Shlomo Yitzhaki (1944–2023): In Memoriam
纪念以色列经济学家什洛莫·伊扎基，回顾其在税收、不平等、基尼方法等领域的贡献，以及他领导以色列中央统计局的工作。
Shlomo Yitzhaki, a leading expert on the measurement of inequality and more generally on public finance, passed away in Jerusalem on April 17 2023 at the age of 79. He had been the head of the Central Bureau of Statistics of Israel between 2001 and 2012 and a Professor of Economics at the Hebrew University. Shlomo Yitzhaki was born in Bagdad in 1944 and moved to Israel with his family in 1951. He studied at the Hebrew University in Jerusalem where he obtained his Ph.D. in 1976. In 1975–1977 Yitzhaki was a post-doctoral researcher at Harvard University while in 1982 he was a guest scientist at the National Bureau of Economic Research and in 1994 a visitor at the IMF. He was also several times an advisor to the World Bank. In 1974 he was an advisor to the Ben-Shachar commission in charge of revising the tax system in Israel and in 2000 a member of the Ben-Bassat commission on tax reform. In 1993–1994 he was the head of the Sapir Forum on economic policy and in the years 1995–1998 of the Falk Institute on economic research in Israel. As head of Israel's Central Bureau of Statistics (CBS) he was responsible for introducing a new approach to implementing the 2008 Israeli Census. During Yitzhaki's tenure as head of the CBS, the latter became an active associate of several international statistical and economic organizations, in particular of the OECD of which Israel became a regular member in 2010. But Shlomo Yitzhaki was also a very active researcher and published more than 100 articles in international and Israeli academic journals in the fields of statistics, economics, finance, and sociology. He was also the author with the late Edna Schechtman of an important book entitled The Gini Methodology: A Primer on a Statistical Methodology, published by Springer Verlag in 2013. It is always difficult to classify the publications of a scholar by field or rather subfield. Nevertheless, we tried to do it and came up with five main domains in which Yitzhaki published articles: taxation and public finance (almost 40 publications); inequality, deprivation, and well-being (around 45 articles); finance (close to 20 articles); econometrics (again close to 20 articles); migration (4–5 articles). To this list should be added a dozen articles in other domains. A quick look at Google Scholar shows that four of Yitzhaki's articles were cited more than 1,000 times: the chapter he wrote with Joel Slemrod for the Handbook of Public Economics (Slemrod and Yitzhaki, 2002) on “Tax avoidance, evasion and administration” was cited more than 1,500 times; the article he published in 1985 in the Review of Economics and Statistics with Robert Lerman on “Income inequality effects by income source: A new approach and applications to the United States” was cited more than 1,400 times (Lerman and Yitzhaki, 1985); his article with Oded Stark and Edward Taylor on “Remittances and inequality” was published in 1986 in the Economic Journal and was cited more than 1,000 times; finally his article on “Relative deprivation and the Gini coefficient” was published in 1979 in the Quarterly Journal of Economics and was also cited more than 1,000 times. Note that Yitzhaki had also four articles published in the American Economic Review. Rather than listing all the important journals in which he published, let us try to summarize Yitzhaki's main contributions to the economic literature. As mentioned previously, Yitzhaki published many articles on taxation and public finance but, because of space constraints, we mention only a few. In the paper co-authored with Slemrod (1991) and entitled “Welfare Dominance: An Application to Commodity Taxation,” the authors start from the fact that developing countries rely heavily on commodity taxation as a major source of revenue and instrument to fight poverty and modify the income distribution. But in most such countries data are not available for estimating the excess burden of taxation so that the theory of optimal taxation cannot be used to guide public policy. The paper then borrows ideas from the literature on (second degree) stochastic dominance and proposes a method that allows identifying commodities that a large class of social welfare functions would consider as worth taxing or subsidizing. Mayshar and Yitzhaki (1995) then extend the approach of Yitzhaki and Slemrod (1991) by considering multiple (rather than only two) commodities and looking for Dalton-improving incremental tax reforms. A tax reform is considered as “Dalton-improving” if it improves social welfare for all possible social welfare functions conforming to Dalton's principle of transfers. Remember that the latter principle says that society will be better off when a unit of income is transferred from a richer to a poorer individual. Although such a Dalton-improving method has some shortcomings, it has the advantage, when comparing it to an approach based on a social welfare function, that it imposes a minimal structure on social norms and thus does not require the arbitrary selection of a particular social welfare function. When compared to an approach focusing on Pareto improvement, it is more likely to lead to practical policy recommendations concerning desirable tax reforms. In another original paper, Yitzhaki (1987), using Federal income tax returns in the United States, shows that corporate stock owned by investors with a high income appreciates faster than the stock owned by low-income investors. Several explanations may be given to such findings, such as differences in risk aversion or tax evasion, but Yitzhaki argues that, if confirmed by other studies, such conclusions imply that there are returns to scale in the capital market. Therefore, capital is likely to be unevenly accumulated. In the paper previously mentioned on remittances and inequality, Stark et al. (1986) stress the fact that the impact of migrant remittances on the rural income distribution depends, among other factors, on a village's migration history. Focusing on Mexican data the authors show that in a village with many internal migrants but few migrants that experienced migration to the United States, remittances from Mexico-to-United States migrants have an important disequalizing impact on the distribution of incomes in the village, while remittances from internal migrants improve the village's income distribution. On the contrary, in a village with a long history of having migrants going to the United States, remittances have an equalizing impact on incomes. Moving now to Yitzhaki's contributions in the domain of inequality, deprivation and welfare, we note that he had already started his