*
Esfandiar Maasoumi
Department of Economics
Southern Methodist University
Dallas, TX 75275-0496, U.S.A.
E-mail: Maasoumi@mail.smu.edu
And
Almas Heshmati
Department of Economic Statistics
Stockholm School of Economics
Box 6501, S-113 83 Stockholm, Sweden
E-mail: Almas.Heshmati@hhs.se
ABSTRACT
Sweden's income distribution for the whole population and for subgroups, including its immigrants, has been extensively studied. The interest in this area has grown with increasing availability of data, including panels.
The previous studies are based on indices of inequality or mobility. While indices are useful for complete ordering and have an air of “decisiveness” about them, they lack universal acceptance of the value judgements inherent to the welfare functions that underlay any index. In contrast, uniform partial order relations are studied in this paper which rank welfare situations over very wide classes of welfare functions. We conduct bootstrap tests for the existence of first and second order stochastic dominance amongst Sweden's income distributions over time and for several subgroups of immigrants. Analysis of immigrant’s income is motivated by the fact that the development of income for immigrants has been different and strongly affected by their length of residence and countries of origin. We consider several non-consecutive waves of a panel of incomes in Sweden. Two income definitions are developed. One is pre-transfers and taxes, gross income, the other is a post-transfers and taxes, disposable income. The comparison of the distribution of these two variables affords a partial view of
Sweden's welfare system. We have focused on the incomes of Swede's and immigrant groups of single individuals identified by country of origin, length of residence, age, education, gender, marital status and other relevant characteristics. We find that first order dominance is rare, but second order relations hold in several cases, especially amongst disposable income distributions. Sweden's incomes and welfare policies favor the elderly, females, larger families, and longer periods of residency. We find, in general, the higher the educational credentials, the higher is the burden of this equalization policy.
Keywords: Sweden, Immigrants, Optimal policy, Stochastic Dominance, Welfare ranking,
Bootstrap, Income Distribution, Nonparametric Testing.
JEL Classification: D31, D63, O15.
* Maasoumi expresses his appreciation for research funds from the Robert and Nancy Dedman Endowed Chair.
Heshmati acknowledges financial support from the Center for Public Sector Research (CEFOS) and the Swedish
Council for Research in Humanities and Social Sciences (HSFR), and Service Research Forum. We are grateful to Björn Gustafsson for providing the data, a referee, and especially thankful for extensive and helpful comments and criticisms from Anders Klevmarken. We also thank, without implicating, numerous participants at seminars in the US and Sweden, especially those at the International Panel Data Conference, Goteborg,
Sweden (1998).

1. INTRODUCTION
Sweden's income distribution for the whole population and for subgroups, including its immigrants, has been extensively studied. The interest in this area has grown with increasing availability of panels of data. Some attention has also been paid to income dynamics and mobility. See Creedy, Hart and Klevmarken (1980), Björklund (1993), Palme
(1995), and Zandvakili and Gustafsson (1998). All these studies are based on indices of inequality or mobility; See Gustafsson (1994). While indices are useful for complete ordering and have an air of “decisiveness” about them, they lack broad acceptance of their underlying value judgements. This lack of consensus is problematic for policy analysis and decision making. When Lorenz or Generalized Lorenz (GL) curves of incomes cross, it is possible to portray contradictory pictures of inequality and “welfare” by different choices of indices of inequality or mobility. In addition, indices are summary measures and, therefore, often fail to reveal the finer details at different income levels, and for different population groups. This is inadequate for informed and targeted policy decisions.
Uniform partial order relations can be studied, however, which rank welfare situations over very wide classes of welfare functions. This type of welfare analysis avoids overly narrow cardinalization of welfare functions as is done by indices. Stochastic dominance relations require far less degrees of normative cardinalization. These relations also consider the whole distributions of outcomes, and so are able to reveal crucial details, and potentially important distinctions between different parts of the distribution. Fortunately, we can now conduct statistical tests for the existence of such order relations. If dominance relations are inferred, one has discovered a significant result toward consensus building, it would be redundant to search over inequality indices. We will have discovered dominated
"strategies", policies, programs, and distributions. If dominance is not found, one has discovered an equally significant result bearing on the meaning and even the value of index based welfare orderings and pronouncements. Lack of dominance relations means that welfare functions cross, and that, in turn, means that the choice of any index is very subjective and must be rigorously defended as a "majority" decision in specific situations.
The literature on this general topic is rich both within the “income inequality” tradition, as well as in a number of “causal” studies that have empirically examined the possible sources of “earnings mobility” and “wage dispersion”. As examples in the latter
1

tradition, Buckberg and Thomas (1995, 1996) and Montgomery and Stockton (1994) attribute wage dispersion to changes in employment in the durable manufacturing sector and investment in computer equipment, as well as the variance in the quality of labor and capital intensities across the sectors within manufacturing. Card (1996) and Bluestone (1990) investigate the impact of age/education and schooling, as well as industrial restructuring on wage dispersion. Among other studies of interest are Lindbeck and Snower (1996) who outline a theory that considers the versatility of work, the dispersion of wages by occupation and education, Gottchalk and Moffitt (1994) who argue that a growing “instability” in wages is causing the observed dispersion in wages, and Blau and Kahn (1996) who conduct a comparative study of wage dispersion among ten countries. Also see Juhn, Murphy and
Pierce (1991, 1993). This is all index based.
The analysis in the wage dispersion literature is predominantly based on an index, namely the “variation” in a welfare attribute (earnings). As was established by the early debate on stochastic dominance (SD) vs “mean-variance” analysis, only for (near?) Gaussian and/or quadratic utility functions would the latter rankings be equivalent to SD rankings.
While econometric analysis is largely dependent on explaining “variation”, unless broader dominance relations hold, other indices can be found to contradict any welfare rankings implied by variances. Lacking consensus, the econometric findings remain unconvincing.
It seems that there is a wide chasm between a degree of clarity in modern welfare theory, on the one hand, and the welfare underpinnings (or lack thereof) of even the best practice econometric analysis of “earnings mobility” or “wage dispersion”, on the other.
Panel data and related techniques in this literature have been very promising with regard to identifying statistical “causes” and other conditioning attributes. We now pay much more attention to dynamics specification and endogeneity aspects of panel data models. But one might ask: What is being explained by these models? What is the effect? And, not surprisingly, we find that “causal” econometric models generally explain “variation” in the dependent variable, earnings or earnings growth, say. In the welfare context it is reasonably safe to say that “variation” or “variance” have very dubious welfare standing. Dramatically different populations (distributions) may have identical or nearly identical variances. The welfare function underlying variance is dismissed out of hand by a comfortable majority of welfare theorists and philosophers.
2

For instance, one might agree that earnings “mobility” in the US owes much to skills, education, and women's increasing participation in the labor force. Most everyone would agree that “mobility” is a “good” thing. But very few, almost all of them in a small group of welfare theorists, can tell you what “mobility” is, let alone the sense in which it is “good”! It is doubtful that many would agree to a welfare criterion that celebrates a high probability of millionaires going bankrupt and bankrupts becoming rich, in one period, and vice a versa in the next period. Yet markov chain models determining probabilities of movement, and panel data models “explaining” the statistical covariates in this setting, are essentially limited to explaining the “variation”, and implying that it is a good thing. Even movement on the basis of returns to education, say, must have a clearly understood sense in which it is socially desirable.
In a recent survey one of us has offered a synthesis which finds that, so far, the only coherent welfarist definitions for “mobility” are in terms of welfare functions that are increasing and concave. This is Pareto and inequality averse. These are also the very properties that are required in defining First and Second Order Stochastic Dominance (FSD and SSD). Such welfare functions register an increase in well being when there is upward mobility in a community, both in the mean, and toward greater equality (in the Pigou-Dalton sense), see Maasoumi (1998a and 1998b). Lorenz and Generalized Lorenz (GL) dominance also incorporate the same values. Indeed GL and SSD are formally identical.
In this paper we consider statistical test procedures for first and second order stochastic dominance. The tests studied here are multivariate generalizations of the
Kolmogorov-Smirnov statistics when weak dependence is permitted in the processes. We demonstrate this with several waves of a panel of incomes in Sweden. Two income definitions are developed. One is pre-government household gross income, the other is a post-government disposable income in calculation of which all transfer payments and taxes are taken into account. The comparison of the distribution of these two variables allows a partial look at the impact of Sweden's welfare system in this context. Several population subgroups can be studied separately and in comparison with others. We have focused on single individual Swedes and immigrants identified by country of origin, length of residency, age, education, gender, marital status and other characteristics.
In practice, numerical SD rankings often encounter a predictable difficulty since many distributions and (Lorenz) curves cross, making it difficult to be decisive. This has led
3

to the development of higher order dominance conditions that represent increasing degrees of cardinalization.
At the same time, the realization that all such comparisons are based on sample based
(typically, nonparametric) estimates of distribution functions (or curves) suggests that such comparisons are fundamentally statistical and should be tested accordingly. Interestingly, the statistical approach tends to deliver more “clear-cut” (statistical) decisions than is possible by numerical analysis!
Statistical theory for “ranking” populations has a long history and has developed quite rapidly in the last fifteen years or so. This history is reviewed in Maasoumi (2000). The basic characteristic of tests for rankings is that of ordered populations and hypotheses. Likelihood ratio and Wald-type tests have been and are being developed. These tests supplement other well known procedures based on one-sided Wilcoxan rank, and the multivariate versions of the Kolmogorov-Smirnov tests. Our two nonparametric tests for First and Second order
Stochastic Dominance (FSD and SSD, respectively) have also been studied by McFadden
(1989), Klecan, Mcfadden, and McFadden (1991), and Kaur, Prakasa Rao and Singh (1994).
These tests require Monte Carlo and bootstrap techniques for implementation.
The rest of the paper is organized as follows. Section 2 describes the tests for stochastic dominance, their distributional characteristics and the bootstrap techniques used. In
Section 3 the data are presented. Section 4 contains the empirical results and their implications. Section 5 concludes.
2. TESTS FOR STOCHASTIC DOMINANCE
In testing for Lorenz or GL curve comparisons, the "distances" at a finite number of ordinates are compared. These ordinates are typically represented by quantiles and/or conditional interval means. Thus, the distribution theory of the proposed tests are derived from the existing asymptotic theory for ordered statistics or conditional means and variances.
Beach, Davidson, and Slotsve (1995), and more recently Davidson and Duclos (1998) outlined the asymptotic distribution theory for cumulative/conditional means and variances which are the essential ingredients of Lorenz and GL curves, and in testing for stochastic dominance. To control for the size of the sequence of tests at several points the union
4

