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Equivalence scales for continuous distributions of expenditure

100%
Kot S. M.
Equilibrium. Quarterly Journal of Economics and Economic Policy
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2023
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vol. 18
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issue 1
185-219
EN
Research background: In the actual sizable populations of households, the standard microeconomic concept of equivalence scales is intractable since its necessary condition of equality of household welfare levels is unlikely to be fulfilled. Purpose of the article: This paper aims to develop a concept of an equivalence scale, which can be suitable for continuous distributions of expenditures in the population. Methods: Using household welfare intervals, we get the random equivalence scale (RES) as the ratio of expenditure distributions of the compared populations of households. Findings & value added: We derive the parametric distribution of RES for the lognormal distributions of expenditures. The truncated distribution of RES is applied to account for possible economies of scale in the household size. A society?s inequality aversion can be helpful when selecting a single equivalence scale. We estimate RES for Poland using microdata on expenditures and subjective assessments of household welfare intervals. The estimated equivalence scales turned out to be very flat and dependent on welfare.
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Estimating the parameter of inequality aversion on the basis of a parametric distribution of incomes

100%
Kot S. M.
Equilibrium. Quarterly Journal of Economics and Economic Policy
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2020
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vol. 15
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issue 3
391-417
EN
Research background: In applied welfare economics, the constant relative inequality aversion function is routinely used as the model of a social decisionmaker?s or a society?s preferences over income distributions. This function is entirely determined by the parameter, ?, of inequality aversion. However, there is no authoritative answer to the question of what the range of ? an analyst should select for empirical work. Purpose of the article: The aim of this paper is elaborating the method of deriving ? from a parametric distribution of disposable incomes. Methods: We assume that households? disposable incomes obey the generalised beta distribution of the second kind GB2(a,b,p,q). We have proved that, under this assumption, the social welfare function exists if and only if ? belongs to (0,ap+1) interval. The midpoint ?mid of this interval specifies the inequality aversion of the median social-decisionmaker. Findings & Value added: The maximum likelihood estimator of ?mid has been developed. Inequality aversion for Poland 1998?2015 has been estimated. If inequality is calculated on the basis of disposable incomes, the standard inequality?development relationship might be complemented by inequality aversion. The ?augmented? inequality?development relationship reveals new phenomena; for instance, the stage of economic development might matter when assessing the impact of inequality aversion on income inequality.
3
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The atlas of inequality aversion: theory and empirical evidence on 55 countries from the Luxembourg Income Study database

88%
Kot S. M., Paradowski P. R.
Equilibrium. Quarterly Journal of Economics and Economic Policy
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2022
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vol. 17
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issue 2
261-316
EN
Research background: In the distributive analysis, the constant relative inequality aversion utility function is a standard tool for ethical judgements of income distributions. The sole parameter ? of this function expresses a society?s aversion to inequality. However, the profession has not committed to the range of ?. When assessing inequality and other welfare characteristics, analysts assume an arbitrary level of ?, common to all countries and years. This assumption seems unjustified. Purpose of the article: This paper aims to estimate the parameter ? for each country and year individually using datasets from the Luxembourg Income Study Database in all available years, which dates back to the 1970s. Methods: We utilise the method of estimating ?, which assumes the generalised beta of the second kind distribution of incomes. The estimator of ? is derived from the mathematical condition of the existence of the social welfare function.  Findings & value added: We have elaborated an ?atlas? of  388 estimates of ? for 55 countries across time. Inequality aversion is country-year specific, with a minimum of 0.97 and a maximum of 3.8. Ninety per cent of all estimates are less than 2.5. Inequality aversion is negatively correlated with income inequality, but it is independent of economic development. Thus, inequality aversion appears as an additional dimension of the classical inequality-development relationship. This article contributes to solving a fundamental problem of Welfare Economics: directly measuring the social utility of income (welfare) function. The estimates of ? for 55 countries imply a complete knowledge of these countries' constant relative inequality aversion utility functions.
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The entanglement of attitudes toward inequality: the theoretical background and measurement for the EU countries in 2021