research on Gini's mean difference (GMD), its possible applications, and developments, in the 1970s. This index has fascinated him his entire scientific life; and as he admits in a dedication, with a wink typical for him, he has also taken the index home with him.1 His insights from about 40 years of research form the foundations of The Gini Methodology: A Primer on a Statistical Methodology. This book is fascinating because, starting with a basic definition of the index, it unfolds an entire research agenda that reaches into very different areas of quantitative research, always linking formal statistical theory with real-life applications. In doing so, the book spans from possible alternative formulations of the index and connections to other measurement concepts, inequality decompositions, Gini regressions, to the application of the Gini index to statistical inference. The basic idea of the book is that in virtually all variance-based analyses, variance can be replaced by the GMD (and its variants). Substituting the GMD for the variance makes sense, as the authors show, when the assumption of (multivariate) normality does not hold. Then the GMD “reveals more” (Lambert & Decoster, 2005) than means, variances, and Pearson's correlation coefficients. Most importantly from a statistical/empirical viewpoint, the GMD allows researchers to assess whether (a) the statistical association between random variables is symmetric; (b) whether and to what extent a population is stratified; and (c) whether the linearity assumption in regression analyses is supported by the data. The assumption of symmetry is convenient but not innocuous, particularly when the distribution of a variable is not known, or when the variable is latent—impossible to observe directly—or ordinal—lacking a natural quantitative measurement unit (e.g. intelligence, subjective well-being, or worries). The question then becomes whether monotonic increasing transformations change the sign of correlations and thus the conclusion of the empirical investigation. The Gini method allows an answer, as it has two asymmetric correlations associated with it, and linearly transforming a variable changes only one of the two Gini correlations. Hence, the differences in the correlations allow an assessment of the robustness of empirical associations. The property that the Gini has two asymmetric correlation coefficients can also be used in many other areas. For example, Schröder and Yitzhaki (2017a) propose a procedure to determine what a “reasonably large sample size” should be in empirical applications that rely on the central limit theorem.2 If a population is not perfectly stratified along income or other outcomes of interest, the Gini index, in contrast to other indices, is not decomposable by population subgroups (Mookherjee & Shorrocks, 1982). For some applications this can be viewed as a disadvantage. However, it can also be used to learn more about the underlying distribution. As shown in Chapter 4 of Yitzhaki and Schechtman's (2013) book, there is a third term, i.e., a quantitative measure of the extent of overlapping between the population subgroups, shedding light on the extent of stratification and how systematic the separation of the population into subgroups is. As shown in Chapter 22, the specific decomposition properties of the Gini index can be used to assess the role of ethnic background for social stratification. The framework can also be helpful for assessments of societal welfare when certain sub-populations—e.g. migrants—move in and out of the sample over time. The GMD also allows researchers to study the suitability of the linearity assumption between the dependent and an explanatory variable in OLS and other types of regressions. In this respect, the so-called LMA curve, which relies on the GMD, is more helpful. The LMA is the vertical difference between two absolute concentration curves: the absolute concentration curve of Y given X, under the assumption that the two variables are statistically independent, which is a line, minus the actual absolute concentration curve of Y as a function of F(X). Coming back to the topic of ordinal variables, the LMA allows researchers to explore if regression coefficients are sensitive to monotonic increasing transformations of the independent variable (e.g. if the relationship between happiness and age or income hinges on the measurement scale of happiness). Schröder and Yitzhaki (2017b) use the LMA to show under which transformations it is possible to find regression OLS coefficients to be positive for one transformation but negative for another. This finding has important implications for other contexts such as the measurement of educational achievements, cognitive and non-cognitive abilities, health, etc. The book also covers applications of the Gini method to social welfare and relative deprivation (the idea that people's perception of well-being is affected by their own income as well as by the income of those around them), as originally developed in Yitzhaki (1979). Yitzhaki proposes a modified version of the Gini coefficient that incorporates the concept of relative deprivation by comparing individuals' income to the average income of those in the same income group. This relative Gini index considers the fact that individuals who are relatively poorer than others in their income group may experience greater relative deprivation than those who are poorer but belong to a relatively poorer income group. By incorporating the concept of relative deprivation, the relative Gini is a measure of income inequality and its impact on social welfare. Yitzhaki concludes that policymakers should consider the concept of relative deprivation in designing policies aimed at reducing income inequality and promoting social welfare. On a more personal note, Shlomo Yitzhaki was for Jacques Silber the prototype of honesty. When Shlomo was persuaded that his position was justified, nothing could convince him to modify his stance, whatever the price he may have to pay for having such an opinion. This is not a common feature among human beings, but this is also one of the reasons for which he deserved our admiration. For Carsten Schröder, Shlomo Yitzhaki was not only a brilliant scientist but also a very honest person with a great sense of humor. So, although, as he himself wrote, the Gini radiated throughout his life, his family was extremely important to him. And without his loving and congenial wife as well as his beloved children Nili and Guy and his grandchildren, Shlomo Yitzhaki would have been unthinkable. Shlomo Yitzhaki also always had an ear for Juniors and Seniors who sought his advice, and they certainly thank him for this.