intersection (UI) and Studentized Maximum Modulus technique for multiple comparisons must be employed.
More recently several non-parametric tests have been proposed for FSD and SSD which recognize that the underlying distribution functions are unknown and must be estimated. In the spirit of Kolmogorov-Smirnov (KS) tests, and for the case of i.i.d
observations on independent variables (prospects), Kaur et al (1994) propose a consistent test of SSD which also depends on the union intersection methodology.
Alternatives to these multiple comparison techniques have been suggested which are typically based on Wald type joint tests of equality of the same ordinates, see Bishop, Chow and Formby (1994) and Anderson (1996). Xu, Fisher and Wilson (1995), and Xu (1995) take proper account of the inequality nature of such hypotheses and adapt econometric tests for inequality restrictions to testing for FSD and SSD, and to GL dominance, respectively. Their tests follow the work in econometrics of Gourieroux et al (1982), Kodde and Palm (1986), and Wolak (1991). The asymptotic distributions of these χ − bar squared tests are mixtures of chi-squared variates with probability weights which can be difficult to compute. The computation of the χ − bar squared statistic requires Monte Carlo or Bootstrap estimates of covariance matrices, as well as inequality restricted estimation which requires optimization with quadratic programming.
McFadden (1989) and Klecan, McFadden, and McFadden (1991) have proposed tests of first and second order “maximality” for stochastic dominance which are extensions of the
Kolmogorov-Smirnov statistic. McFadden (1989) assumed i.i.d.
observations and independent variates, and derived the asymptotic distribution of the test, in general, and its exact distribution in some cases (see Durbin (1973, 1985), and Kaur et al (1994)). Klecan et al (1991) study this test by allowing for general weak dependence within the processes, and exchangeability between the variables. They demonstrate with an application to ranking investment portfolios. We use a bootstrap implementation of these tests in this paper. In the following subsections some definitions and results are summarized which help to describe our tests.
Definitions and Tests
5

Let X and Y be two income variables at either two different points in time, before and after taxes, or for different regions or countries. Let X X
2
, ....., X n
be n not necessarily i.i.d
observations on X, and Y Y
2
Y m
be similar observations on Y. Let U
1
denote the class of all utility functions u such that u ′ ≥ 0 , (increasing). Also, let U
2
denote the class of all utility functions in U
1
for which u ′′ ≤ 0 (strict concavity), and U
3
denote a subset of U
2
for which u ′′′ ≤ 0 . Let X and Y denote the i th order statistics, and assume F x ( ) are continuous and monotonic cumulative distribution functions ( cdf ,s) of X and Y, respectively. Quantiles q p ( ) are implicitly defined by, for example,
[ ≤ ( )] = p .
Definition 2.1.
X First Order Stochastic Dominates Y, denoted X FSD Y, if and only if any one of the following equivalent conditions holds:
(1) E u X ≥ E u Y for all u U
1
, with strict inequality for some u.
(2) F x ≤ G x for all x in the support of X, with strict inequality for some x.
(3) ( ) ≥ ( ) for all 0 ≤ ≤ 1 .
Definition 2.2. X Second Order Stochastic Dominates Y, denoted X SSD Y, if and only if any of the following equivalent conditions holds:
(1) E u X ≥ E u Y
(2) ∫ x
−∞
( )
some x.
≤ ∫
−∞ x
(3) ∫
0 p
( ) ≥ ∫
0 p
, for all u U
2
, with strict inequality for some u.
, for all x in the support of X and Y, with strict inequality for
, for all 0 ≤ ≤ 1 , with strict inequality for some value(s) p.
Let the Lorenz curve of X, say, be defined as L x = 1 µ x
) ∫
−∞ x
, and its
= µ x
( ) . The latter was introduced by Shorrocks (1983). Most measures of inequality are "relative" since they only prize equality, not the levels of incomes. Lorenz
6

curves represent such measures. To prize both levels and equality, comparisons would be made by GL which reflects members of the class of increasing and equality preferring
(concave) welfare functions defined above. When either Lorenz or Generalized Lorenz
Curves of two distributions cross, unambiguous ranking by FSD and SSD is not possible.
Whitmore introduced the concept of third order stochastic dominance (TSD) in finance, see
(e.g.) Whitmore and Findley (1978). Shorrocks and Foster (1987) showed that the addition of a “transfer sensitivity” requirement leads to TSD ranking of income distributions. This requirement is stronger than the Pigou-Dalton principle of transfers since it makes regressive transfers less desirable at lower income levels. TSD is defined as follows:
Definition 2.3.
X Third Order Stochastic Dominates Y, denoted X TSD Y, if and only if any of the following equivalent conditions holds:
(1) E u X ≥ E u Y for all u U
3
, with strict inequality for some u.
(2) ∫
−∞ x ∫
−∞ v
[ ( ) − ( )] ≤ 0, for all x in the support, with strict inequality for some x, with the end-point condition: ∫ +∞
−∞
[ ( ) − ( )]
(3) When E X = E Y , X TSD Y iff λ ≤ λ
≤ 0 .
, for all Lorenz curve crossing points i = 1 2 n + 1 ) ; where λ denotes the “cumulative variance” for incomes up to the i th crossing point. See Davies and Hoy (1996).
When n = 1, Shorrocks and Foster (1987) show that X TSD Y if (a) the Lorenz curve of X cuts that of Y from above, and (b) Var X ≤ ( ) .
1
The tests of FSD and SSD are based on empirical evaluations of conditions (2) or (3) in the above definitions. Mounting tests on conditions (3) typically relies on the fact that quantiles are consistently estimated by the corresponding order statistics at a finite number of sample points. Mounting tests on conditions (2) requires empirical cdf s and comparisons at a finite number of observed ordinates. FSD implies SSD.
1 This would appear to revive the coefficient of variation as a useful index of inequality. But a distinction needs to be made between the sequence of inequality restrictions between all conditional variances as well as the unconditional one, on the one hand, and only the latter condition, on the other.
7

Our analysis of the KS type tests requires a definition of "maximal" sets due to
McFadden, as follows:
Definition 2.4.
Let Æ = {X
1
, X
2
, ....., X
K
} denote a set of K distinct random variables. Let
F
K
denote the cdf of the k th variable. The set Æ is first (second) order maximal if no variable in Æ is first (second) order weakly dominated by another.
Let X
.
n
= ( x
1 n
, x
2 n
, ....., x
Kn
) , n = 1 2 N , be the observed data. We assume X
.
n is strictly stationary and α − mixing . As in Klecan et al (1991), we also assume F X i
) , i = 1 2 K are exchangeable random variables, so that our resampling estimates of the test statistics converge appropriately. This is less demanding than the assumption of independence which is not realistic in many applications (as in before and after tax scenarios). We also assume F k
is unknown and estimated by the empirical distribution function F kN
( X k
) . Finally, we adopt the mathematical regularity conditions pertaining to von
Neumann-Morgenstern (VNM) utility functions that generally underlie the expected utility maximization paradigm. We also assume that all the expectations involved are finite. The following theorem defines our tests and the hypotheses being tested:
Theorem 2.1.
Given the mathematical regularity conditions;
(a) The variables in Æ are first-order stochastically maximal; i.e.,
(1) d = min max x
[
( ) − ( )
]
> 0, if and only if for each i and j, there exists a continuous increasing function u such that
( i
) > ( j
) .
(b) The variables in Æ are second order stochastically maximal; i.e.,
(2) S = min max x
∫ x
−∞
[
F i
( ) − F j
( )
] d > 0 , if and only if for each i and j, there exists a continuous increasing and strictly concave function u such that ( i
) > ( j
) .
(c) Assuming the stochastic process X
.
n
, n = 1 2 N , to be strictly stationary and
α − mixing with α j = Ο ( j − δ ) , for some δ > 1 , we have:
8

d
2 N
→ d , and S
2 N
→ S , where d
2 N
and S
2 N
are the empirical versions of our test statistics defined as :
(3) d
2 N
= min max x
[
( ) − F jN
]
(4) S
2 N
= min max x
∫
0 x
[
F iN
( ) − F jN
( )
] d .
Proof.
See Theorems 1. and 5 of Klecan et al (1991).
The null hypothesis tested by these two statistics is that, respectively, Æ is not first
(second) order maximal-- i.e., X i
FSD (SSD) X j
for some i and j . We do not reject the null when the statistics are negative to a statistical degree of confidence. Since the null hypothesis in each case is composite, power is conventionally determined in the least favorable case of identical marginals, F i
= F j
. As is shown in Kaur et al (1994) and Klecan et al (1991), when
X and Y are independent, tests based on d
2 N
and S
2 N
are consistent. Furthermore, the asymptotic distribution of these statistics are non-degenerate in the least favorable case, being
Gaussian.
But, as is also noted by Klecan et al (1991), the sample-based test statistics have, in general, neither a tractable distribution, nor an asymptotic distribution for which there are convenient computational approximations. The situation for d
2 N
is somewhat better in some special cases----see Durbin (1973, 1985), and McFadden (1989) who assume i.i.d.
observations (not crucial), and independent variables in Æ (consequential). Unequal sample sizes may be handled as in Kaur et al (1994).
In this paper we estimate the empirical distributions by bootstrap methods. In our algorithm we compute d
2 N
and S
2 N
for a finite number q of the income ordinates. This requires a computation of sample frequencies, cdf s and sums of cdf s, as well as the differences of the last two quantities at all the q points. Next, bootstrap samples (typically
1000) are generated from which empirical distributions of the differences, of the d
2 N
and
S
2 N
statistics, and their bootstrap confidence intervals are determined. The bootstrap probability of these statistics being negative and/or falling in these intervals leads to an inference of dominance to a degree of statistical confidence.
9

