Empirical Rules of Thumb for Choice under Uncertainty.

A substantial body of empirical evidence shows that individuals overweight extreme events and act in conflict with the expected utility theory. These findings were the primary motivation behind the development of the rank-dependent utility theory. The purpose of this paper is to demonstrate that some plausible empirical rules of thumb for choice under uncertainty can be rationalized by the rank-dependent utility theory.rank-dependent utility; maximin; maximax; mid-range

Asymptotic Distribution Theory of Empirical Rank-dependent measures of Inequity

A major aim of most income distribution studies is to make comparisons of income inequality across time for a given country and/or compare and rank different countries according to the level of income inequality. However, most of these studies lack information on sampling errors, which makes it difficult to judge the significance of the attained rankings. The purpose of this paper is to derive the asymptotic properties of the empirical rank-dependent family of inequality measures. A favourable feature of this family of inequality measures is that it includes the Gini coefficients, and that any member of this family can be given an explicit and simple expression in terms of the Lorenz curve. By relying on a result of Doksum [14] it is easily demonstrated that the empirical Lorenz curve, regarded as a stochastic process, converges to a Gaussian process. Moreover, this result forms the basis of the derivation of the asymptotic properties of the empirical rank-dependent measures of inequality.

Ranking Intersecting Lorenz Curves

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou-Dalton principle of transfers forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance. The dominance results for Lorenz curves do also apply to generalized Lorenz curves and thus provide convenient characterizations of the corresponding social welfare orderings.generalized Gini families of inequality measures, rank-dependent measures of inequality, Gini coefficient, partial orderings, Lorenz dominance, Lorenz curve, general principles of transfers

On the Measurement of Long-Term Income Inequality and Income Mobility

This paper proposes a two-step aggregation method for measuring long-term income inequality and income mobility, where mobility is defined as an equalizer of long-term income. First, the income stream of each individual is aggregated into a measure of permanent income, which accounts for the costs associated with income fluctuations. Consequently, mobility will have an unambiguously positive impact on social welfare in the sense that for two societies that have identical short term income distributions, the social welfare will be greatest for the socie ty which exhibits most mobility. The second step consists of aggregating permanent incomes across individuals into measures of social welfare, inequality and mobility. To this end, we employ an axiomatic approach to justify the introduction of a generalized family of rank-dependent measures of inequality, where the distributional weights, as opposed to the Mehran-Yaari family, depend on income shares as well as on population shares. Moreover, a subfamily is shown to be associated with social welfare functions that have intuitively appealing interpretatio ns. Further, the generalized family of inequality measures provides several new interpretations of the Gini-coefficient. The proposed family of income mobility also proves to encompass standard measures of income mobility, depending on the assumptions made about the interpersonal preferences and the credit market.Income inequality, income mobility, social welfare, the Gini coefficient, permanent income, annuity.

Designing Optimal Taxes with a Microeconometric Model of Household Labour Supply

The purpose of this paper is to present an exercise where we identify optimal income tax rules under the constraint of fixed tax revenue. To this end, we estimate a microeconomic model with 78 parameters that capture heterogeneity in consumption-leisure preferences for singles and couples as well as in job opportunities across individuals based on detailed Norwegian household data for 1994. For any given tax rule, the estimated model can be used to simulate the choices made by single individuals and couples. Those choices are therefore generated by preferences and opportunities that vary across the decision units. Differently from what is common in the literature, we do not rely on a priori theoretical optimal taxation results, but instead we identify optimal tax rules – within a class of 6-parameter piece-wise linear rules - by iteratively running the model until a given social welfare function attains its maximum under the constraint of keeping constant the total net tax revenue. We explore a variety of social welfare functions with differing degree of inequality aversion and also two alternative social welfare principles, namely equality of outcome and equality of opportunity. All the social welfare functions turn out to imply an average tax rate lower than the current 1994 one. Moreover, all the optimal rules imply – with respect to the current rule – lower marginal rates on low and/or average income levels and higher marginal rates on relatively high income levels. These results are partially at odds with the tax reforms that took place in many countries during the last decades. While those reforms embodied the idea of lowering average tax rates, the way to implement it has typically consisted in reducing the top marginal rates. Our results instead suggest to lower average tax rates by reducing marginal rates on low and average income levels and increasing marginal rates on very high income levels.Labour supply, optimal taxation, random utility model, microsimulation.

