism may promote the existence of stochastic bubbles moreover under pessimism the rdu assumption may generate multiple bubbly equilibria the rdu assumption also leads to new conditions ensuring the absence of pareto optimality of the competitive equilibrium without bubbles these conditions still govern the existence of bubbles

cautious risk takers investor preferences and demand for active management actively managed mutual funds have distinct return distributions from their passive benchmarks and our theoretical analysis using tail sensitive risk preferences suggests that active value and growth funds may serve to reduce downside risk and capture upside potential respectively furthermore tail sensitivity measures estimated from the empirical pricing kernel have significant explanatory power for active fund flows even after controlling for business cycles and market wide sentiment finally active funds unlike their passive counterparts have exposures to option strategies hedging downside risk or capturing upside potential

value added content of trade a comprehensive approach abstract this letter provides an approach to decompose the value added content of trade into foreign and domestic components when intermediates are traded the measure adds to the existing literature by considering both exports and imports simultaneously in this way this approach generalizes the commonly applied vertical specialization measures based on exports only which are encompassed

price changes supply elasticities industry organization and dairy output distribution long run price elasticities of milk supply are decomposed into price elasticities of yield herd size and farm population for northeastern u s dairy farms these elasticities are shown to vary with farm size because of size related differences in capital intensity specialization yield and herd size variability and rates of entry exit into dairy in the short run price responsiveness is shown to decrease with farm size in the long run large farms are shown to be most price responsive results suggest that lower milk prices could make revenue distribution less equal in both the short and long run by altering output and population distributions

key sectors in input output production networks an application to brexit this paper presents the first detailed and holistic description of the european production network epn and provides different rankings of the most systemically important industries involved in brexit employing techniques of complex networks analysis and input output traditional tools the study identifies those industries that are key in the complex structure of the uk eu trade relationships the method developed would help policy makers to better understand which tariff would have a more distortive impact which export sector should be pushed which imports should be safeguarded such information may have foremost importance in the negotiations between the uk and eu our findings suggest that brexit would be not just a problem for the uk as it is often portrayed but any form of brexit could propagate affecting the global production system further by inspecting industries centrality within the epn we find that the uk could be less exposed to trade barriers than eu countries

bargaining and boldness abstract we study a multiperson bargaining problem with general risk preferences through the use of shaked s game of cycling offers with exogenous breakdown if preferences are smooth then as the risk of breakdown vanishes the limiting outcome is one in which bargainers are equally marginally bold where a bargainer s marginal boldness measures his willingness to risk disagreement in return for a marginal improvement in his position under smoothness any ordinal nash solution is an equally marginally bold outcome however unlike the concept of the ordinal nash solution a unique equally marginally bold outcome exists in natural cases in particular if all bargainers have risk averse preferences of the rank dependent expected utility type for these preferences the equally marginally bold outcome maximizes a bargaining power adjusted asymmetric nash product where the degree of asymmetry is determined by the disparity in the marginal valuation of certainty among bargainers journal of economic literature classification numbers c72 c78 d81

intermediate inputs external rebalancing and relative price adjustment abstract the traditional multi sector macro model without production inputs is a value added trade model this paper shows that calibrating such a misspecified value added trade model to available gross flow trade data a common practice in the literature can lead to mismeasured i preference weights and ii price elasticities further the calibrated model can give substantially different predictions regarding the relative price response to external rebalancing when compared to a preferred alternative model with inputs that is consistent with gross flow trade data we find that mismeasured preference weights and price elasticities both contribute sizably to deviations in model predictions and estimate correctly measured parameters for the value added trade model

how income transfer programs affect work savings and the income distribution a critical review for helpful comments on earlier drafts we thank without implicating moses abramovitz yves balcer john bishop alan blinder richard burkhauser michael darby irwin garfinkel alan gustman daniel hamermesh martin holmer george jakubson robert lampman paul menchik robert moffitt michael murray joseph quinn timothy smeeding eugene smolensky barbara wolfe and two anonymous referees