3. The DATA
The Swedish Income Panel data are obtained from the filed annual income tax returns.
Due to high labor force participation in Sweden most adults file an income tax return on an annual basis. Furthermore, many public sector transfers are considered as taxable income.
From 1978, information on income tax returns has been recorded in computer readable form and completed with other relevant information. Comparability of income variables over time is relatively high.
The data consist of one percent sample of individuals born in Sweden, and 10 percent of the immigrant population in Sweden during the period of 1982 to 1990. The sample contains individuals aged 18-105 years and living in Sweden continuously. In order to reduce the large annual sample size to a manageable level, the sample is restricted to immigrants that have entered Sweden sometime between 1968 and 1989. The difficulties associated with the measurement of pre- and post transfers incomes per weighted/unweighted household member resulted in our choice of analyzing only a sample of “single” individuals. Thus, the final sample contains a total of 43724 individuals each observed during the 9 years 1982 to 1990.
The total number of observation is 393516. There are a few missing values on country of origin (748), gross income (4321) and disposable income (4712).
The data are divided into two groups, Swedes (235814) and immigrants (156954). A number of time invariant characteristics are used to group individuals. These are, gender
(male and female), age intervals (18-40, 41-65, 65-105), level of education (secondary, high school, university), years of immigration to Sweden (1968-70, 1971-80, 1981-90), country of origin (Sweden, other Nordic countries, Europe, and other countries), marital status
(unmarried, married but living separately or divorced, and widow/widower), and the number of children (0, 1 or 2 and more).
2
Our results consider two income definitions. "Gross income" is the sum of labor income (wage and salaries, self-employment income), capital income (dividends and interest), capital gains/losses, and agricultural income less any income losses. "Disposable
2
The i ndividuals in our sample are in fewer groups than in the data sources. This was to facilitate comparisons on the largest number of characteristics and yet remain tractable. Information on the level of education was available for 1990. For the nine years of observation we selected only three representative years to compare.
10

income" is the sum of Gross income and “public transfers” less total taxes. Public transfers cover transfers that are subject to income tax. It includes taxable transfers such as pension payments (base pension, additional pension), sickness benefits, unemployment benefits, labor market training program benefits, housing/rent support, social assistance, and fraction of student loans less repayment of student loans.
3
Tax is measured as the final total tax paid. The incomes, taxes and transfers are measured per household equivalent capita and are transformed to 1990 fixed prices using the consumer price index. In calculation of household equivalent number we use 1 for adults and 0.5 weight for children.
Since we do not sample from consecutive time series observations we reduce the problem of dependence that might require Moving Blocks and other relevant bootstrap techniques. A simple percentile method should be adequate for our cross section samples at distant points in time. For their Monte Carlo approach to computing critical values, Klecan et al (1991) assume exchangeability of variables in the two distributions being compared.
Summary statistics of the two income data, transfer and tax variables are given in the respective tables and also in Appendix A. The number of individuals born in Sweden is
26234 (60%). Though the analysis is based on separate Swede and immigrant samples, the former segment is used as a reference group in our comparisons. It should be noted that immigrants are eligible to become a citizen of Sweden after five years of residence. Thus, we define immigrants by the individual’s country of birth. The individuals are observed during the entire period of study, 1982-1990. The overall sample average and standard deviation of gross incomes (73348, 71042) are larger than the corresponding pair for disposable incomes
(72565, 26651).
In our tables, the numbers in parenthesis are the mean and standard deviations of respective variables. The mean transfer and taxes (32568, 33776) are close but their dispersions are somewhat different (32031, 39299). We find that disposable incomes have much smaller dispersion than gross incomes. It would appear that taxes and transfers are effective income equalizers. A number of individuals (18%) reported zero gross incomes, zero disposable incomes (2%), zero transfer payments (61%) and zero tax payments (9%). A larger fraction of the sample (60%) is males. Single male immigrants are over-represented.
3 Since our sample contains only single households. The non-taxable transfers such as child benefits and payments targeted to single parents are not causing any measurement errors.
11

The mean gross income and taxes vary over time depending on the state of the economy. The mean transfers, taxes and disposable income is continuously increasing over time.
4
We find a positive relationship between the productive age and the mean and dispersions of the levels of income, transfers and taxes. The male segment earns on average a higher gross income but the difference shrinks when the disposable income is considered.
Females receive higher transfers although they have a higher frequency of non-zero income than males. In general more females are in part time employment and are paid lower salaries.
The immigrants' mean income and transfers (taxes) increase with the length of their residence. The large dispersion in incomes and transfers by years of immigration can be due to high frequency of pre-retirements among immigrants entering Sweden in the earlier years.
Recent waves of immigrants are more "skilled" in terms of education. When the distribution of income by country of origin is considered, the net transfer (transfers-taxes) is negative for the Swedes and other Nordic countries, while it is positive for the European and other
(Middle East, North African and Latin American) countries. In terms of both types of incomes the divorced and unmarried appear "better off" than the widow/widowers.
5
The levels of incomes are increasing with the number of children but at a decreasing rate. Singles with only one child receive less transfer than households with no children. The pattern holds with less dispersion for immigrants. The levels of gross and disposable incomes are positively correlated with the level of education for both Swedes and immigrants. This relation is weaker for disposable incomes.
4. EMPIRICAL ANALYSIS
4.1 The whole distribution over time
The first panel of Table 1 gives some statistical summaries, including the number of observations. In the second panel our test statistics are summarized by their mean and
4 To our knowledge there is no study of income distribution among immigrants in Sweden. Borjas (1994) provides an excellent survey of the economics of immigration. For a comprehensive analysis of the tax and benefit reforms in Sweden and an assessment of their effects on the income distribution, labor supply, welfare and equality in general, see Björklund, Palme and Svensson (1995), Björklund and Freeman (1995), Aronsson and Palme (1998), and Lindbeck (1997).
5 The group of divorced and widow/widowers are older than the unmarried including married females but not living with husband. Part of the level differences in their income could be attributed to the income age effects.
12

standard errors, as well as the probability of the test being negative. All of these are from
1000 bootstrap samples. The first group is denoted the “X” distribution, and the second by
“Y”. Thus, “FSDxoy” denotes ”first order stochastic dominance of X over Y”, “SSDxoy” is similarly defined for second order dominance, “FOmax” and “SOmax” denotes the “first and second order maximality” test, and so on.
Table 1 ignores individual/group attributes. It provides the test results for a selection of years (1982, 1986, and 1990) which shed light on the movement of the overall income distributions over the time period in our sample frame. Depending on the economic conditions and political majority, the time patterns of dominance might be different than the current one which is valid for non-consecutive selected years of observation.
Mean incomes are seen to be increasing while variances are also increasing for both
Swedes and immigrants. For Swedes, in terms of gross incomes, no first and second order dominance is observed. These three years are first and second order maximal. But, as can be seen from the disposable income distributions, taxes and transfers make a big difference.
Indeed, both 1990 and 1986 second order dominate 1982. The 1990 distribution FSD 1982 at the 95% level. 1990 and 1986 are maximal. This would suggest that the welfare enhancing/equalizing impact of the welfare programs/taxes, so significant before 1986, has tapered off in the last part of the 1980s.
For the immigrants gross income distributions, the second panel of Table 1, 1982 SSD
1986. The tax/transfer programs appear to cause a strong reversal of this as, in terms of the disposable incomes, 1986 FSD 1982. Again, 1990 and 1986 gross incomes are maximal
(unrankable), while for disposable incomes 1986 SSD 1990. Inequality would seem to be the cause of this welfare decline in the latter half of 1980s. The immigrant 1982 and 1990 disposable incomes are unrankable, confirming the regression of the welfare levels to the
1982 levels. The 1982 gross incomes FSD the 1990 distribution, somewhat puzzlingly so, but are unrankable after taxes and transfers.
4.2 Test results for age groups
The results for the age groups (18-40, 41-65 and 65-105) are similarly separated for
Swedes and immigrants. The most notable result in Table 2 is in terms of disposable incomes:
All the disposable incomes are maximal, they cannot be ranked by FSD or SSD. There is
13