On the Measurement of Long-Term Income Inequality and Income Mobility

This paper proposes a two-step aggregation method for measuring long-term income inequality and income mobility, where mobility is defined as an equalizer of long-term income. The first step consists of aggregating the income stream of each individual into a measure of permanent income, which accounts for the costs associated with income fluctuations and allows for credit market imperfections. The second step aggregates permanent incomes across individuals into measures of social welfare, inequality and mobility. To this end, we employ an axiomatic approach to justify the introduction of a generalized family of rank-dependent measures of inequality, where the distributional weights, as opposed to the Mehran-Yaari family, depend on income shares as well as on population shares. Moreover, a subfamily is shown to be associated with social welfare functions that have intuitively appealing interpretations. Further, the generalized family of inequality measures provides new interpretations of the Gini-coefficient.income inequality, income mobility, social welfare, Gini coefficient, permanent income, credit market, annuity

Robust Inequality Comparisons

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations Aaberge (2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves which was proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families and thus the least restrictive social preferences required to reach unambiguous ranking of a set of Lorenz curves. From the weight-functions of these inequality measures we obtain intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967-2005.Lorenz curve, Lorenz dominance, rank-dependent measures of inequality, Gini coefficient, generalized Gini families of inequality measures

Evaluation of an In-Work Tax Credit Reform in Sweden: Effects on Labor Supply and Welfare Participation of Single Mothers

The purpose of this paper is to evaluate a recent Swedish in-work tax credit reform where we pay particular attention to labor market exclusion; i.e. individuals in as well as outside the labor force are included in the analysis. To highlight the importance of the joint effects from the tax and the benefit systems it appears particular relevant to analyze the labor supply behavior of single mothers. To this end, we estimate a structural microeconometric model of labor supply and welfare participation. The model accounts for heterogeneity in consumption-leisure preferences as well as for constraints in job opportunities. The results of the evaluation show that the reform generates welfare-gains for virtually every single mother, and moreover benefits low-income households. Finally, due to increased labor supply and decline in welfare participation we find that this reform is almost self-financing.labor supply, single mothers, in-work tax credit, social assistance, random utility model

On the Definition and Measurement of Chronic Poverty

As an alternative to the conventional methods for measuring chronic poverty, this paper proposes to use an interpersonal comparable measure of permanent income as a basis for defining and measuring chronic poverty. This approach accounts for the fact that individuals may undertake inter-period income transfers if it is to their advantage. Moreover, it allows for individual-specific interest rates on borrowing and saving as well as for the presence of liquidity constraints. Due to its general nature the proposed method proves useful for evaluating the theoretical basis of the standard methods for measuring chronic poverty.Intertemporal choice, liquidity constraints, permanent income, chronic poverty.

Accounting for Family Background when Designing Optimal Income Taxes: A Microeconometric Simulation Analysis

The purpose of this paper is to introduce and adopt a generalised version of Roemer's (1998) Equality of Opportunity (EOp) framework, which we call extended EOp, for analysing second-best optimal income taxation. Unlike the pure EOp criterion of Roemer (1998) the extended EOp criterion allows for alternative weighting profiles in the treatment of income differentials between as well as within types when types are defined by circumstances that are beyond people's control. This study uses parental education as a measure of exogenous circumstances. An empirical microeconometric model of labour supply in Italy is employed to simulate and identify income tax-transfer rules that are optimal according to the extended EOp criterion. We look for second-best optimality, i.e. the tax-transfer rules are not allowed to depend on family background, they only depend on income: family background is taken indirectly into account. The rules are defined by a universal (not individualized) lump-sum transfer (positive or negative) and by one or two marginal tax rates. A rather striking result of the analysis is that the optimal tax-transfer rule turns out to be a universal lump-sum tax (with marginal tax rates equal to zero), under Roemer's pure EOp criterion as well as under the generalised EOp criterion with moderate degrees of aversion to within-type inequality. A higher degree of within-type inequality aversion instead produces EOp-optimal rules with positive marginal tax rates. When the EOp-version of the Gini welfare function is adopted, the optimal tax rule turns out to be close to the actual 1993 Italian tax system, if not for the important difference of prescribing a universal lump-sum positive transfer of 3,500,000 ITL (=1807 Euros), which has no comparable counterpart in the actual system. On the other hand, when using the conventional equality of outcome (EO) criterion, the pure lump-sum tax always turns out to be optimal, at least with respect to the classes of two- and three-parameter rules. We also compute optimal rules under the additional constraint that universal lump-sum taxes are not feasible. Overall, the results do not conform to the perhaps common expectation that the EO criterion is more supportive of "interventionist" (redistributive) policies than an extended EOp approach.equality of opportunity, equality of outcome, labour supply, optimal income taxation