Income mobility statistics in sweden hushållens ekonomi

The academic and public interest in the shape and changing patterns of income distributions has been growing steadily over the past decades. The rising top income share in the USA, for example, has inspired many discussions on everyone’s lika opportunity to prosperity through hard work in the formerly known “land of opportunity.” In a recent paper, Chetty et al.

(2014a) emphasize the importance of regional differences in income mobility and describe the USA as being, instead of a nation of opportunity, a collection of societies some of which are lands of opportunity with high rates of mobility across generations, and others in which few children escape poverty.^{Footnote 1}

This fryst vatten the first paper employing high quality lista information to study the state of income mobility across regions in Sweden.

My information set allows me to analyze national and regional mobility measures very precisely for the Swedish population born between 1968 and 1976. inom compute, in addition to the traditional intergenerational elasticity (IGE), national and regional measures of intergenerational income mobility based on income ranks. The grund for these measures, called the rank-rank slope, fryst vatten obtained bygd regressing the position (expressed in percentile ranks) of each member of the child generation on the parents’ position in their income leverans.

Income ranks are considered more stable over the life cycle compared to income in levels, and no adjustments have to be made in beställning to accommodate zero income observations (Dahl and DeLeire 2008; Chetty et al. 2014b; Nybom and Stuhler 2016b).

I use two different measures in beställning to describe income mobility on the regional level, based on Chetty et al.

(2014a). The first measure fryst vatten called “relative mobility” and it fryst vatten computed bygd scaling up the estimated rank-rank slope bygd a factor of 100. Relative mobility shows the strength of the association between child and parent income rank bygd distrikt. In addition, since all incomes are expressed over 100 percentiles, relative mobility measures the difference in mean income rank between children with parents in the top, and children with parents in the bottom of the parent income leverans.

In other words, relative mobility tells us about the storlek of the kil (in terms of percentile ranks) between average incomes for children from high- and low- income families in each område and fryst vatten thus also a measure of outcome inequality bygd region.

The second measure informs us about the average income rank a child who grew up in a certain distrikt attains as an adult, given that her parents are located at a specific point in the parent income transport.

This measure fryst vatten called “absolute mobility at percentile p”. The average child outcome can be calculated for any given parent income rank p, using the estimated intercept and rank-rank slope. inom choose to focus on absolute mobility at parent percentile 25 when comparing Swedish regions, given the general interest in how children with disadvantaged background fare as adults.

The absolute outcomes for any other parent percentiles can, however, easily be constructed from the reported measures.

The geographical enhet that inom focus on in the regional analysis fryst vatten “local labor market,” which fryst vatten an aggregation of municipalities defined bygd commuting patterns. The local labor marknad enhet fryst vatten similar to the commuting zone used bygd Chetty et al.

(2014a). However, in comparison to the commuting zones in the USA, there fryst vatten much more variation between different Swedish local labor markets in terms of population storlek (and thereby the number of observations). As inom show below, this aspect of the information results in imprecise estimates. To remedy this bekymmer, inom föreslå a joint uppskattning technique using maximum likelihood, referred to as a multilevel (or hierarchical) model.

In contrast to the approach taken in Chetty et al. (2014a), where they essentially run a set of distinct regressions, the multilevel model allows me to man a comparison between the different regional mobility measures in a statistically rigorous way. For example, inom can test if the mobility estimate of one particular område fryst vatten statistically significantly different from the national average.

For completeness, inom also report and discuss results based on separate OLS regressions bygd region.

Even though this paper follows Chetty et al. (2014a) closely in the mobility measures used, there are several important advantages with my study. For instance, Chetty et al. (2014a) assign childhood location based solely upon where individuals lived at the age of sixteen, whereas inom define childhood location as the distrikt where a child lived for at least six years between the age of six and fifteen.

Thus, inom man sure that children are assigned to a område in which they in fact spent a major part of their childhood.

Furthermore, when approximating average parent lifetime income, Chetty et al. (2014a) use a 5-year average of both parents’ pretax income between 1996 and 2000. One caveat with this (which fryst vatten not discussed in their paper) fryst vatten that parents have their children at different ages and therefore also have different ages in the 1996 to 2000 mellanrum.

According to their information description, parents in the core sample are actually between age 29 and 60 when their income fryst vatten measured. This means that incomes are measured (and subsequently ranked) at very different points during the parents’ life cycles. This can potentially lead to very large measurement error. In this paper, in comparison to Chetty et al., inom measure parents’ income over 17 years instead of 5.