week evidence for FSD (hence SSD) of the oldest immigrant group's disposable income over the corresponding middle group (with .899 probability).
The welfare programs have been welfare equalizing between age groups. This is evidenced by observing several cases of FSD and SSD between the gross incomes. For example, the Swedes in the two younger age groups SSD the oldest (and are maximal between themselves). For the immigrants, this phenomenon is even stronger: every younger group First order dominates its older group (s) before taxes and transfers. Because of potential biases in the simple percentile bootstrap, the .97 probability for FSD of the youngest group over the middle group may be marginal. It may be safer to say that the youngest group
SSD the middle group. Also, since our samples include only "singles", it would be interesting to investigate whether these results hold for the whole population.
4.3 Test results for marital status
Table 3 gives the results of our tests for grouping according to the “marital status” of the individuals. Although individuals are all singles we can distinguish a few groups which we expect to differ in their income distributions and well being. The sample is divided into unmarried, divorced and widow/widower.
Table 3 shows that the unmarried, "true singles", are better off than the divorced and widowed singles, in that order, before taxes and transfers. This inference is based on strong evidence of SSD for both Swedes and immigrants, and weaker evidence for FSD. Almost all of this evidence disappears after taxes and transfers, with one exception: only the divorced single Swedes FSD the Swede widows. The divorced Swedes do not lose their pre-tax advantage, they enhance it a little with taxes and transfers. By this standard, the "unmarried immigrants" do very badly by the welfare system.
4.4 Test results for countries of origin
In Table 4 we look at the comparisons by country of origin. The group of Swedish single individuals is used as a control group. In terms of gross incomes, there is only one FSD
Relation. Other Nordic FSD European. This relation is unchanged by taxes and transfers.
"Other Nordic" immigrants SSD Swedes, but are maximal with "other" immigrants. Indeed, there is weak evidence (.93 probability) that they are dominated by the "other" group in the
SSD sense. Swedes and "others" are maximal in their gross incomes. The gross incomes are thus approximately ranked as, "other Nordic" and "others" slightly better than Swedes who
14

are slightly better off than the "European" immigrants. It would be interesting to extend this study by controlling for age as well as other attributes.
Turning to disposable incomes, Swedes and "other Nordic" groups are maximal amongst themselves, and strongly dominate other groups in the FSD sense (the exception is that Swedes SSD Europeans. European and "other" immigrants are now unrankable. The welfare system benefits from the tax and transfers with the "other" immigrants, and transfers to singles in other groups.
4.5 Grouping by Education
Table 5 has the same design as the previous tables but reports our tests for three different education levels. First we note the strong returns to educational credentials. In terms of gross incomes, there is a strong FSD ranking of higher educational credentials over the lower ones. The only weak exception is amongst the immigrants of High school and university degrees. Given the value of the SSD test, however, it is likely that, for this group, third order dominance would hold at a higher probability.
Disposable income distributions indicate that the net effect of transfers and taxes is to decrease the mean disposable income of the two more "educated" groups, and increase that of the least educated. The variance for all groups has decreased significantly as a result of taxes paid and benefits received.
The dominance statistics indicate that, for Swedes, there is a notable welfare equalization amongst educational levels, with the university educated bearing the brunt of taxes and transfers. For the immigrant groups, this reversal of welfare fortunes is even stronger as there are now several FSD relations amongst the disposable income distributions
(the two groups with less than university experience are only SSD ranked).
4.6 Number of children
Table 6 summarizes the findings for individuals with no children, with one, and with
2 or more children. Having one child is "better" than two or more children, but individuals with no child are equally ranked with the other groups. For immigrants, and in terms of disposable incomes, however, having more children is SSD over fewer and no children, respectively. The welfare system has a clear equalizing benefit for immigrants with children.
Interestingly, this is not so for Swedes as all the disposable income distributions are maximal!
15

4.7 Test results for years of immigration
The nature of immigration to Sweden has changed when we compare those arrived in the 1960s and early 1970s with immigrants arrived in later decades. The 1960s immigrants are mostly individuals with low levels of education who immigrated to Sweden at a time of labor shortage in the manufacturing sectors. These are often employed in less skilled and heavy jobs and paid the minimum wage. A relatively high proportion of them are pre-retired and are paid by insurance wages which are much lower than full time wages. The immigrants entering Sweden in the late 1970s and 1980s are mostly refugees with relatively higher levels of education. The latter group is found to have a higher potential in getting highly paid employment. The stream of immigration and their countries of origin differ over time depending on war and other factors causing immigration from different parts of the World to
Europe.
It may be argued that immigrants expect to find a “better life” when they immigrate. It is equally plausible to expect that their lot will improve with time if they succeed and stay. It is also true that more recent immigrants are more skilled or better off when they become resident. Table 7 sheds some light on these issues. Clearly, the length of residence is positively related to mean incomes, whether gross or disposable. For all groups, the mean incomes are reduced after taxes and transfers.
The test results indicate, however, that there are no significant order relations in terms of gross incomes. But after the welfare effects are taken into account, all of the more established groups dominate the more recent groups in the SSD sense. Greater length of residency is favored by the system, especially when equality (SSD) is the criterion.
4.8 Test results for gender
Table 8 indicates that the mean gross incomes of males are greater than females'.
This disparity is greatly reduced for the mean disposable incomes. Note that our income measure here is an aggregate of incomes over the entire period. Thus some aspects of mobility are taken into account over this period of time. Because of this, there is no notable disparity between Swedes and immigrants of the same gender. There is a great reduction in the variances of incomes, however, after taxes and transfers are included.
16

In terms of gross incomes both Swede and immigrant male distributions SSD the female gross distributions. In fact, the immigrant males' gross income FSD the immigrant female distribution. Immigrant males are uniformly better off than immigrant females before taxes. But, there is too much dispersion in the Swedish male distribution of gross incomes for it to FSD the corresponding distribution for females. After taxes and transfers, however, all of these dominance relations are wiped away. There is a gender maximality. The only significant second order dominance in existence is that of Swedish males over immigrant males. This would seem to be a remarkable success if the intended purpose of the welfare policies has been to bring about welfare parity between male and females.
Graphs:
Several graphs are given at the end of the paper that correspond to the table results discussed in the previous sections. Strictly speaking, cdf graphs should be compared only for the same income definition, gross incomes with gross incomes, disposable ones with disposable incomes. This is because the income ranges used for testing are different for every pair of distributions so as to achieve the widest coverage in their supports.
5. SUMMARY AND CONCLUSIONS
The potential for conducting meaningful statistical ranking of welfare situations is clearly very good. The bootstrap and other resampling tools can be profitably used in the difficult case of inequality restrictions, such as stochastic dominance relations, where even asymptotic approximations are difficult. The use of unrestricted bootstrap confidence intervals in our inferences is a useful innovation when it is difficult to impose the null restrictions in nonparametric settings. Statistical ranking is sound and, somewhat surprisingly, rather decisive in many cases.
In this paper we consider statistical test procedures for first and second order stochastic dominance. Previous studies suggests that bootstrap is an attractive alternative to the existing approximate asymptotic inference methods. The comparison of the distribution of the two income variables in our study allows a partial look at the impact of Sweden's welfare system in this context. Several population subgroups are studied separately and in comparison with others. We have focused on single individual immigrants identified by country of origin, length of residency, age, education, gender, marital status and other characteristics.
17

Our results suggest that although the sample of singles studied is a small and relatively homogeneous segment of the population of individuals, we observe some clear patterns of economic well being. We find that first order dominance is rare, but second order dominance holds in several cases. An extension of the sample to incorporate groups of individuals targeted for various tax and public transfer policy measures would shed additional light on the state of welfare of individuals and the impact of those policies implemented. This is important in the design and evaluation of welfare programs.
Taxes and public transfers are shown to be effective measures in reducing the variance of disposable income. The contribution to the welfare of households with children, specially the Lone Mothers and the aged population, those with less educational credentials, and generally less able, is an important corner stone in the Swedish welfare system.
A further significance of our results is that they allow a proper interpretation of inequality studies and impressions based on indices of inequality and mobility.
Data and Definition of Variables:
Income: Includes zero incomes.
Period: 1982-1990.
Sample: Single individual with/without children.
Observations: balanced panel of 43724 individuals, 393516 observations.
Gross Income = (labor income + capital income + temporary employment + agriculture – losses)
Transfers = (base pension + additional pension + unemployment benefit + labor market training
program benefit + housing/rent support benefits + social security benefit
+ 1/2 student loans + etc ..)
Taxes = Total taxes
Disposable Income = (Gross Income + Transfers – Taxes)
All variables are given in SEK and transformed to 1990 prices using consumer price index.
Glossary of Tests:
FSDxoy
FSDyox
FOmax
First order stochastic dominance of x over y
First order stochastic dominance of y over x
First order maximal
SSDxoy
SSDyox
Second order stochastic dominance of x over y
Second order stochastic dominance of y over x
SOmax Second order maximal
Prob Reject the null of no dominance when the statistics are negative.
Tables and Graphs follow.
18