who produces for whom in the world economy la part du commerce en produits intermediaires dans le commerce international appele aussi commerce vertical n a cesse d augmenter depuis vingt ans cet article propose une nouvelle mesure du commerce international le commerce en valeur ajoutee qui re alloue les flux commerciaux aux pays et aux secteurs produisant les intrants en 2004 le commerce vertical represente 27 du commerce total les repartitions geographique et sectorielle du commerce en valeur ajoutee sont tres differentes de celles du commerce standard la difference entre le commerce en valeur ajoutee et le commerce standard est plus importante dans le cas du commerce regional mais ce n est pas plus le cas en asie qu en amerique

the probability premium a graphical representation we illustrate that pratt s probability premium can be given a simple graphical representation allowing a direct comparison to the equivalent but more prevalent concept of risk premium under expected utility we also show that the probability premium s graphical representation under the dual theory mimics that of the risk premium under expected utility

accounting for the differences between gross and value added trade balances one of the main stylised facts that has emerged from the recent literature on global value chains is that bilateral trade imbalances in gross terms can differ substantially from those measured in value added terms however the factors underlying the extent and sign of the differences between the two measures have so far not been investigated here we propose a novel decomposition of bilateral gross trade balances that accounts for the differences between gross and value added concepts the bilateral analysis contributes conceptually to the literature on double counting in trade by identifying the trade flow in which value added is actually recorded for the first time in international trade statistics we apply our decomposition framework to the development of intra eu 27 trade balances from 1995 to 2011 and show that a growing share of intra eu bilateral trade balances is due to demand in countries other than the two direct trading partners the latter accounted for 25 per cent of the total variance of intra eu gross bilateral trade balances in 2011 which marks a considerable rise from 3 per cent in 1995

a theory of subjective compound lotteries abstract we develop a savage type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries our theory permits issue preference that is agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues hence we establish subjective foundations for the anscombe aumann framework and other models with two different types of probabilities we define second order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second order risk which implies issue preference and behavior consistent with the ellsberg paradox

the mystery of the excess trade balances bilateral trade deficits are a perennial policy issue former deputy assistant u s trade representative for japan and china merit janow 1994 p 55 notes that during the first george bush administration high deficits coupled with the continuing allegations from u s business interests about the closed nature of the japanese market were resulting in serious domestic political pressures for improved access to the japanese market recently robert c feenstra et al 1998 p 1 made similar comments vis a vis china some analysts have interpreted the large u s china bilateral trade deficit as prima facie evidence of unacceptably high levels of protectionism in china and have advocated stringent entry conditions for china s admission into wto given the policy salience of bilateral trade deficits it is peculiar that no one has ever examined them empirically for a broad set of countries one reason for the scant study is that economists are naturally and sensibly loath to accept the terms of the policy debate which considers bilateral trade deficits ipso facto harmful a second reason is that economists believe there may be very natural explanations for bilateral imbalances one such explanation finds its origins in macroeconomic identities that equate current account deficits to an excess of investment over saving from this it may be argued that bilateral imbalances will arise naturally in trade between countries in aggregate surplus and those in aggregate deficit indeed this is the principal explanation that the profession has given policymakers and it forms the foundation of many u s bilateral trade initiatives such as the structural impediments initiative and the framework talks janow 1994 p 55 observes that there was and is little disagreement among economists that the causes of large aggregate and bilateral deficits are largely attributable to macroeconomic factors italics added a second account may rely on what may be termed triangular trade in which cross country differences in the patterns of demand and supply mean that a country will run bilateral deficits with those countries that are unusually important suppliers of the goods for which the deficit country happens to be an unusually strong demander in this paper we use the canonical gravity model of bilateral trade to form predictions about bilateral trade balances we develop two key variants of the model in which bilateral trade imbalances arise due to aggregate macroeconomic imbalances or due to triangular trade and we implement these empirically for a broad set of countries our results paint a dismal picture the central explanations that economists provide to explain bilateral balances perform miserably there are two key failures first actual bilateral trade imbalances are much larger than those predicted there is a mystery of excess trade balances second even after we allow for both macroeconomic imbalances and idiosyncrasies in the structure and levels of demand and production the models perform poorly in explaining bilateral trade balances these failures of economists standard explanations of bilateral trade imbalances require that we move beyond the simple gravity framework to consider alternative explanations homogeneous goods highly specialized intermediates and the role of policy