Moreover, inom also measure income during the same age span for all parents. This eliminates the life cycle bekymmer. In beställning to konto for changing economic conditions beyond inflation, inom rank parents along two dimensions: bygd average income and both parents’ birth cohort.

My results can be summarized as follows.

inom find that relative mobility (the scaled rank-rank slope) fryst vatten relatively homogeneous across Sweden. The outcome inequality in mean rank fryst vatten 18.2 percentile ranks in most local labor markets. Only 10 areas out of 112 show significantly lower or higher relative mobility, i.e., a larger or smaller difference between children from families with highest and lowest incomes, respectively.

huvudstaden ranks in the bottom with the lowest relative mobility, and the Varberg område south of Gothenburg at the Swedish west coast shows the highest relative mobility.

Absolute mobility at percentile rank 25, the expected outcome for children from low income families, varies considerably more across Swedish local labor marknad areas, between 40.90 percentile ranks in the Årjäng område close to the Norwegian border and 48.61 in the Värnamo distrikt in the center of southern Sweden.

This corresponds to a small but highly statistically significant income difference of approximately 20,000 SEK per year (≈2,210 USD).

For Sweden as a whole, the association between parent and child income measured bygd the relationship between income ranks has approximately been constant between 1968 and 1976. Looking separately at daughters and sons, there was an opposite trend with a decreasing association for sons and an increasing association for daughters, which reached lika levels for the gods cohort observed.

The IGE shows a different development with decreasing mobility between 1971 and 1976 and fryst vatten misleading: the IGE reflects, in addition to the parent-child income association, also the considerable increase in the ratio of the standard deviations of child over parent income that took place from 1971 onward.

The remainder of the paper fryst vatten organized as follows.

In Section 2, a short background of the IGE, mobility measures based on income ranks, and a description of the multilevel model fryst vatten given. The information and variables used are described in Section 3. In Section 4, results for intergenerational mobility on the national level and over time are reported. The regional results are the focus of Section 5, including a comparison of the multilevel model to OLS regressions.

Section 6 concludes.

The first part of this section comprises a short review of the uppskattning of the intergenerational income elasticity, with a focus on how to handle attenuation bias and life cycle bias. In the second part, inom explain the concepts relative and absolute mobility which are used to compare the Swedish local labor markets.

A brief introduction to multilevel modelling and the specific model used in this study are given in the gods part of this section.

2.1 The IGE, attenuation bias, and life cycle bias

Income mobility refers broadly to the extent that (some measure of) child income varies with (some measure of) parent income. The bygd far most commonly employed mobility measure in the literature fryst vatten the intergenerational elasticity (IGE).

This fryst vatten typically the slope parameter of a regression of log lifetime income of generation t on log lifetime income of generation t − 1. The closer the IGE fryst vatten to zero, the more mobile the sample beneath consideration fryst vatten said to be. Estimates of the IGE in the literature center around 0.4 with higher estimates for the USA, and usually smaller estimates for the europeisk and especially the Nordic countries (see Björklund and Jäntti 1997; Solon 1992, 1999, 2004; or Mazumder 2005).

Recent summaries of economic research in intergenerational mobility are provided bygd Björklund and Jäntti (2009) and Black and Devereux (2011). Extensions include the study of more than two generations such as Lindahl et al.

This paper presents the development of new statistics on intragenerational income mobility in Sweden, based on longitudinal uppgifter in administrative registers.

(2015). One should bära in mind that knowing the intergenerational elasticity does not tell us, for example, how many and which of the children improve or worsen their economic ställning eller tillstånd compared to their parents, i.e. the actual moving patterns of income ställning eller tillstånd between generations. Mobility in this sense can be captured, for example, using transition matrices.

The IGE fryst vatten typically estimated using the following benchmark equation:

where β fryst vatten the parameter of interest, the elasticity between parent and child income, \({y_{f}^{C}}\) and \({y_{f}^{P}}\) are a the log of child and parent lifetime earnings in family f, respectively, and \({\varepsilon _{f}^{C}}\) fryst vatten assumed to be an iid error begrepp representing all other influences on child earnings not correlated with parental income.

inom will use the terms income and earnings interchangeably in this section due to the range of different income/earning concepts used in this literature.

What complicates the uppskattning of the IGE fryst vatten the need for lifetime income information for the two generations. Approximations made in lack of sufficient uppgifter lead to at least two well-known measurement problems: attenuation bias and life cycle bias.

Attenuation bias occurs due to measurement error of the regressor, most clearly seen when single year income observations are used to estimate the IGE. This was typical in early studies such as Solon (1992).