Table 1. Test for stochastic dominance over time
Gross Income
Characteristics
1.A Swedes:
1982
1986
1990
Test
1982 (x) vs 1986 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
1982 (x) vs 1990 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
1986 (x) vs 1990 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
24014 67202 67005
26198 73607 80238
26235 79320 100695
Mean Std Prob
0.0673 0.0041 0.0000
0.0491 0.0043 0.0000
0.0491 0.0043 0.0000
0.2371 0.0249 0.0000
0.0616 0.0084 0.0000
0.0616 0.0084 0.0000
0.1206 0.0037 0.0000
0.0875 0.0043 0.0000
0.0875 0.0043 0.0000
0.4313 0.0268 0.0000
0.1295 0.0084 0.0000
0.1295 0.0084 0.0000
0.0623 0.0035 0.0000
0.0376 0.0043 0.0000
0.0376 0.0043 0.0000
0.1623 0.0224 0.0000
0.0667 0.0116 0.0000
0.0667 0.0116 0.0000
Characteristics
1.B Immigrants:
1982
1986
1990
14081 67319 60524
17431 72008 69579
17489 73764 77670
Test
1982 (x) vs 1986 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
1982 (x) vs 1990 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
1986 (x) vs 1990 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
Mean Std Prob
0.0019 0.0032 0.2940
0.1132 0.0064 0.0000
0.0019 0.0032 0.2940
-0.1128 0.0064 1.0000
0.8865 0.0864 0.0000
-0.1128 0.0064 1.0000
-0.0096 0.0023 1.0000
0.2030 0.0066 0.0000
-0.0096 0.0023 1.0000
-0.1886 0.0065 1.0000
1.9837 0.0883 0.0000
-0.1886 0.0065 1.0000
0.0474 0.0036 0.0000
0.0570 0.0051 0.0000
0.0471 0.0034 0.0000
0.0019 0.0499 0.5140
0.2773 0.0388 0.0000
0.0019 0.0499 0.5140
Disposable Income
24014 62878 30207
26198 73921 33759
26235 77794 36994
Mean Std Prob
0.1205 0.0040 0.0000
-0.0001 0.0001 0.8890
-0.0001 0.0001 0.8890
0.7105 0.0181 0.0000
-0.0163 0.0015 1.0000
-0.0163 0.0015 1.0000
0.1488 0.0034 0.0000
-0.0001 0.0001 0.9500
-0.0001 0.0001 0.9500
0.9541 0.0182 0.0000
-0.0154 0.0015 1.0000
-0.0154 0.0015 1.0000
0.0719 0.0037 0.0000
0.0010 0.0009 0.1020
0.0010 0.0009 0.1020
0.3048 0.0225 0.0000
0.0008 0.0014 0.2720
0.0008 0.0014 0.2720
14081 61976 31068
17431 73674 32630
17489 75848 33704
Mean Std Prob
0.1245 0.0108 0.0000
-0.0259 0.0079 1.0000
-0.0259 0.0079 1.0000
1.5458 0.1495 0.0000
-0.0261 0.0081 1.0000
-0.0261 0.0081 1.0000
0.1125 0.0109 0.0000
0.0190 0.0088 0.0180
0.0190 0.0088 0.0180
1.0567 0.1575 0.0000
0.0313 0.0224 0.0180
0.0313 0.0224 0.0180
0.0054 0.0058 0.1800
0.0206 0.0047 0.0000
0.0053 0.0056 0.1800
-0.0126 0.0079 0.9680
0.1529 0.0581 0.0000
-0.0128 0.0062 0.9680
19

Table 2. Stochastic dominance by age groups (based on mean income 1982-1990, age in 1990).
Gross Income Disposable Income
Characteristics
2.A Swedes:
18-40
41-65
66-105
Test
18-40 (x) vs 41-65 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
18-40 (x) vs 66-105 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
41-65 (x) vs 66-105 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
Characteristics
2.B Immigrants:
18-40
41-65
66-105
Characteristics
18-40 (x) vs 41-65 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
18-40 (x) vs 66-105 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
41-65 (x) vs 66-105 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
6566 98875 62132
10633 105894 82856
9035 19258 39897
Mean Std
Mean Std
-0.0138 0.0067 0.9760
0.2001 0.0110 0.0000
-0.0138 0.0067 0.9760
-0.1625 0.0090 1.0000
2.4098 0.1640 0.0000
-0.1625 0.0090 1.0000
-0.0525 0.0058 1.0000
0.5625 0.0115 0.0000
-0.0525 0.0058 1.0000
-0.3891 0.0107 1.0000
7.3634 0.1522 0.0000
-0.3891
Prob
0.0974 0.0071 0.0000
0.0657 0.0040 0.0000
0.0657 0.0040 0.0000
0.2297 0.0330 0.0000
0.1243 0.0130 0.0000
0.1241 0.0126 0.0000
0.0002 0.0002 0.0990
0.7193 0.0056 0.0000
0.0002 0.0002 0.0990
-0.6431 0.0054 1.0000
2.8537 0.0247 0.0000
-0.6431 0.0054 1.0000
-0.0000 0.0001 0.5270
0.6513 0.0052 0.0000
-0.0000 0.0001 0.5270
-0.6163 0.0055 1.0000
2.2636 0.0194 0.0000
-0.6163 0.0055 1.0000
4539 79629 48721
9205 90253 62569
3744 18555 36985
Prob
0.0107 1.0000
-0.0579 0.0031 1.0000
0.5369 0.0083 0.0000
-0.0579 0.0031 1.0000
-0.3674 0.0091 1.0000
7.0302 0.1017 0.0000
-0.3674 0.0091 1.0000
6566 75979 24889
10633 82888 29656
9035 58405 17581
Mean Std Prob
0.0699 0.0081 0.0000
0.0078 0.0036 0.0050
0.0078 0.0036 0.0050
0.4100 0.0681 0.0000
0.0262 0.0188 0.0750
0.0262 0.0188 0.0750
0.0030 0.0015 0.0150
0.4247 0.0072 0.0000
0.0030 0.0015 0.0150
0.0091 0.0065 0.0250
2.5564 0.0549 0.0000
0.0091 0.0065 0.0250
0.0019 0.0017 0.1170
0.5020 0.0060 0.0000
0.0019 0.0017 0.1170
0.0038 0.0042 0.2120
3.1470 0.0427 0.0000
0.0038 0.0042 0.2120
4539 68630 25104
9205 79285 26755
3744 59682 18392
Mean Std Prob
0.0423 0.0222 0.0200
0.0313 0.0223 0.0780
0.0199 0.0146 0.0980
0.2411 0.2463 0.1150
0.0987 0.1931 0.4860
0.0001 0.0362 0.6010
0.1014 0.0318 0.0000
0.0207 0.0235 0.1940
0.0199 0.0225 0.1940
0.8864 0.4746 0.0400
0.0576 0.0891 0.2320
0.0385 0.0616 0.2720
0.2238 0.0227 0.0000
-0.0139 0.0107 0.8990
-0.0139 0.0107 0.8990
2.3033
0.2613 0.0000
-0.0139 0.0108 0.8990
-0.0139 0.0108 0.8990
20

Table 3. Stochastic dominance by marital status (based on mean income 1982-1990, status in 1990).
Gross Income Disposable Income
Characteristics
3.A Swedes:
Unmarried
Divorced
Widows
10732 92508 67946
9054 86810 87789
6422 26480 49341
Test Mean Std Prob
Unmarried (x) vs Divorced (y)
FSDxoy 0.0141 0.0029 0.0000
FSDyox
FOmax
SSDxoy
SSDyox
0.0798 0.0062 0.0000
0.0141 0.0029 0.0000
-0.0737 0.0054 1.0000
0.2952 0.0259 0.0000
SOmax -0.0737 0.0054 1.0000
Unmarried (x) vs Widows (y):
FSDxoy 0.0002 0.0002 0.1160
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
0.5503 0.0066 0.0000
0.0002 0.0002 0.1160
-0.5070 0.0067 1.0000
2.3707 0.0296 0.0000
-0.5070 0.0067 1.0000
Divorced (x) vs Widows (y):
FSDxoy
FSDyox
FOmax
-0.0001 0.0001 0.7770
0.4580 0.0072 0.0000
-0.0001 0.0001 0.7770
SSDxoy
SSDyox
SOmax
-0.4580 0.0072 1.0000
1.5824 0.0240 0.0000
-0.4580 0.0072 1.0000
10732 75514 26576
9054 77940 28653
6422 60736 21427
Mean Std Prob
0.0482 0.0055 0.0000
0.0125 0.0063 0.0150
0.0125 0.0063 0.0150
0.2343 0.0399 0.0000
0.0001 0.0017 0.5770
0.0001 0.0017 0.5770
-0.0007 0.0016 0.7340
0.3411 0.0076 0.0000
-0.0007 0.0016 0.7340
-0.0010 0.0022 0.8430
2.0501 0.0575 0.0000
-0.0010 0.0022 0.8430
-0.0022 0.0011 0.9850
0.3657 0.0078 0.0000
-0.0022 0.0011 0.9850
-0.0022 0.0011 0.9860
2.1915 0.0513 0.0000
-0.0022 0.0011 0.9860
Characteristics
3.B Immigrants:
Unmarried
Divorced
Widows
6829 86525 59036
7795 74097 61071
2807 32324 49664
Test Mean Std Prob
Unmarried (x) vs Divorced (y):
FSDxoy
FSDyox
FOmax
SSDxoy
-0.0062 0.0040 0.9450
0.1066 0.0080 0.0000
-0.0062 0.0040
0.9450
-0.0980 0.0068 1.0000
SSDyox
SOmax
1.4055 0.1175 0.0000
-0.0980 0.0068 1.0000
Unmarried (x) vs Widows (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
-0.0366 0.0037 1.0000
0.4462 0.0105 0.0000
-0.0366 0.0037 1.0000
-0.3279 0.0104 1.0000
5.5393 0.1358 0.0000
SOmax -0.3279 0.0104 1.0000
Divorced (x) vs Widows (y):
FSDxoy
FSDyox
-0.0340 0.0037 1.0000
0.3220 0.0110 0.0000
FOmax
SSDxoy
SSDyox
SOmax
-0.0340 0.0037
1.0000
-0.2003 0.0120 1.0000
3.9431
0.1404 0.0000
-0.2003 0.0120 1.0000
6829 73450 27512
7795 74377 24997
2807 63952 23070
Mean Std Prob
0.0288 0.0163 0.0320
0.0387 0.0215 0.0370
0.0193 0.0119 0.0690
0.1405 0.1581 0.1530
0.1391 0.1854 0.3230
0.0150 0.0376 0.4760
0.1260 0.0244 0.0000
0.0050 0.0150 0.3750
0.0050 0.0150 0.3750
1.2030 0.3312 0.0000
0.0146 0.0369 0.3850
0.0146 0.0366 0.3850
0.1298 0.0230 0.0000
0.0056 0.0123 0.3270
0.0056 0.0123 0.3270
1.1816 0.2965 0.0000
0.0162 0.0325 0.3610
0.0162 0.0325 0.3610
21

