the retail price of inequality abstract this paper studies the relation between a city s income distribution and its retail price level using panel data we find that an increase in the presence of lower middle income households relative to poor or upper income households is associated with lower prices our findings suggest that greater income inequality raises the prices that poor households face thus making it harder for them to invest in human capital

price indexes inequality and the measurement of world poverty i discuss the measurement of world poverty and inequality with particular attention to the role of purchasing power parity ppp price indexes from the international comparison project global inequality increased with the latest revision of the icp and this reduced the global poverty line relative to the us dollar the recent large increase of nearly half a billion poor people came from an inappropriate updating of the global poverty line not from the icp revisions even so ppp comparisons between widely different countries rest on weak theoretical and empirical foundations i argue for wider use of self reports from international monitoring surveys and for a global poverty line that is truly denominated in us dollars

how the baby boomers retirement wave distorts model based output gap estimates hours per capita measures based on the private sector as usually included in the set of observables for estimating macroeconomic models are affected by low frequent demographic trends and sectoral shifts that cannot be explained by standard models further model based output gap estimates are closely linked to the observable hours per capita series hence hours per capita that are not measured in concordance with the model assumptions can distort output gap estimates this paper shows that sectoral shifts in hours and the changing share of prime age individuals in the working age population lead indeed to erroneous output gap dynamics regarding the aftermath of the global financial crisis model based output gaps estimated using standard hours per capita series are persistently negative for the us economy this is not caused by a permanently depressed economy but by the retirement wave of baby boomers which lowers aggregate hours per capita after adjusting hours for changes in the age composition to bring them in line with the model assumptions the estimated output gap gradually closes in the years following the global financial crisis

existence of equilibrium in single and double private value auctions we show existence of equilibria in distributional strategies for a wide class of private value auctions including the first general existence result for double auctions the set of equilibria is invariant to the tie breaking rule the model incorporates multiple unit demands all standard pricing rules reserve prices entry costs and stochastic demand and supply valuations can be correlated and asymmetrically distributed for double auctions we show further that at least one equilibrium involves a positive volume of trade the existence proof establishes new connections among existence techniques for discontinuous bayesian games

the effects of statistically dependent values on equilibrium strategies of bilateral k double auctions abstract this paper describes how introducing statistical dependency among trader values changes the equilibrium bidding strategies in bilateral k double auctions and uses the special case of affiliation to illustrate the range of equilibrium responses to a change in the value distribution consistent with standard intuition a change from independent to strictly affiliated valuations can result in high value buyers and low value sellers bidding closer to their actual values while low value buyers and high value sellers distort their bids farther from their true values however there also exist equilibria for which either type of trader responds to a change in the distribution of values in the opposite direction whether a given trader bids more aggressively or less aggressively can also be non monotonic with respect to the trader s value

on the importance of the participation margin for labor market fluctuations abstract conventional analyses of labor market fluctuations ascribe a minor role to labor force participation we show by contrast that flows based analyses imply that the participation margin accounts for around one third of unemployment fluctuations a novel stock flow apparatus establishes these facts delivering three further contributions first the role of the participation margin appears robust to adjustments for spurious transitions induced by reporting error second conventional stocks based analyses are subject to a stock flow fallacy neglecting offsetting forces of worker flows on the participation rate third increases in labor force attachment among the unemployed during recessions are a leading explanation for the role of the participation margin

measuring global poverty why ppp methods matter abstract we present theory and evidence to suggest that in the context of analyzing global poverty the eks approach to estimating purchasing power parities yields more appropriate international comparison of real incomes than the geary khamis approach our analysis of the 1996 and 2005 international comparison project data confirms that the geary khamis approach substantially overstates the relative incomes of the world s poorest nations and this leads to misleading comparisons of poverty across regions and over time the eks index of real income is much closer to being a true index of economic welfare and is therefore preferred for assessment of global poverty

the cyclicality of separation and job finding rates this paper uses cps gross flow data to analyze the business cycle dynamics of separation and job finding rates and to quantify their contributions to overall unemployment variability cyclical changes in the separation rate are negatively correlated with changes in productivity and move contemporaneously with them while the job finding rate is positively correlated with and tends to lag productivity contemporaneous fluctuations in the separation rate explain between 40 and 50 percent of fluctuations in unemployment depending on how the data are detrended this figure becomes larger when dynamic interactions between the separation and job finding rates are considered