cumulative prospect theory option returns and the variance premium the variance premium and the pricing of out of the money otm equity index options are major challenges to standard asset pricing models we develop a tractable equilibrium model with cumulative prospect theory cpt preferences that can overcome both challenges the key insight is that the variance premium can be written as the expected return on a portfolio of otm call and put options and the probability weighting feature of cpt can explain the puzzlingly low returns observed for these options using gmm on a sample of u s index option returns between 1996 and 2010 we show that the cpt model ts well observed option prices and therefore the variance premium in a dynamic setting probability weighting and time varying equity return volatility combine to match the observed time series pattern of the variance premium

identifying the economic and environmental impacts of china s trade in intermediates within the asia pacific region abstract using value added and employment as the representatives of economic benefits and carbon emissions as the proxy of environmental costs of trade this study analyzes the impacts of china s trade in intermediates with major trading partners in the asia pacific region australia canada japan korea mexico taiwan and the usa on its economy and environment during 2000 2014 through hypothetical extraction method and structural decomposition analysis results show that china s trade in intermediates within the region induced a higher share of carbon emissions than those of value added and employment the economic and environmental impacts of china s trade in intermediates with the seven trading partners were mainly driven up by the intensifying international industrial linkages technical factors induced considerable negative effects on the impacted carbon emissions and employment at the sectoral level the expanding intermediate trade of heavy industries brought the major part of increasing impacts on carbon emissions value added and employment the impacted employment shifted toward high skilled occupations especially in heavy industries and services and the impacted low skilled employment decreased in most sectors finally related policy implications are deduced

the future of the income tax the federal income tax has been under attack by the economics profession for more than a decade the attack comes from two directions supply siders who believe that progressive income taxation impairs economic incentives and more traditional economists who would substitute a progressive expenditure tax for the income tax 2 at one time support for the expenditure tax was confined to a few members of our profession including such distinguished names as john stuart mill irving fisher nicholas kaldor and james meade today it is fair to say that many if not most economists favor the expenditure tax or a flat rate income tax this group has joined the opponents of progressive taxation in the attack on the income tax despite an incessant barrage from both groups no country in the world is planning to abandon the income tax or is even considering a personal expenditure tax a wave of tax reform beginning with the u s reform in 1986 has been sweeping the world aimed at improving the income tax not at eliminating it tax preferences formerly regarded as sacrosanct are being removed and there is a distinct movement toward comprehensive income taxation 3 however individual income tax rates are being cut tax progressivity has been declining almost everywhere and reliance on the income tax has been diminishing it will come as no surprise to this audience that i approve of the base broadening feature of the current tax reform movement but i believe that the reduction in the redistributive effect of the income tax has gone too far in this paper i shall show that the progressivity of the u s tax system never very pronounced except during and immediately after the two world wars has been declining for more than two decades and that the tax reform act of 1986 reversed this decline but only slightly consequently we have a long way to go to improve the equity of the tax system i believe this can be done without punitive tax rates that will hurt economic incentives i begin with a brief review of recent changes in the u s distribution of income and follow this with an analysis of the effect of taxes on the income distribution i next examine arguments for and against the income tax with particular emphasis on its effects on economic incentives and its merits when compared with the expenditure tax i then evaluate the income tax as it emerged from the 1986 tax reform and conclude with tjoseph pechman passed away on august 19 1989 his presidential address was delivered at the onehundred second meeting of the american economic association december 29 1989 atlanta georgia joseph a pechman economic studies program the brookings institution 1775 massachusetts avenue nw washington dc 20036 i have benefited from the comments and suggestions on an earlier draft of this paper by henry j aaron richard goode jane g gravelle robert w hartman donald w kiefer herbert e klarman robert d reischauer clifford m winston and h peyton young but they should not be held responsible for the views expressed in this paper i am indebted to richard kasten for various simulations i am also grateful to stephen j kastenberg for research assistance and to diane a shugart valerie m owens and sara c hufham for secretarial assistance some of the more extreme supply siders argued that large tax cuts pay for themselves see for example laffer 1981 but i believe it is fair to say that this view has been totally discredited for a more reasonable supply side view see the economic report of the president 1982 2see for example michael j boskin 1978 david e bradford 1980 charles l ballard don fullerton john shoven and john whalley 1985 paul courant and edward gramlich 1982 martin feldstein 1978 robert hall and alvin rabushka 1985 john kay and mervyn king 1983 charles mclure 1987 mieszkowski 1980 and lawrence summers 1981 it is interesting that the recent popularity of the expenditure tax among economists was stimulated by a tax lawyer william d andrews 1974 3see pechman 1988