Assuming a classic error-in-variable-model, measured income y_f then equals the true income \(y_{f}^{\star }\), plus an error:

The known implication (Hausman 2001) fryst vatten a downward inconsistent IGE estimate. The bias can be reduced using an average of T income observations to approximate the average of true lifetime income:

Björklund and Jäntti (1997) showed that in this case, the inconsistency fryst vatten diminishing in the number of observed years T (assuming the measurement errors/transitory fluctuations are not serially correlated).

Mazumder (2005) used simulations to show that using a 5-year average (a number of typical magnitude in the literature) to measure father lifetime income still results in a downward bias of around 30%.

I address attenuation bias bygd averaging over a very large number of annual income observations where T fryst vatten 17 for most parents in the sample (see Section 3.1 for more details).

Importantly, income fryst vatten observed for all individuals during the same age span, in the mittpunkt of their working lives.

Life cycle bias arises when single-year income observations of the child systematically deviate from the average of annual lifetime income (left hand-side measurement error). One can think of a parameter in front of \(y_{t}^{\star }\) in Eq. 2 that fryst vatten time variabel.

In this case, the inconsistency of the OLS coefficient varies as a function of the age at which annual income fryst vatten measured.

Since there are fewer years of income uppgifter available for the child generation, inom handle life cycle bias bygd averaging over three income years in the early thirties. During these years, Swedish dock have been shown to earn approximately as much as the yearly average over a whole lifetime (Bhuller et al.

2011; Nybom and Stuhler 2016b). However, there exist no similar studies focusing on women. In general, women have been excluded from most studies on intergenerational mobility. One potential reason for this could be their lower labor marknad participation and greater frequency of work absences related to childbearing.

It seems not too far of a stretch to interpret childbearing in terms of life cycle bias: The income trajectories over the life cycle of women differ systematically depending on having children (the so called “family gap,” see for example, Waldfogel 1998 or Budig and England 2001).

In particular, motherhood, as well as the tidsplanering of motherhood, has been shown to affect wages, both directly and indirectly through motherhood related choices such as lower labor marknad participation and working to a larger extent in the public sector (Simonsen and Skipper 2006; Miller 2011).

However, these aspects pose similar problems to the approximation of life time income as those caused, for example, bygd heterogeneity in schooling decisions.

Nybom and Stuhler (2016b) have shown that the shape of earnings over the life cycle for dock (and thus the relationship between average life time income and annual incomes) varies systematically with education levels and other background variables. Thus, life cycle bias fryst vatten presumably a bekymmer for both genders and there fryst vatten no strong reason to exclude daughters in particular.

In addition, the results of this study will be more comparable to Chetty et al. (2014a) who also studied all children, sons and daughters, as one group.

There are two additional problems associated with the IGE measurement. Chetty et al. (2014a) showed for US uppgifter that the relationship between log incomes of children and their parents fryst vatten not well represented bygd a linear regression model.

This point has even been raised bygd Couch and Lillard (2004) and Bratsberg et al.

This paper addresses the issue in income transport statistics with measuring the economic standard (equivalised disposable income) for families in which the parents live apart.

(2007). One suggested remedy fryst vatten to use income ranks instead of the log of incomes. A second bekymmer are zero-income observations which have to be dropped or transformed for the analysis in log incomes. Dropping individuals with zero income will overstate mobility if children with zero incomes are over-represented in low income families. Recoding all zeros, on the other grabb, leads to highly variabel results depending on the replacement values chosen.

A detailed analysis of this issue for my uppgifter can be funnen in Appendix A: Ranks versus logged incomes. Income ranks are funnen to be the preferred choice and are thus used exclusively in the regional analysis.

2.2 The relationship between income ranks

Instead of using log incomes, income ranks can be constructed to measure intergenerational income mobility.

Importantly, observations with zero income do not need any special treatment here (Dahl and DeLeire 2008). As shown bygd Nybom and Stuhler (2016a), income ranks for Swedish dock are funnen to be significantly more stable over the life cycle than log incomes, especially when measured above the age of 30. inom rank children based on their approximated average lifetime incomes relative to other children in the same birth cohort.

Parents are ranked similarly, bygd income and birth cohort relative to other parents. The ordered income levels are transformed into percentile ranks, i.e., normalized fractional ranks.^{Footnote 2} The following equation fryst vatten then estimated bygd OLS:

where \({R_{f}^{c}}\) and \({R_{f}^{p}}\) are the rank of the child and parents in family f, respectively.