existence of equilibrium in large double auctions abstract we show the existence of a pure strategy symmetric increasing equilibrium in double auction markets with correlated conditionally independent private values and many participants the equilibrium we find is arbitrarily close to fully revealing as the market size grows our results provide strategic foundations for price taking behavior in large markets

why some anti immigrant parties fail and others succeed a two step model of aggregate electoral support over the past 2 decades some anti immigrant parties have managed to gain substantial electoral support in various european countries most notably austria freiheitliche partei osterreichs and flanders vlaams blok however in other countries the success of such parties either has been insignificant or did not last the most popular models of support for anti immigrant parties focus primarily on the demand side of the electoral process the authors develop a model to explain differences in aggregate level support for these parties which also takes into account the supply side this model builds upon an explanation provided by kitschelt the model is tested empirically for 13 european anti immigrant parties in the period from 1989 to 1999 altogether yielding 25 party year combinations the authors test the sociostructural model and their alternative model at the level of political parties the sociostructural model explains 3 of the variance in success whereas the authors model explains 83

explaining variation in the success of extreme right parties in western europe methodological problems associated with selection bias and interaction effects have hindered the accumulation of systematic knowledge about the factors that explain cross national variation in the success of extreme right parties the author uses a statistical analysis that takes account of these problems to examine the effect of electoral institutions unemployment and immigration on the support for these parties the data set used in this analysis is new and spans 19 countries and 165 national elections there are four substantive conclusions the first is that it is important to distinguish between neofascist and populist parties on the extreme right because their fortunes depend on different factors the second is that populist parties do better in countries where the district magnitude is larger and more seats are allocated in upper tiers the third is that although immigration has a positive effect on populist parties irrespective of the unemployment level unemployment only matters when immigratio

do positional goods inhibit saving evidence from a life cycle experiment abstract we investigate the effect of positional goods goods for which one s consumption relative to others matters on saving based on results from a life cycle consumption saving experiment in a group treatment we allow inter personal comparisons by assigning subjects to groups and displaying rankings based partly on consumption a baseline individual treatment is similar but without the additional information we find more under saving saving less than the optimal amount and lower money earnings for subjects in the group treatment both effects are economically relevant with magnitudes of roughly 6 7 of expected income and 7 8 of average earnings respectively additional analysis shows that the result is driven by those subjects who are not ranked in the top three in their group keeping up with the joneses and males in particular

measuring the trends in inequality of individuals and families income and consumption we present evidence on the level of and trend in inequality from 1985 2010 in the united states using disposable income and consumption for a sample of individuals from the consumer expenditure ce survey differing from the findings in other recent research we find that the trends in income and consumption inequality are broadly similar between 1985 and 2006 but diverge during the great recession with consumption inequality decreasing and income inequality increasing given the differences in the trends in inequality in the last four years using both income and consumption provides useful information

income mobility profiles abstract an income mobility profile is a graphical tool to portray income mobility and identify the association between individual movements and initial status which despite its importance when assessing the social relevance of mobility is often discounted by aggregate mobility indices

is the united states still a land of opportunity recent trends in intergenerational mobility abstract we present new evidence on trends in intergenerational mobility in the united states using administrative earnings records we find that percentile rank based measures of intergenerational mobility have remained extremely stable for the 1971 1993 birth cohorts for children born between 1971 and 1986 we measure intergenerational mobility based on the correlation between parent and child income percentile ranks for more recent cohorts we measure mobility as the correlation between a child s probability of attending college and her parents income rank we also calculate transition probabilities such as a child s chances of reaching the top quintile of the income distribution starting from the bottom quintile based on all of these measures we find that children entering the labor market today have the same chances of moving up in the income distribution relative to their parents as children born in the 1970s however because inequality has risen the consequences of the birth lottery t

inequality in indonesia what can we learn from top incomes abstract using taxation and household survey data this paper estimates top income shares for indonesia during 1920 2004 our results suggest that top income shares grew during the 1920s and 1930s but fell in the post war era we observe a sharp rise in top income shares during the late 1990s coinciding with the 1997 98 economic crisis where comparable data are available top income shares in indonesia are generally higher than in other countries a finding that is at odds with the view that indonesia is a relatively egalitarian society this suggests that top income shares may provide a more complete picture of developing country inequality in comparative perspective