an explanation of each way wagers in three models of risky choice punters may engage in betting on both a selection in an event to finish first or in one of the number of places e g second third or fourth when the amounts staked with bookmakers at fixed odds on the win and place are equal it is called an each way bet each way bets are apparently popular with punters but inconsistent with prominent models of wagering which assume gamblers are everywhere risk seeking in this note we derive the conditions for win and place bets to be optimal in these three models of risky choice the mathematical conditions for the each way wager to be optimal as opposed to a win and place wager with different stakes are complicated and appear likely to occur rarely in practice however bettors obviously see the attraction in giving themselves two ways to bet on the one horse or two ways to win and betting each way we suggest part of the each way betting attraction is that they are quick and easy to compute a heuristic to solve an otherwise complex betting strategy

levels and long term trends in earnings inequality overcoming current population survey censoring problems using the gb2 distribution over its history the march current population survey cps has increasingly captured the upper tail of the distribution of all sources of income this together with time consistency problems in top coding means that users of both the public use and restricted access cps will understate the level of wage earnings and income inequality in earlier years and overstate their growth over time we address this problem by modeling the personal earnings of full time full year workers using the generalized beta distribution of the second kind calculating gini coefficients from the estimated parameters and comparing them with past findings

stochastic dominance in regret theory the regret theory of choice under uncertainty is known to admit intransitivities in preference relations in this paper the stochastic dominance properties of the theory are examined it is shown that the usual definition of first stochastic dominance is not satisfied by regret theoretic preferences and that in general violations of first stochastic dominance are not merely permitted but required an exact characterization of the stochastic dominance rule corresponding to regret theoretic preferences is presented this concept is weaker than the usual definition but stronger than the notion of statewise dominance in which one prospect yields a preferred outcome with probability 1 theories of choice under uncertainty have proliferated in recent years after a long period in which the expected utility eu approach of von neumann and morgenstern 1944 was pre eminent the breakdown of the dominance in eu theory reflects the increasing body of evidence that the choices made by many people systematically violate the predictions of the theory the axiomatic foundations of the theory and in particular the independence axiom have also received severe questioning ever since the famous critique of allais 1953

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

wagering on more than one outcome in an event in cumulative prospect theory and rank dependent utility in this letter we illustrate a previously unrecognised implication of cumulative prospect theory and rank dependent utility we demonstrate that the representative individual in both models will often engage in wagering on more than one outcome in an event for instance when playing european roulette the representative agents in cpt or rdu will always optimally wager on more than one outcome this implication contrasts with expected utility models of wagering based on risk seeking preferences due to the assumption of a convex segment of the utility function

the nash bargaining solution for decision weight utility functions abstract a simple derivation of the non expected utility nash outcome as defined in rubinstein et al 1992 rubinstein a safra z thomson w 1992 on the interpretation of the nash bargaining solution and its extension to non expected utility preferences econometrica 60 1171 1186 is given for the class of decision weight utility functions conditions for existence and uniqueness are provided