75%
Kot S. M.
Statistics in Transition new series
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2026
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vol. 27
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issue 2
15-30
EN
This paper assumes two types of social planners who evaluate income distributions in terms of social welfare, economic inequality, and poverty. The first type, SPε, denotes individuals who have an aversion to income inequality as measured by the normative parameter ε. The second, SPv, comprises individuals who have an aversion to rank inequality, as measured by the normative parameter v. Since every member of a society may play the role of a social planner, there could be as many levels of ε and v as there are society members. It raises the question of which ranges of v and ε values are ethically sensible when conducting empirical welfare studies. This paper proposes the answer to this question by introducing the concepts of inequalityentangled SPv and SPε. If a randomly selected SPv had vi, one could automatically find εi of the inequality-entangled SPε, and vice versa. The inequality-entangled SPv and SPε consistently evaluate inequality, social welfare, and poverty. This paper moreover proposes a method for eliciting the pairs (vi, εi), i = 1, 2, …, n, from empirical income distributions. Moreover, a single pair (v*, ε*) exists, representing all n pairs. Additionally, the study applies the inequality-entanglement methodological framework to assess social welfare, inequality and poverty for 27 European Union member countries in 2021.
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Zastosowanie zasady równych ofiar do oceny sprawiedliwości taryfy podatku dochodowego od osób fizycznych (PIT) w Polsce

63%
Słoczyński T.
Gospodarka Narodowa. The Polish Journal of Economics
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2012
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vol. 259
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issue 10
23-47
EN
The aim of the paper is to perform an empirical analysis of the compatibility of the Polish personal income tax (PIT) function with the equal absolute sacrifice principle, which is a major principle of a fair division of tax burden. Throughout the empirical analysis, the author uses analytical methods proposed by Fisher (1927) and Young (1990). The Fisher method is based on calculating the variation in individual sacrifice according to an assumed utility function of income. The Young method is based on selecting the isoelastic utility function of income, which makes all taxpayers sacrifice most equally. Subsequently, a new tax function is determined, which guarantees equal absolute sacrifice according to the selected utility function of income, and compared with the actual tax function. The empirical analysis carried out by the author shows that the Polish personal income tax (PIT) function in 1999-2008 provided a good fit with the equal absolute sacrifice principle, while the sacrifice of most taxpayers was equalized according to reasonable utility functions. However, the author identified three groups of taxpayers whose sacrifice was significantly lower than required by the equal absolute sacrifice principle as well as described the time variation in the compatibility of the Polish tax function with the equal absolute sacrifice principle and in the progressivity of this function.
PL
Celem artykułu jest empiryczna analiza zgodności taryfy podatku dochodowego od osób fizycznych (PIT) w Polsce z zasadą równych ofiar absolutnych, tj. jedną z podstawowych zasad sprawiedliwego podziału obciążeń podatkowych. Do realizacji tego celu zastosowano metody analizy zaproponowane przez Fishera [1927] i Younga [1990]. Metoda Fishera polega na określeniu zmienności ofiar ponoszonych przez podatników zgodnie z pewną, założoną na potrzeby analizy, postacią funkcji użyteczności dochodu. Metoda Younga polega na wyznaczeniu tej spośród izoelastycznych funkcji użyteczności dochodu, która w największym możliwym stopniu zrównuje ofiary ponoszone przez podatników; następnie wyznacza się taryfę podatku, która zrównuje ofiary wszystkich podatników względem otrzymanej funkcji użyteczności dochodu, i porównuje tę taryfę z faktyczną taryfą opodatkowania. Według przeprowadzonej analizy taryfa podatku dochodowego od osób fizycznych (PIT) w Polsce w latach 1999-2008 była dość dobrze dopasowana do wymogów zasady równych ofiar absolutnych a ofiary większości podatników były zrównywane względem sensownych empirycznie funkcji użyteczności. Niemniej, wyróżniono trzy grupy podatników, których obciążenia podatkowe były niższe niż postulowane na gruncie zasady równych ofiar absolutnych, a także opisano zmienność w czasie zgodności taryfy opodatkowania w Polsce z zasadą równych ofiar absolutnych oraz progresywności tej taryfy.
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The estimation of the costs of children based on random equivalence scales