bargaining under incomplete information this paper presents and analyzes a bargaining model of bilateral monopoly under uncertainty under the bargaining rule proposed the buyer and the seller each submit sealed offers that determine whether the good in question is sold and the transfer price the nash equilibrium solution of this bargaining game implies an offer strategy of each party that is monotonic in its own reservation price and depends on its assessment of the opponent s reservation price issues of relative bargaining advantage and efficiency are examined for a number of special cases finally we discuss the appropriateness of the nash solution concept

the politics of inequality voter mobilization and left parties in advanced industrial states why is it that some countries have witnessed significant increases in inequality since the 1960s while at the same time experiencing very little change in the way politics is conducted and why is it that in other countries where inequality has increased much less the left has become substantially more redistributive the answer the authors argue has to do with the interaction between inequality and political mobilization of low income voters the authors make two points in this article first high levels of inequality move left parties to the left second although increasing inequality pushes the core constituencies of left parties to the left it also makes some individuals less likely to be involved in politics the authors argue that left parties will respond to an increase in inequality only when low income voters are politically mobilized they explore these claims through a comparative analysis of left party programs in 10 organisation for economic cooperation and development countries over the period 1966 to 2002

the developing world is poorer than we thought but no less successful in the fight against poverty a new data set on national poverty lines is combined with new price data and almost 700 household surveys to estimate absolute poverty measures for the developing world we find that 25 of the population lived in poverty in 2005 as judged by what poverty typically means in the world s poorest countries this is higher than past estimates substantial overall progress is still indicated the corresponding poverty rate was 52 in 1981 but progress was very uneven across regions the trends over time and regional profile are robust to various changes in methodology though precise counts are more sensitive

what unites right wing populists in western europe re examining grievance mobilization models in seven successful cases unlike for the green party family no empirically backed scholarly consensus exists about the grievances mobilized by populist right parties in western europe to the contrary three competing grie

toward a strategic foundation for rational expectations equilibrium a step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information if there are sufficiently many buyers and sellers and their bids are restricted to a sufficiently fine discrete set of prices then generically there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents in particular the large double auction equilibrium is almost efficient and almost fully aggregates the agents information

international business cycles world region and country specific factors the paper investigates the common dynamic properties of business cycle fluctuations across countries regions and the world we employ a bayesian dynamic latent factor model to estimate common components in macroeconomic aggregates output consumption and investment in a 60 country sample covering seven regions of the world the results indicate that a common world factor is an important source of volatility for aggregates in most countries providing evidence for a world business cycle we find that region specific factors play only a minor role in explaining fluctuations in economic activity we also document similarities and differences across regions countries and aggregates jel f41 e32 c11 c32

the limitations of decentralized world redistribution an optimal taxation approach abstract a centralized scheme of world redistribution that maximizes a border neutral social welfare function subject to the disincentive effects it would create generates a drastic reduction in world consumption inequality dropping the gini coefficient from 0 69 to 0 25 in contrast an optimal decentralized i e with no cross country transfers redistribution has a miniscule effect on world income inequality thus the traditional public finance concern about the excess burden of redistribution cannot explain why there is so little world redistribution actual foreign aid is vastly lower than the transfers under the simulated world income tax suggesting that voluntary world transfers subject to a free rider problem produces an outcome that is consistent with rich countries such as the united states either placing a much lower value on the welfare of foreigners or else expecting that a very significant fraction of cross border transfers is wasted the product of the welfare weight and one minus the share of transfers that are wasted constitutes the implicit weight that the united states assigns to foreigners we calculate that value to be as low as 1 2000 of the value put on the welfare of an american suggesting that u s policy is consistent with social preferences that place essentially no value on the welfare of the citizens of the poorest countries or that implicitly assumes that essentially all transfers are wasted

the world distribution of income falling poverty and convergence period we estimate the world distribution of income by integrating individual income distributions for 138 countries between 1970 and 2000 country distributions are constructed by combining national accounts gdp per capita to anchor the mean with survey data to pin down the dispersion poverty rates and head counts are reported for four specific poverty lines rates in 2000 were between one third and one half of what they were in 1970 for all four lines there were between 250 and 500 million fewer poor in 2000 than in 1970 we estimate eight indexes of income inequality implied by our world distribution of income all of them show reductions in global inequality during the 1980s and 1990s