Table 4. Stochastic dominance by country of origin (based on mean income 1982-1990).
Gross Income Disposable Income
Characteristics
Swede
Nordic
European
Others
26234 74300 76784
10522 75429 59213
5481 68563 67229
1482 62171 51655
Test Mean Std Prob
Swede (x) vs Other Nordic (y):
FSDxoy 0.0627 0.0052 0.0000
FSDyox
FOmax
SSDxoy
SSDyox
0.0218 0.0024 0.0000
0.0218 0.0024 0.0000
0.1170 0.0139 0.0000
-0.0522 0.0145 0.9990
SOmax
Swede (x) vs European (y):
-0.0522 0.0145 0.9990
FSDxoy 0.0038 0.0017 0.0010
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
0.0509 0.0071 0.0000
0.0038 0.0017 0.0010
-0.0152 0.0073 0.9810
0.1389 0.0240 0.0000
-0.0152 0.0073 0.9810
Swede (x) vs Others (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
0.0802 0.0119 0.0000
0.1418 0.0112 0.0000
0.0802 0.0119 0.0000
0.0802 0.0119 0.0000
0.2816 0.0366 0.0000
0.0802 0.0119 0.0000
Other Nordic (x) vs European (y):
FSDxoy
FSDyox
FOmax
SSDxoy
-0.0186 0.0038 1.0000
0.1046 0.0094 0.0000
-0.0186 0.0038 1.0000
-0.0523 0.0090 1.0000
SSDyox
SOmax
1.4406 0.1292 0.0000
-0.0523 0.0090 1.0000
Other Nordic (x) vs Others (y):
FSDxoy 0.0920 0.0138 0.0000
FSDyox
FOmax
SSDxoy
0.0435 0.0123 0.0000
0.0434 0.0121 0.0000
0.5440 0.1260 0.0000
SSDyox
SOmax
Europeans (x) vs Others (y):
FSDxoy
FSDyox
-0.0445 0.0345 0.9370
-0.0445 0.0344 0.9370
0.1408 0.0132 0.0000
0.0308 0.0094 0.0000
FOmax
SSDxoy
SSDyox
SOmax
0.0308 0.0094 0.0000
0.9845 0.1336 0.0000
-0.0970 0.0117 1.0000
-0.0970 0.0117 1.0000
26234 72727 27075
10522 74493 23260
5481 70510 29978
1482 63671 26250
Mean Std Prob
0.0955 0.0055 0.0000
0.0075 0.0021 0.0000
0.0075 0.0021 0.0000
0.4413 0.0337 0.0000
-0.0003 0.0007 0.6990
-0.0003 0.0007 0.6990
0.0046 0.0038 0.1150
0.0481 0.0048 0.0000
0.0046 0.0038 0.1150
-0.0184 0.0020 1.0000
0.4113 0.0541 0.0000
-0.0184 0.0020 1.0000
-0.0097 0.0016 1.0000
0.1152 0.0095 0.0000
-0.0097 0.0016 1.0000
-0.0239
0.0044 1.0000
1.2038 0.0980 0.0000
-0.0239 0.0044 1.0000
-0.0677 0.0096 1.0000
0.1691 0.0191 0.0000
-0.0677 0.0096 1.0000
-0.0688 0.0098 1.0000
2.3682 0.2329 0.0000
-0.0688 0.0098 1.0000
-0.0537 0.0140 1.0000
0.1716 0.0246 0.0000
-0.0537 0.0140 1.0000
-0.0539 0.0141 1.0000
2.2011 0.3364 0.0000
-0.0539 0.0141 1.0000
0.0611 0.0241 0.0050
0.0269 0.0211 0.0970
0.0224 0.0171 0.1020
0.4401 0.3031 0.0460
0.0218 0.1052 0.6750
-0.0069 0.0371 0.7210
22

Table 5. Stochastic dominance by levels of education (based on income and education in 1990).
Gross Income Disposable Income
Characteristics
5.A Swedes:
Secondary
University
9154 66649 75490
7955 106148 81642
3412 153449 158136
Test Mean Std Prob
Secondary (x) vs High School (y):
FSDxoy 0.2518 0.0068 0.0000
FSDyox
FOmax
SSDxoy
SSDyox
-0.0028 0.0009 1.0000
-0.0028 0.0009 1.0000
2.5311 0.0736 0.0000
-0.2239 0.0065 1.0000
SOmax -0.2239 0.0065 1.0000
Secondary (x) vs University (y):
FSDxoy 0.3658 0.0086 0.0000
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
-0.0148 0.0023 1.0000
-0.0148 0.0023 1.0000
4.8292 0.1070 0.0000
-0.3039 0.0071 1.0000
-0.3039 0.0071 1.0000
High School (x) vs University (y):
FSDxoy
FSDyox
FOmax
0.2155 0.0097 0.0000
-0.0089 0.0018 1.0000
-0.0089 0.0018 1.0000
SSDxoy
SSDyox
SOmax
2.1742 0.0933 0.0000
-0.0835 0.0064 1.0000
-0.0835 0.0064 1.0000
9154 74374
Mean Std
29514
7955 85558 34703
3412 103352 52988
Prob
0.1610 0.0090 0.0000
0.0219 0.0039 0.0000
0.0219 0.0039 0.0000
0.7718 0.0785 0.0000
0.1670 0.0356 0.0000
0.1670 0.0356 0.0000
0.2209 0.0139 0.0000
0.0583 0.0080 0.0000
0.0583 0.0080 0.0000
0.6584 0.1392 0.0000
0.4958 0.0729 0.0000
0.4702 0.0578 0.0000
0.0434 0.0136 0.0010
0.0879 0.0154 0.0000
0.0432 0.0132 0.0010
-0.0431 0.0106 1.0000
0.9990 0.1945 0.0000
-0.0431 0.0106 1.0000
Characteristics
5.B Immigrants:
Secondary
University
5674 60842 69575
5461 90420 71534
1919 131670 95008
Test Mean Std Prob
Secondary (x) vs High School (y):
FSDxoy
FSDyox
FOmax
SSDxoy
0.2358 0.0119 0.0000
-0.0259 0.0043 1.0000
-0.0259 0.0043 1.0000
2.9148 0.1542 0.0000
SSDyox
SOmax
-0.2036 0.0122 1.0000
-0.2036 0.0122 1.0000
Secondary (x) vs University (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
0.2745 0.0192 0.0000
-0.0368 0.0088 1.0000
-0.0368 0.0088 1.0000
3.3086 0.2701 0.0000
-0.2412 0.0191 1.0000
SOmax -0.2412 0.0191 1.0000
High School (x) vs University (y):
FSDxoy
FSDyox
0.0525 0.0166 0.0000
0.0061 0.0175 0.4080
FOmax
SSDxoy
SSDyox
SOmax
0.0050 0.0156 0.4080
0.4187 0.2715 0.0150
-0.0112 0.0843 0.8120
-0.0293 0.0368 0.8270
5674 74074 28152
5461 80402 32471
1919 95161 44901
Mean Std Prob
0.0021 0.0224 0.4880
0.1057 0.0260 0.0000
0.0020 0.0223 0.4880
-0.0873 0.0283 0.9970
1.1510 0.3903 0.0000
-0.0874 0.0273 0.9970
-0.0628 0.0191 0.9980
0.2364 0.0358 0.0000
-0.0628 0.0191 0.9980
-0.1820 0.0362 1.0000
3.2570 0.5445 0.0000
-0.1820 0.0362 1.0000
-0.0467 0.0183 0.9960
0.1873 0.0314 0.0000
-0.0467 0.0183 0.9960
-0.1069 0.0344 0.9990
2.6096 0.5055 0.0000
-0.1069 0.0344 0.9990
23

Table 6: Stochastic dominance by number of children (based on income and No of children in 1990).
Gross Income Disposable Income
Characteristics
6.A Swedes:
Child
1
24132 79769 104055
1567 81047 48666 and children 536 54053 35150
Test Mean Std Prob
0 child (x) vs 1 child (y):
FSDxoy
FSDyox
Fomax
SSDxoy
SSDyox
0.3363 0.0093 0.0000
0.1582 0.0106 0.0000
0.1582 0.0106 0.0000
0.3363 0.0093 0.0000
-0.0235 0.0194 0.8840
SOmax -0.0235 0.0194 0.8840
0 child (x) vs 2 and more children (y):
FSDxoy 0.2134 0.0195 0.0000
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
0.3196 0.0121 0.0000
0.2134 0.0195 0.0000
0.2134 0.0195 0.0000
0.2878 0.0269 0.0000
0.2124 0.0181 0.0000
1 child (x) vs 2 and more children (y):
FSDxoy
FSDyox
FOmax
-0.0138 0.0061 0.9790
0.3741 0.0225 0.0000
-0.0138 0.0061 0.9790
SSDxoy
SSDyox
SOmax
-0.0280 0.0138 0.9830
3.0555 0.2180 0.0000
-0.0280
0.0138 0.9830
24132 78723 37799
1567 70012 23968
536 58707 19998
Mean Std Prob
0.0411 0.0124 0.0000
0.1824 0.0064 0.0000
0.0411 0.0124 0.0000
0.0617 0.0225 0.0050
0.4614 0.0338 0.0000
0.0617 0.0225 0.0050
0.0009 0.0022 0.5400
0.3283 0.0121 0.0000
0.0009 0.0022 0.5400
-0.0048 0.0071 0.7600
1.0697 0.0490 0.0000
-0.0048 0.0071 0.7600
0.0942 0.0304 0.0000
0.0154 0.0187 0.2140
0.0148 0.0174 0.2140
0.6140 0.3443 0.0380
0.0306 0.0706 0.3000
0.0148 0.0292 0.3380
N Mean Std dev Characteristics N Mean Std dev
6.B Immigrants:
Child
1
15576 75373 80739
1254 71168 45606 and children 659 40664 29979
15576 77022 34746
1254 70004 22179
659 59216 17412
Mean Std Prob Test Mean Std Prob
0 child (x) vs 1 child (y):
FSDxoy
FSDyox
FOmax
SSDxoy
0.2723 0.0114 0.0000
0.2355 0.0089 0.0000
0.2355 0.0089 0.0000
1.2894 0.0680 0.0000
SSDyox
SOmax
0.0352 0.1039 0.3790
0.0352 0.1039 0.3790
0 child (x) vs 2 and more children (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
0.1839 0.0160 0.0000
0.3681 0.0074 0.0000
0.1839 0.0160 0.0000
0.4070 0.0485 0.0000
2.2996 0.0959 0.0000
SOmax 0.4070 0.0485 0.0000
1 child (x) vs 2 and more children (y):
FSDxoy
FSDyox
-0.0306 0.0143 0.9700
0.3606 0.0206 0.0000
FOmax
SSDxoy
SSDyox
SOmax
-0.0306 0.0143 0.9700
-0.0339 0.0184 0.9700
3.6866 0.2776 0.0000
-0.0339 0.0184 0.9700
0.1670 0.0155 0.0000
0.0206 0.0066 0.0010
0.0206 0.0066 0.0010
1.2800 0.1215 0.0000
-0.0378 0.0044 1.0000
-0.0378 0.0044 1.0000
0.0558 0.0064 0.0000
0.1386 0.0133 0.0000
0.0558 0.0064 0.0000
0.4246 0.0737 0.0000
0.3278 0.1389 0.0130
0.2877 0.0972 0.0130
0.1824 0.0488 0.0000
-0.0023 0.0474 0.5370
-0.0030 0.0461 0.5370
1.9241 0.7602 0.0020
-0.0789 0.0627 0.9690
-0.0808 0.0479 0.9710
24