63%
Kot S. M.
Śląski Przegląd Statystyczny
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2020
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issue 18 (24)
EN
This paper measures the cost of children using the random equivalence scale (RES). From the general population perspective, the deterministic microeconomic equivalence scales appear as continuous random variables. The stude derived the distribution of RES, assuming the lognormal distribution of income. The truncated distribution of RES can account for possible economies of scale in income or expenditure. The positional measures of the truncated distribution of RES may serve as single equivalence scales. A society’s attitude towards inequality may help chose such scales. RES for Poland 2015 was estimated using microdata from the Household Budget Survey. Polish households exhibited a remarkable level of economies of scale in that year and the equivalence scales declined with expenditure. It was observed that the cost of bringing up a child is not constant; generally, it decreases with increasing household size.
PL
W artykule koszt utrzymania dziecka jest mierzony za pomocą losowej skali ekwiwalentności (RES). Z perspektywy populacji generalnej deterministyczne mikroekonomiczne skale ekwiwalentności ukazują się jako ciągłe zmienne losowe. W niniejszej pracy uzyskano rozkład RES na podstawie lognormalnego rozkładu dochodów. Ucięty rozkład RES umożliwia uwzględnienie korzyści wielkości dochodów lub wydatków. Za pojedyncze skale ekwiwalentności mogą służyć miary położenia w uciętym rozkładzie RES. W wyborze konkretnej skali pomocna może być postawa społeczeństwa wobec nierówności. W pracy oszacowano RES dla Polski w 2015 r. na podstawie mikrodanych z Sondażu Budżetów Gospodarstw Domowych. W owym roku polskie gospodarstwa domowe wykazywały znaczące korzyści wielkości wydatków. Ponadto skale ekwiwalentności malały wraz ze wzrostem wydatków. Zaobserwowano, że koszt utrzymania kolejnego dziecka nie jest stały – malał on wraz ze wzrostem wielkości gospodarstwa domowego.
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Zasada równych ofiar i alternatywne propozycje reformy systemu podatkowego w Polsce. Wnioski z kampanii wyborczej w 2005 r

63%
Słoczyński T.
Polityka Społeczna
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2014
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vol. 41
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issue 1(478)
11-17
XX
Autor dokonuje analizy empirycznej zgodności alternatywnych propozycji reformy systemu podatkowego w Polsce z zasadą równych ofiar. Analizuje projekty reform, które zostały przedłożone przez wybrane partie polityczne (Prawo i Sprawiedliwość, Platformę Obywatelską, Partię Demokratyczną oraz Samoobronę) podczas kampanii wyborczej w 2005 r. Stwierdza, że żadna z ww. propozycji nie może być traktowana jako z pewnością bardziej „sprawiedliwa” od faktycznej taryfy opodatkowania w 2006 r. Ponadto znaczny wpływ na uzyskiwane wyniki może mieć awersja do nierówności polskiego społeczeństwa.
EN
In this paper I provide an empirical analysis of the compatibility of alternative proposals for tax reform in Poland with the equal sacrifice principle. Precisely, I consider proposals which were put forward by various political parties (Law and Justice, Civic Platform, the Democratic Party, and the Self-Defence) during the 2005 election campaign. I conclude that neither of these proposals can be regarded as undoubtedly more compatible with this principle than the actual tax function in 2006. Also, the results are largely dependent on the inequality aversion of the Polish society.
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