explaining social policy preferences evidence from the great recession to what extent do personal circumstances as compared to ideological dispositions drive voters preferences on welfare policy addressing this question is difficult because a person s ideological position can be an outcome of material interest rather than an independent source of preferences the article deals with this empirical challenge using an original panel study carried out over four years tracking the labor market experiences and the political attitudes of a national sample of americans before and after the eruption of the financial crisis the analysis shows that the personal experience of economic hardship particularly the loss of a job had a major effect on increasing support for welfare spending this effect was appreciably larger among republicans than among democrats a result that was not simply due to a ceiling effect however the large attitudinal shift was short lived dissipating as individuals employment situations improved the results indicate that the personal experience of an economic shock has a sizable yet overall transient effect on voters social policy preferences

equilibria in open common value auctions abstract a sufficient condition for uniqueness of nash equilibrium in second price common value auctions is identified we establish that there exists a continuum of equilibria in irrevocable exit common value auctions for the case of two bidders we provide plausible sufficient conditions under which the expected seller revenue is maximized at the symmetric equilibrium an example in which the auctioneer s revenue at the symmetric equilibrium in a second price auction is strictly greater than the revenue at many asymmetric equilibria in the corresponding irrevocable exit auction is provided

positional deprivation and support for radical right and radical left parties we explore how support for radical parties of both the left and right may be shaped by what we call positional deprivation where growth in income of individuals at a given point in the income distribution is outpaced by income growth elsewhere in that distribution we argue that positional deprivation captures the combination of over time and relative misfortune that can be expected to distinctly spur support for radical left and right parties we explore this possibility by matching new measures of positional deprivation to individual level survey data on party preferences in 20 european countries from 2002 to 2014 we find that positional deprivation is robustly correlated with supporting radical populist parties first positional deprivation generally measured as average income growth across deciles of a country s income distribution minus a respondent s own decile s growth is associated with respondents retreat from mainstream parties and with support for both radical right and particularly radical left parties second positional deprivation relative to the highest and the lowest ends of the income spectrum play out differently for radical right and for radical left support a respondent s positional deprivation relative to the wealthiest decile s growth in his or her country tends to spur support for radical left but not radical right parties in contrast positional deprivation relative to the poorest decile s growth in a respondent s country tends to spur support for radical right but not left parties the results suggest that the combination of over time and relative economic misfortune may be key to how economic experience shapes radical backlash of the left and right

resource rents redistribution and halving global poverty the resource dividend summary this paper considers the proposal that each country distributes its resource rents directly to citizens as a universal and unconditional cash transfer or resource dividend and estimates its potential impact on global poverty for the years 2000 06 using a global dataset on resource rents and the distribution of income i find that if every developing country implemented the policy then the number of people living below 1 a day would be cut by between 27 and 66 depending on the year and the assumptions made looking ahead poverty could be better than halved as long as commodity prices do not drop below their 2004 level

inequality among world citizens 1820 1992 this paper investigates the distribution of well being among world citizens during the last two centuries the estimates show that inequality of world distribution of income worsened from the beginning of the 19th century to world war ii and after that seems to have stabilized or to have grown more slowly in the early 19th century most inequality was due to differences within countries later it was due to differences between countries inequality in longevity also increased during the 19th century but then was reversed in the second half of the 20th century perhaps mitigating the failure of income inequality to improve in the last decades jel d31 f0 n0 o0

the impact of young workers on the aggregate labor market an increase in the share of youth in the working age population of one state or region relative to the rest of the united states causes a sharp reduction in that state s relative unemployment rate and a modest increase in its labor force participation rate this is inconsistent with many theories of the labor market but can be easily explained by a model of frictional unemployment with on the job search the theory makes strong predictions regarding the behavior of wages which are shown to be consistent with the data the paper also reconciles its findings with an existing body of apparently contradictory empirical evidence