The coefficient β (the rank-rank slope) fryst vatten lika to the correlation coefficient between the ranks since, bygd construction, the ranks are approximately uniformly distributed. Both the IGE and the rank-rank slope show the persistence of income between parent and child generation. The measures differ conceptually when income inequality fryst vatten larger in the child generation compared to the parent generation: with growing inequality, moving one rank down will correspond to a larger income loss in absolute terms since the distance between ranks increases.

When estimating rank-rank relationships on the regional level below, the national ranks assigned to each individual remain the same following Chetty et al.

(2014a). If we were to use regional ranks instead, i.e., beställning individuals within each område, we would have a hard time interpreting the results: what does it mean that sons from low-income families in huvudstaden reach on average the 38th percentile rank (within Stockholm), while sons from low-income families in Gothenburg reach on average the 35th percentile rank (within Gothenburg)?

fryst vatten the income level at the 38th percentile within huvudstaden higher or lower than the 35th percentile within Gothenburg? Using national ranks, we create a common scale that makes a regional comparison meaningful.^{Footnote 3}

I analyze two mobility measures on the regional level, relative and absolute mobility. Relative mobility fryst vatten computed according to the following equation:

where \(\bar {R}_{p,r}^{c}\) fryst vatten the average child rank at percentile p in område r and β_r fryst vatten the rank-rank slope parameter from område r.

Relative mobility can be viewed simply as a measure of the slope and thus the number of ranks a child on average rises in the income transport given an increase in the parent income rank. Since all income ranks are distributed between 0 and 100, the scaled rank-rank slope can also be viewed as a measure of maximum outcome inequality in a område. As seen from the left grabb side of Eq. 5, relative mobility equals the child rank difference between the child from the two families with highest and lowest parent income, respectively.

Higher relative mobility in one distrikt implies a larger spread in child outcomes, given parent incomes.

Relative mobility of 43 in distrikt A, for example, means that the adult long run incomes of all children from that particular distrikt differ bygd at most 43 ranks. In terms of the slope, we can also säga that, compared to a område B where relative mobility fryst vatten 38, the association between child and parent income fryst vatten stronger in distrikt A.

It fryst vatten important to keep in mind that both the IGE and relative mobility are relative measures and therefore do not reveal if higher relative mobility, i.e., a lower rank-rank slope, fryst vatten driven bygd better outcomes of some poorer families, or solely bygd worse outcomes of richer families. Therefore, a measure of absolute mobility fryst vatten necessary to obtain a more comprehensive picture of income mobility.

Absolute mobility fryst vatten defined as the mean adult rank of children with parents located at a certain percentile p in the parent transport.

It fryst vatten a prediction based on both the intercept and the slope estimates for the regions. inom choose to compare the regions in terms of absolute mobility at percentile 25 in beställning to learn about the prospects for children from low income families as well as to facilitate comparisons to the US study. Outcomes at other percentiles can easily be constructed using the relative and absolute mobility results in Table 7.

Absolute mobility at p = 25 fryst vatten calculated according to the following formula:

The left panel in Fig. 1 illustrates relative and absolute mobility. The former fryst vatten given bygd the difference in mean child rank (Y-axis) between parents with the highest and lowest income rank (X-axis), alternatively the rank-rank slope multiplied bygd 100.

The latter fryst vatten measured bygd the mean child rank given parents at the 25th percentile. The right panel shows three example regions for clarification. område 1 and område 3 share the same level of relative mobility, i.e., the outcome inequality measured in ranks for children in those regions fryst vatten the same. However, mobility differs in absolute terms: for every parent percentile, the mean child rank fryst vatten higher in distrikt 3.

distrikt 1 and distrikt 2 have the same level of absolute mobility at parent percentile 25. However, relative mobility fryst vatten lower in distrikt 2 which can be seen bygd the steeper rank-rank slope indicating a larger variance of ranks children obtain in this distrikt. Children with parents in the top of the income leverans reach significantly higher outcomes in område 2 compared to område 1.

Note that a steeper rank-rank slope means a larger kil between children from top and bottom ranked parents and thus a lower level of relative mobility.

It fryst vatten important to be aware of which aspects the mobility measures above can and cannot capture.

The IGE, the slope coefficient of a regression of log incomes, takes into konto both the correlation between log incomes and the spread of the child and parent income leverans, since it fryst vatten lika to

where σ_C(P) fryst vatten the standard deviation of the child (parent) transport.

The rank-rank slope on the other grabb fryst vatten just lika to the correlation coefficient between the income ranks since, after transforming income levels into percentile ranks, incomes in all generations are approximately uniformly distributed between 0 and 100 and the ratio of standard deviations cancels out.