household portfolio diversification a case for rank dependent preferences the proliferation of novel preference theories in financial economics is hampered by a lack of non experimental evidence and by the theories additional complexity which has not been shown to be critical in applications in this article i present arguments in support of preferences with rank dependency using the survey of consumer finances data i document two widespread patterns inconsistent with expected utility i many households simultaneously invest in well deversified funds and in poorly diversified portfolios of stocks and ii some households with substantial savings do not invest anything in equities i show that portfolio choice models with rank dependent preferences plausibly parameterized and under fully rational assumptions are quantitatively consistent with the observed diversification these results call for further efforts to integrate the models of rank dependent preferences in portfolio theory and asset pricing the decision theoretic literature has long acknowledged the shortcomings of the expected utility theory of von neumann and morgenstern 1944 several generalizations of the theory are inspired by the experimental evidence and aimed at improving its descriptive accuracy however there are few applications of new models of preferences in finance and expected utility continues to dominate the field 1 two principal hurdles slow the proliferation of novel preferences in financial economics first the lack of empirical non experimental or field data confirming that the behavior motivating non expected utilities is widespread outside the laboratory settings second the additional and often significant complexity of the alternative preferences which has not been shown to be critical in applications where the models based on expected utility fall short of reasonable predictions this article presents empirical and theoretical this paper was previously circulated under the title household portfolio diversification the paper has benefited from the comments of shlomo benartzi luca benzoni markus brunnermeier john dickhaut maria perozek raj singh hersh shefrin and workshop participants at minnesota finance bag lunch 2003 wharton conference household financial decision making and portfolio choice and 2003 summer meetings of econometric society i would like to thank cam harvey the editor and an anonymous referee for many helpful comments and suggestions a special thanks to jack kareken for comments and editorial help on an earlier draft i am grateful to donna zerwitz for editorial assistance the views expressed herein are those of the author and not necessarily of the federal reserve bank of minneapolis or the federal reserve system all errors and omissions are the sole responsibility of the author address correspondence to valery polkovnichenko finance 3 122 csom 319 19 th

networks of value added trade global value chains gvcs require new methods for evaluating interconnections among countries which can no longer be accurately appraised by standard bilateral gross trade flows this paper uses tools of network analysis to examine the evolution of value added trade from 1995 to 2011 gvcs are very centralised and asymmetric networks with a few large economies acting as hubs which exposes them to the propagation of idiosyncratic shocks as gvcs expanded the networks of foreign value added in exports became denser more complex and intensively connected the regional dimension of gvcs is still dominant but is progressively giving place to a more global network networks of foreign value added in goods exports outpace those of services exports however foreign inputs of services are important for exports of both goods and services there is a striking rise of china as a supplier of value added while germany and the united states maintain a central role in gvcs over the whole period

an index of loss aversion to a considerable extent risk aversion as it is commonly observed is caused by loss aversion several indexes of loss aversion have been proposed in the literature the one proposed in this paper leads to a clear decomposition of risk attitude into three distinct components basic utility probability weighting and loss aversion the index is independent of the unit of payment the main theorem shows how the indexes of different decision makers can be compared through observed choices

optimism and pessimism in games this paper considers the impact of ambiguity in strategic situations it extends the earlier literature by allowing for optimistic responses to ambiguity ambiguity is modelled by ceu preferences we propose a new solution concept for players who may express ambiguitypreference then we study comparative statics of changes in ambiguity attitude in games with strategic complements this gives a precise statement of the impact of ambiguity on economic behaviour

growing unequal changes in the distribution of earnings across canadian cities this paper investigates changes in the distribution of earnings across 87 metropolitan areas in canada it does so using micro data taken from the 20 per cent long form sample of the census for the years 1996 2001 and 2006 results point to overall increases in urban inequality and to greater heterogeneity in inequality across the urban hierarchy with larger cities growing particularly unequal over time cross sectional and panel regression models suggest that city size unemployment deindustrialisation and the percentage of a city s population composed of visible minorities contribute to increased inequality in contrast a city s level of economic development has a mitigating effect on inequality although this effect appears to fade away over time the effects of changes in a city s age education and gender profiles on inequality are mixed