differences in relative prices and international differences in growth rates the new growth literature following paul m romer 1986 and robert e lucas jr 1988 has formulated models in which growth rates can differ systematically across countries a large empirical literature has used cross sectional techniques to examine the cause of international differences in growth rates this paper examines whether this work has used data which have been constructed in such a way as to introduce inadvertently a spurious correlation between growth and income levels this effect occurs because relative prices evolve because of different rates of technological progress in different industries many of the new growth models assume single goods or goods produced by the same technology so this phenomenon has so far escaped analysis if technological progress is more rapid in some sectors than others relative prices will change during the process of development the change of relative prices has two effects on measured growth rates first the choice of base prices affects the growth rate this phenomenon is sometimes called the gerschenkron effect second using any base prices or weights introduces a spurious correlation between income and growth less developed countries would tend to have lower growth rates not because they grew more slowly but because of data construction techniques for the sake of simplicity these phenomena will be called the gerschenkron or the level effect and the spurious correlation effect 3 this paper examines the international comparison program icp and the penn world tables pwt which are based on the icp the penn world tables are the data most widely used in empirical studies of international differences in economic growth both the icp and pwt use international prices to adjust for differences in the purchasing power of currencies these prices most closely resemble hungarian prices using such prices tends to produce time series with lower growth rates than those in the national accounts for countries less developed than hungary conversely the growth rates would be higher for countries more developed than hungary however the growth rates of poorer countries are not systematically lower in the penn world tables the paper examines why the growth rates are not distorted and makes some specific recommendations for data construction and use virginia polytechnic institute and state university blacksburg va 24061 0316 part of this work was supported by a grant from the institute of international studies at brown university and by a summer internship at the division of international finance at the federal reserve board i am grateful to peter garber david weil oded galor and anonymous referees for helpful comments alan heston and robert summers have also helped me understand icp and pwt methodology of course i alone am responsible for any mistakes in this paper iexamples include steve dowrick and duc tho nguyen 1989 robert j barro 1991 j bradford de long and lawrence h summers 1991 and n gregory mankiw et al 1992 2a series of papers by christina d romer 1986a b 1989 has already emphasized the importance of data construction techniques in another context 3there is a third effect a real acceleration effect caused by shifting consumption patterns and the reallocation of resources between sectors growth accountants such as angus maddison 1987 adjust estimates of total factor productivity for this sort of shift william j baumol et al 1989 have also referred to this phenomenon for an analysis in terms of a simple multisector solow model see nuxoll 1992a

on the demographic adjustment of unemployment the unemployment rate is one of the most important business cycle indicators but its interpretation can be difficult because slow changes in the demographic composition of the labor force affect the level of unemployment and make comparisons across business cycles difficult to purge the unemployment rate from demographic factors labor force shares are routinely used to control for compositional changes this paper shows that this approach is ill defined because the labor force share of a demographic group is mechanically linked to that group s unemployment rate as both variables are driven by the same underlying worker flows we propose a new demographic adjustment procedure that uses a dynamic factor model for the worker flows to separate aggregate labor market forces and demographic specific trends using the u s labor market as an illustration our demographic adjusted unemployment rate indicates that the 2008 2009 recession was much more severe and generated substantially more slack than the early 1980s recession

global income distribution from the fall of the berlin wall to the great recession we present an improved panel database of national household surveys between 1988 and 2008 in 2008 the global gini index is around 70 5 having declined by approximately 2 gini points china graduated from the bottom ranks changing a twin peaked global income distribution to a single peaked one and creating an important global median class 90 of the fastest growing country deciles are from asia while almost 90 of the worst performers are from mature economies another winner was the global top 1 hence the global growth incidence curve has a distinct supine s shape with gains highest around the median and top

the structure of inequality and the politics of redistribution against the current consensus among comparative political economists we argue that inequality matters for redistributive politics in advanced capitalist societies but it is the structure of inequality not the level of inequality that matters our theory posits that middle income voters will be inclined to ally with low income voters and support redistributive policies when the distance between the middle and the poor is small relative to the distance between the middle and the rich we test this proposition with data from 15 to 18 advanced democracies and find that both redistribution and nonelderly social spending increase as the dispersion of earnings in the upper half of the distribution increases relative to the dispersion of earnings in the lower half of the distribution in addition we present survey evidence on preferences for redistribution among middle income voters that is consistent with our theory and regression results indicating that the left parties are more likely to participate in government when the structure of inequality is characterized by skew