Table 7. Stochastic dominance by year of immigration to Sweden (based on income in 1990) .
Gross Income Disposable Income
Characteristics
1968-1970
1971-1980
1981-1990
Test
2225 90791 166995
4656 82961 75830
1834 78957 90041
Mean Std Prob
1968-1970 (x) vs 1971-1980 (y):
FSDxoy
FSDyox
0.0191 0.0114 0.0020
0.0537 0.0128 0.0000
FOmax
SSDxoy
SSDyox
SOmax
0.0186 0.0107 0.0020
0.0187 0.0122 0.0620
0.0663 0.0282 0.0080
0.0169 0.0109 0.0700
1968-1970 (x) vs 1981-1990 (y):
FSDxoy
FSDyox
0.0068 0.0035 0.0000
0.1161 0.0159 0.0000
FOmax
SSDxoy
SSDyox
SOmax
0.0068 0.0035 0.0000
-0.0234 0.0156 0.9280
0.1643 0.0338 0.0000
-0.0234 0.0156 0.9280
1971-1980 (x) vs 1981-1990 (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
0.0048 0.0049 0.1090
0.0800 0.0131 0.0000
0.0048 0.0049 0.1090
-0.0190 0.0128 0.9410
0.6303 0.1363 0.0000
-0.0190 0.0128 0.9410
2225 81440 50761
4656 74607 36729
1834 69770 39899
Mean Std Prob
0.0014 0.0019 0.1000
0.0647 0.0092 0.0000
0.0014 0.0019 0.1000
-0.0401 0.0053 1.0000
0.3321 0.0476 0.0000
-0.0401 0.0053 1.0000
0.0049 0.0037 0.0200
0.1386 0.0121 0.0000
0.0049 0.0037 0.0200
-0.0694 0.0081 1.0000
0.5997 0.0616 0.0000
-0.0694 0.0081 1.0000
-0.0095 0.0077 0.8790
0.1008 0.0151 0.0000
-0.0095 0.0077 0.8790
-0.0307 0.0101 0.9990
1.0846 0.1898 0.0000
-0.0307 0.0101 0.9990
Table 8. Stochastic dominance by gender (based on mean income 1982-1990) .
Gross Income Disposable Income
Characteristics male
Swedish male
Immigrant
10630 96689 84164
15604 59048 67178
6909 91122 64936 female 10579 59752 55606
Test Mean Std Prob
Swedish male (x) vs Swedish female (y):
FSDxoy -0.0000 0.0001 0.5050
FSDyox
FOmax
SSDxoy
SSDyox
0.2305 0.0059 0.0000
-0.0000 0.0001 0.5050
-0.1749 0.0054 1.0000
1.2794 0.0285 0.0000
SOmax -0.1749 0.0054 1.0000
Swedish male (x) vs Immigrant male (y):*
FSDxoy 0.0299 0.0058 0.0000
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
0.0434 0.0068 0.0000
0.0295 0.0053 0.0000
0.0484 0.0118 0.0000
0.1488 0.0366 0.0000
0.0481 0.0114 0.0000
10630 79531 30784
15604 68092 23105
6909 77130 29590
10579 69183 22820
Mean Std Prob
0.0062 0.0027 0.0080
0.1911 0.0063 0.0000
0.0062 0.0027 0.0080
0.0109 0.0090 0.1380
1.2603 0.0454 0.0000
0.0109 0.0090 0.1380
0.0210 0.0071 0.0010
0.0255 0.0044 0.0000
0.0188 0.0050 0.0010
-0.0073 0.0031 0.9940
0.1910 0.0545 0.0000
-0.0073 0.0031
0.9940
25

Swedish male (x) vs Immigrant female (y):*
FSDxoy 0.0000 0.0002 0.3300
FSDyox
FOmax
SSDxoy
SSDyox
0.2388 0.0063 0.0000
0.0000 0.0002 0.3300
-0.1291 0.0060 1.0000
1.2359 0.0313 0.0000
SOmax -0.1291 0.0060 1.0000
Swedish female (x) vs Immigrant male (y):*
FSDxoy
FSDyox
0.2142 0.0059 0.0000
0.0001 0.0001 0.3080
FOmax
SSDxoy
SSDyox
SOmax
0.0001 0.0001 0.3080
0.8499 0.0239 0.0000
-0.2138 0.0059 1.0000
-0.2138 0.0059 1.0000
Swedish female (x) vs Immigrant female (y):*
FSDxoy
FSDyox
FOmax
0.0486 0.0060 0.0000
0.0114 0.0037 0.0000
0.0114 0.0037 0.0000
SSDxoy
SSDyox
0.0656 0.0117 0.0000
-0.0356 0.0160 0.9800
SOmax -0.0356 0.0159 0.9800
Immigrant male (x) vs Immigrant female (y):
FSDxoy
FSDyox
FOmax
SSDxoy
SSDyox
SOmax
-0.0109 0.0036 0.9980
0.1403 0.0076 0.0000
-0.0109 0.0036 0.9980
-0.1116 0.0066 1.0000
1.9153 0.1099 0.0000
-0.1116 0.0066 1.0000
0.0058 0.0036 0.0560
0.1727 0.0062 0.0000
0.0058 0.0036 0.0560
-0.0062 0.0058 0.8890
1.0912 0.0493 0.0000
-0.0062 0.0058 0.8890
0.1500 0.0079 0.0000
0.0392 0.0042 0.0000
0.0392 0.0042 0.0000
0.6745 0.0639 0.0000
0.2324 0.0273 0.0000
0.2324 0.0273 0.0000
0.0722 0.0062 0.0000
0.0091 0.0015 0.0000
0.0091 0.0015 0.0000
0.2632 0.0442 0.0000
0.0509 0.0128 0.0000
0.0509 0.0128 0.0000
0.1655 0.0183 0.0000
0.0139 0.0091 0.0740
0.0139 0.0091 0.0740
1.4933 0.2226 0.0000
0.0266 0.0243 0.0740
0.0266 0.0243 0.0740
Note: The * items (comparisons between Swedes and immigrants) should be viewed with "caution" because of nonproportional sampling.
Appendix A. Summary statistics by various individual characteristics.
Gross Income Disposable Income Transfers Taxes
Characteristics N Mean Std dev Mean Std dev Mean Std dev Mean Sts dev
A. Years of observation:
A1. Swedes:
1982
1986
1990
80238 73921
26235 79320
A.2. Immigrants:
1982
1986
1990
60524 61976
17431 72008
B. Age (based on mean income 1982-1990, age in 1990):
B1. Swedes:
18-40
41-65
66-105
10633 105894 82856 82888 29656 20519 27613 43862 54193
9035 19258
B2. Immigrants:
18-40
41-65
66-105
62569 79285
3744 18555
26

C. Marital status (based on mean income 1982-1990, status in 1990):
C1. Swedes:
Unmarried
Divorced
Widows
87789 77940
6422 26480
C2. Immigrants:
Unmarried
Divorced
Widows
59036 73450
7795 74097
D. Country of origin (based on mean income 1982-1990):
Swede
Nordic
European
Others
67229 70510
1482 62171
E. Levels of education (based on income and education in 1990):
E1. Swedes:
Secondary
School 7955 106148 81642 85558 34703 24960 37910 45789 39797
University
E2. Immigrants:
Secondary
School
University 1919 131670 95008 95161 44901 95161 44902 19301 36031
F. Number of children (based on income and # children in 1990):
F1. Swedes:
Child
2
F2. Immigrants:
Child
1
2
G. Years of immigration (based on income in 1990):
1968-1970
1971-1980
1981-1990
166995 81440
4656 82961
H. Gender (based on mean income 1982-1990):
Swedish 10630 96689 female 15604 59048
30784 26306
67178 68092
Immigrant
Immigrant
6909 91122 female 10579 59752
I. Sample (based on mean income 1982-1990):
Sample
27