using the pareto distribution to improve estimates of topcoded earnings i introduction the public use march current population survey cps is the primary source of data for tracking levels and trends in u s labor earnings and for understanding the factors which influence these trends literatures that have used cps earnings data are vast and include research on the changing returns to education or college major in the labor market autor 2014 gemici and wiswall 2014 earnings differentials across occupations glied ma and pearlstein 2015 earnings volatility hardy and ziliak 2014 elasticity of taxable income burns and ziliak forthcoming and more generally the causes of changes in wage structures and earnings inequality see e g autor katz and kearney 2008 card and dinardo 2002 goldin and katz 2007 juhn murphy and pierce 1993 acemoglu 2002 altonji and blank 1999 and katz and autor 1999 provide reviews of this literature however these literatures that use the public use cps data have been hampered by an attenuated view of the right tail of the labor earnings distribution due to the topcoding of high earnings in the public use cps data 1 importantly the failure to properly correct for inconsistent topcoding has been found to result in biased estimates for a range of outcomes including returns to education hubbard 2011 the size of the earnings gaps between gender and race groups burkhauser and larrimore 2009a the relative economic resources of individuals with and without disabilities burkhauser and larrimore 2009b and population level income inequality burkhauser et al 2012 to correct for topcoding biases public use cps based researchers have generally pursued one of four paths 1 ignoring the topcoding problem 2 making an ad hoc adjustment to topcoded earnings values 3 using a pareto distribution to estimate earnings at the top of the distribution or 4 using cell means or rank proximity swapped data that is based on the still censored internal cps data for example a common ad hoc technique based on estimates from pareto imputations of top earnings is to replace topcoded earnings with a multiple of the topcode threshold so all individuals with topcoded earnings in a year are assumed to have earnings at 1 3 1 4 or 1 5 times the topcode threshold autor katz and kearney 2008 juhn murphy and pierce 1993 katz and murphy 1992 lemieux 2006 however such an approach may misstate top earnings if the wrong multiple is used or if the appropriate multiple changes over time similarly researchers using a pareto imputation of top earnings may misstate those earnings if they are unable to obtain a reasonable fit for the pareto distribution when using available public use data making use of internal march cps files with their much higher censoring levels we show that previous ad hoc estimates and pareto estimations of top earnings based on public use data understate mean earnings at the top of the earnings distribution and hence also understate earnings inequality however as this internal data are also censored albeit at higher levels any results based purely on the internal data will also fail to capture a portion of the income at the very top of the distribution and therefore will also understate inequality hence while cell means based on internal data such as those produced by larrimore et al 2008 and the rank proximity swapped data series which the census began providing in 2010 each allow researchers to replicate results from the internal census data findings using these series will be subject to the same limitations and understatement of true top incomes as the internal values recognizing the limitations of the existing options to correct for topcoding we proceed by using a continuous maximum likelihood estimator along with internal cps data to produce a series of more accurate estimates of top earnings in the cps data our estimates start with actual top earnings from the internal cps combined with a pareto estimate using these data for internally censored observations

recent trends in top income shares in the usa reconciling estimates from march cps and irs tax return data although the majority of research on us income inequality trends is based on public use march cps data a new wave of research using irs tax return data reports substantially higher levels of inequality and faster growing trends we show that these apparently inconsistent estimates are largely reconciled if the inequality measure and the income distribution are defined in the same way using internal cps data for 1967 2006 we closely match irs data based estimates of top income shares reported by piketty and saez 2003 our results imply that any inequality increases since 1993 are concentrated among the top 1 percent of the distribution

truncation bias and the measurement of income inequality 1988 truncation bias and the measurement of income inequality journal of business economic statistics vol 6 no 3 pp 335 337

truncation bias and the ordinal evaiuation of income inequality lorenz dominance analysis is used to examine the effect of top coding on the ordinal evaluation of u s income inequality across time current population survey microdata are adjusted for truncation bias and statistical inference procedures are used to examine biennial changes in unadjusted and adjusted lorenz curves beginning in 1985 the truncation bias has a significant effect on ordinal rankings of income inequality