bilateral trade with the sealed bid k double auction existence and efficiency for k in the unit interval the k double auction determines the terms of trade when a buyer and a seller negotiate transfer of an item the buyer submits a bid b and the seller submits an offer s trade occurs if b exceeds s at price kb 1 k s we model trade as a bayesian game in which each trader privately knows his reservation value but only has beliefs about the other trader s value existence of a multiplicity of equilibria is proven for a class of trader s beliefs for generic beliefs however these equilibria are shown to be ex ante inefficient

understanding the evolution of world business cycles abstract this paper studies the changes in world business cycles during the period 1960 2003 we employ a bayesian dynamic latent factor model to estimate common and country specific components in the main macroeconomic aggregates output consumption and investment of the g 7 countries we then quantify the relative importance of the common and country components in explaining comovement in each observable aggregate over three distinct time periods the bretton woods bw period 1960 1 1972 2 the period of common shocks 1972 3 1986 2 and the globalization period 1986 3 2003 4 the results indicate that the common g 7 factor explains on average a larger fraction of output consumption and investment volatility in the globalization period than it does in the bw period

explaining international and intertemporal variations in income inequality this paper explores the propositions that income inequality is relatively stable within countries and that it varies significantly among countries a new and expanded data set provides broad support for both propositions drawing on a political economy and capital market imperfection arguments to explain the intertemporal and international variation in inequality the empirical analysis shows that the predicted variables associated with the first argument a measure of civil liberties and the initial level of secondary schooling and the second argument a measure of financial depth and the initial distribution of land are indeed important determinants of inequality this paper explores two propositions regarding income inequality they are first income inequality is relatively stable within countries and second it varies significantly across countries to illustrate note that the gini coefficient in india remained almost constant for forty years 1951 92 with mean 32 6 and standard deviation 2 0 2 in contrast the variation in gini coefficients across countries is large 61 9 in honduras in 1968 compared with 17 8 in bulgaria in 1976 if substantiated these propositions have potentially significant implications for poverty the significance of the first is obvious barring any fundamental socio political change poverty reduction will depend crucially on the rate of economic growth given this the significance of the second is that in inegalitarian economies the poor will enjoy a smaller share of any national increment in income than in more egalitarian ones drawing on a new and expanded data set on inequality deininger and squire 1996a the first of the paper s three sections conducts standard statistical tests of the two propositions the sample comprises 573 observations on the most common measure of inequality the gini coefficient for 49 developed and developing countries covering the period 1947 94 the results broadly confirm our two propositions specifically analysis of variance anova shows that about 90 of the total variance in the gini coefficients

international systems and domestic politics linking complex interactions with empirical models in international relations following older debates in international relations literature concerning the relative importance of domestic versus systemic factors newer debates emphasize interdependence among states and the complex interactions between systemic and domestic factors as globalization and democratization advance theories and empirical models of international politics have become more complicated we present a systematic theoretical categorization of relationships between domestic and systemic variables we use this categorization so that scholars can match their theory to the appropriate empirical model and assess the degree to which systemic factors affect their arguments we also present two advances at the frontier of these empirical models in one we combine hierarchical models of moderating relationships with spatial models of interdependence among units within a system in the other we provide a model for analyzing spatial interdependence that varies over time this enables us to examine how the level of interdependence among units has evolved we illustrate our categorization and new models by revisiting the recent international political economy ipe debate over the relationship between trade policy and regime type in developing countries

what do we know about global income inequality in this paper we review the recent literature on global interpersonal income inequality while all estimates agree that the level is very high with a gini of between 0 630 and 0 686 in the 1990s there is no consensus regarding the direction of change we discuss methodological issues including the use of national accounts versus survey based estimates of mean income or consumption and the choice of purchasing power parity exchange rates findings of a rise or fall in global income inequality are not robust across different estimation methods and datasets given the diversity of estimates and various sources of uncertainty including gaps and errors in the underlying data we conclude there is insufficient evidence to determine the direction of change in global interpersonal inequality in recent decades

efficiency of large double auctions we consider large double auctions with private values values need be neither symmetric nor independent multiple units may be owned or desired participation may be stochastic we introduce a very mild notion of a little independence we prove that all nontrivial equilibria of auctions that satisfy this notion are asymptotically efficient for any alpha 0 inefficiency disappears at rate 1 n 2 alpha