Figure 1.a CDF for gross (y) and disposable (d) income of Swedes (s) by year of observation.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% Interval ys1982 ys1986 ys1990 ds1982 ds1986 ds1990
Figure 1.b CDF of gross (y) and disposable (d) income of immigrants (i) by year od observation.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yi1982 yi1986 yi1990 di1982 di1986 di1990
Figure 2.a CDF of gross (y) and disposable (d) income of Swedes (s) by age groups.
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval ys18-40 ys41-65 ys66-
105 ds18-40 ds41-65 ds66-
105
28

Figure 2.b CDF of gross (y) and disposable (d) income of immigrants (i) by age groups.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yi18-40 yi41-65 yi66-105 di18-40 di41-65 di66-105
Figure 3.a CDF of gross (y) and disposable (d) income of Swedes (s) by marital status.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval ysunmarri ed ysdivorced yswidows dsunmarri ed dsdivorce d dswidows
Figure 3.b CDF of gross (y) and disposable (d) income of immigrants (i) by marital status.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yiunmarri ed yidivorce d yiwidows diunmarri ed didivorce d diwidows
29

Figure 4.a CDF of gross (y) and disposable (d) income by country of origin.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yswedes yothernord ic yeuropean yothers dswedes dothernord ic deuropean s dothers
Figure 5.a CDF of gross (y) and disposable (d) income of Swedes (s) by levels of education.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval ysseconda ry yshighsch ool ysuniversit y dsseconda ry dshighsch ool dsuniversit y
Figure 5.b CDF of gross (y) and disposable (d) income of immigrants (i) by levels of education.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yiseconda ry yihighsch ool yiuniversi ty disecond ary dihighsch ool diuniverit y
30

Figure 6.a CDF of gross (y) and disposable (d) income of Swedes (s) by number of children.
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval ys0child ys1child ys2andm ore ds0child ds1child ds2andm ore
Figure 6.b CDF of gross (y) and disposable (d) income of immigrants (i) by number of children.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yi0child yi1child yi2andmo re di0child di1child di2andmo re
Figure 7. CDF of gross (y) and disposable (d) income of immigrants (i) by year of immigration.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval yi1968-
70 yi1971-
80 yi1981-
90 di1968-
70 di1971-
80 di1981-
90
31

Figure 8. CDF of gross (y) and disposable (d) income of Swedes (s) and immigrants (i) by gender.
0.6
0.5
0.4
0.3
0.2
0.1
0
1
0.9
0.8
0.7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
5% interval ysmale ysfemal e dsmale dsfemal e yimale yifemale dimale
REFERENCES
Anderson, G.J. (1996), “Nonparametric tests of stochastic dominance in income distributions”, Econometrica , 64, 5, 1183-1193.
Aronsson, T. and M. Palme (1998),"A Decade of Tax and Benefit Reforms in Sweden:
Effects of Labor Supply, Welfare and Inequality", Economica.
Beach, C. M., R. Davidson, and G. A. Slotsve (1995), “Distribution-free statistical inference for inequality dominance with crossing Lorenz curves”, Unpublished paper N95A03,
GREQAM, Universites d’Aix -Marseille.
Bishop, J. A., K. V. Chow, and J. P. Formby (1994), “Testing for marginal changes in income distributions with Lorenz and Concentration curves”, International Economic Review , 35, 2,
479-488.
Björklund, A. (1993), “A comparison between actual distribution and annual and lifetime income: Sweden 1951-89”, Review of Income and wealth , 39, 377-86.
Björklund, A., and R.B. Freeman (1995), "Generating equality and Eliminating Poverty- The
Swedish way", Occasional Paper No. 60, Center for Business and Policy Studies, Stockholm,
Sweden.
Björklund, A., M. Palme, and I. Svensson (1995), “Tax reforms and income distribution: an assessment using different income concepts”, Swedish economic Policy Review , 2, 229-266.
32

Blau, F. and L. M. Kahn (1996), “International differences in male wage Inequality:
Institutions versus market forces”, Journal of Political Economy , 104, 791-837.
Borjas G. E. (1994) “The Economics of immigration”, Journal of Economic Literature, Vol.
XXXII, 1667-1717.
Bluestone, B. (1990), “The impact of schooling and industrial restructuring on recent trends in wage inequality in the United States”, AEA Papers and Proceedings , May 1990, 303-307.
Buckberg, E. and A. Thomas (1995), “Wage dispersion and job growth in the United States”,
Finance and Development , June 1995, 16-19.
Buckberg, E. and A. Thomas (1996), “Wage dispersion in the 1980's: resurrecting the role of trade through the effects of durable employment changes”, IMF Staff Papers , 43, 336-354.
Card, D. (1996), “Wage dispersion, return to skill, and Black-White wage differentials”,
Journal of Econometrics , 74, 319-361.
Creedy, J., Hart P. E., and Klevmarken, N. A. (1980), “Income mobility in Great Britain and
Sweden”, in Klevmarken, N. A., and Lybeck, J. (Eds), The Structure and Dynamics of
Income , TIETO, Clevedon.
Davies, J., and M. Hoy (1996), “Making inequality comparisons when Lorenz curves intersect”, American Economic Review , Forthcoming.
Davidson, R., and J.-Y. Duclos (1998),"Statistical Inference for the measurement of the
Incidence of Taxes and Transfers", Econometrica , 65, 1453-1465.
Durbin, J. (1973), “Distribution theory for tests based on the sample distribution function”,
SIAM, Philadelphia.
Durbin, J. (1985), “The first passage density of a continuous Gaussian process to a general boundary”, Journal of Applied Probability , 22, 99-122.
Gottschalk, P. and R. Moffitt (1994), “The growth of earnings instability in the U.S. labor market”, Brookings Papers on Economic Activity , 2, 217-272.
Gourieroux, C., Holly, A., and A. Monfort (1982), “Likelihood ratio test, Wald test and
Kuhn-Tucker test in linear models with inequality constraints in the regression parameters”,
Econometrica , 50, 1, 63-80.
Gustafsson B. (1994) “The degree and pattern of income immobility in Sweden”, Review of
Income and Wealth Series , 40, 1, 67-86.
33

Juhn, C., K. M. Murphy, and B. Pierce (1991), “Accounting for the slowdown in Black-
White wage convergence”, In Workers and Their wages: Changing Patterns in the United
States , Marvin H. Kosters (Ed.) Washington: American enterprise Institute Press.
Juhn, C., K. M. Murphy, and B. Pierce (1993), “Wage inequality and the rise in returns to skill”, Journal of Political Economy , 101, 3, 410-442.
Kaur, A., B. L. S. Prakasa Rao, and H. Singh (1994), “Testing for second-order Stochastic
Dominance of two distributions”, Econometric Theory , 10, 849-866.
Klecan, L., R. McFadden, and D. McFadden (1991), “A robust test for Stochastic
Dominance”, Working paper, Economics Dept., MIT.
Kodde, D. A., and F. C. Palm (1986), “Wald criteria for jointly testing equality and inequality restrictions”, Econometrica , 50, 1243-1248.
Lindbeck, A. (1997), “The Swedish experiment”, Journal of Economic Literature , Vol.
XXXV, 1273-1319.
Lindbeck, A. and D. J. Snower (1996), “Reorganization of firms and labor market inequality”, American Economic Review , 86, 315-321.
Maasoumi, E. (1998a), “On Mobility”, Chapter 5, Handbook of Applied Economic Statistics ,
A. Ullah and D. Giles (eds), Marcell Dekker.
Maasoumi, E. (1998b), “Empirical analyses of welfare and inequality”, in M.H. Pesaran and
P. Schmidt (eds.), Handbook of Applied Econometrics, Vol II: Microeconometrics , Basil
Blackwell Publishers.
Maasoumi, E. (2000),"Parametric and Nonparametric Tests of Limited Domain and Ordered
Hypotheses in Economics", In B. Baltagi (ed.), A Companion to Econometric Theory; Basil
Blackwell publishers, Forthcoming.
McFadden, D. (1989), “Testing for Stochastic Dominance”, in Part II of T. Fomby and T.K.
Seo (eds.) Studies in the Economics of Uncertainty (in honor of J. Hadar), Springer-Verlag.
Montgomery, E. and D. Stockton (1994), “Evidence on the causes of the rising dispersion of relative wages”, Industrial Relations , 33, 206-229.
Palme, M. (1995), “Earnings mobility and distribution: comparing statistical model on
Swedish data”, Labour Economics , 2, 213-247.
Shorrocks, A. F. (1983), “Ranking income distributions”, Economica , 50, 3-17.
Shorrocks A. F., and J. Foster (1987), “Transfer sensitive inequality measures”, Review of
Economic Studies , 54, 485-497.
34

Whitmore, G. A. and M. C. Findley (1978), Stochastic Dominance: An approach to decision making under risk , Heath, Lexington: Mars.
Wolak, F. (1991), “The local nature of hypothesis tests involving inequality constraints in nonlinear models”, Econometrica , 59, 981-95.
Xu, K., G. Fisher, and D. Wilson (1995), “New distribution-free tests for stochastic dominance”, Working paper No. 95-02, February, Department of Economics, Dalhousie
University, Halifax, Nova Scotia.
Xu, K. (1995), “Asymptotically distribution-free statistical test for generalized Lorenz curves: An alternative approach”, Department of Economics, Dalhousie University, Halifax,
Nova Scotia, presented at the 7th World Congress of Econometric Society, Japan.
Zandvakili, S. and B. Gustafsson (1998), “Dynamics of income inequality in Sweden”,
Unpublished manuscript, Department of Social Work, Göteborg University.
35