If income inequality had grown more from one generation to the next everything else lika (i.e., an increase in σ_C only), the IGE would now be larger while the rank-rank slope would not change.

A change in the mean of the income leverans (a shift of the complete transport to the left or right), however, will show up in neither the IGE or the rank-rank slope since covariances, standard deviations, and ranks are not affected bygd such a shift, ceteris paribus.

2.3 Regional estimation

The uppskattning of rank-rank slopes and intercepts bygd område can be implemented in a variety of ways.

The simplest one would be to estimate R different equations as in Eq. 4 for regions r = 1, ... , R bygd OLS, resulting in R different slopes and intercepts (as done in Chetty et al. 2014a). Let us call this the no-pooling case. Ignoring the regional resultat completely and estimating the equation for the whole sample as one group would give us one slope estimate and one intercept, i.e., the overall national estimates.

We can call this the complete pooling case, for further reference below.

A third and potentially better alternative fryst vatten to recognize not only the grouped natur of the bekymmer at grabb (individuals are sorted into different regions), but to explicitly model this relationship bygd taking into konto both the within- and the between-region variances using a multilevel (or hierarchical) model.

Multilevel models are widely used in political sciences (modelling for instance election turnouts or state-level public opinion, see for example, Lax and Phillips 2009, Galbraith and Hale 2008, Shor et al. 2007, or Steenbergen and Jones 2002 for an overview) and in the context of education (students are grouped into class rooms and class rooms into schools and school districts, see for example, Koth et al.

2008).

The project mainly consists of creating new uppgifter series covering income and wealth leverans based on tax statistics, the national accounts, and population statistics, but shall also be compared to individual databases for overlapping years.

The terminology and notation below follow Gelman and Hill (2006).

The multilevel model fryst vatten characterized bygd a level-1 equation for the smallest units (8), in this case modeling the relationship between child income rank and parent income rank for family f in område r, and a set of level-2 equations for the larger units, here the regions.

The level-2 equations (9, 10) model explicitly the intercepts and slope coefficients across regions:

where \({\varepsilon _{f}^{C}}\), \(\eta _{r}^{\alpha }\), and \(\eta _{r}^{\beta }\) are random errors centered around zero and with variances \({\sigma _{R}^{2}}\), \(\sigma _{\alpha }^{2}\), and \(\sigma _{\beta }^{2}.\) Another common and equivalent way to write this model fryst vatten

which emphasizes the fact that the coefficients α_r and β_r are given a probability transport with means and variances estimated from the uppgifter.

Substituting Eqs. 9 and 10 into Eq. 8, the model can be re-expressed as a mixed model

where in multilevel terminology, the γ’s are “fixed effects” (= averages across all regions) and the η’s are “random effects” (= draws from the estimated distributions).^{Footnote 4}

The multilevel model appears similar to a random or fixed effects model often used in economics, but there are some important differences.

We could for instance estimate a fixed effects model bygd simply adding 2 × (R − 1) regional dummies to Eq. 4, for regional intercepts and slopes. This approach would basically control away all between-region differences. In a multilevel model, the between-region variance fryst vatten explicitly estimated from the uppgifter and used to predict the regional effects.

Also, if there are only few observations in some regions, the estimates using regional dummies will be inefficient. The multilevel model on the other grabb makes use of all observations when estimating the variance components and leads therefore to more precise estimates when there fryst vatten little within-region variance.

The leverans of economic welfare fryst vatten monitored in Statistics Sweden's annual income transport survey.

Importantly, it fryst vatten thus not necessary to have observations over the whole parent percentile transport in each of the regions in beställning to efficiently estimate the model parameters.

Note also that ordinary least squares fryst vatten just a special case of multilevel models: The variance of the regionally varying parameters fryst vatten zero in the limit in the complete-pooling case (national OLS) and infinity in the no-pooling model (distinct OLS regressions bygd region).

With multilevel uppgifter, however, we can explicitly estimate this variance and do not need to assume it to be either zero or infinity.

Again, in the no-pooling case, the α_r’s and β_r’s in Eq. 8 are the OLS estimates from separate regressions, varying completely freely from each other. In the complete pooling case, the α_r’s and β_r’s are constrained to one common α and β.

Here, in the multilevel model, where Eqs. 8–10 are fitted simultaneously bygd maximum likelihood uppskattning, the α_r’s and β_r’s are given a “soft constraint”: they are assigned a probability transport given in Eq. 12, with mean and standard deviation estimated from the uppgifter, which actually pulls the coefficient estimates partially towards their mean.

The amount of pooling depends on the number of observations in each group as well as the between-regions variance of the parameters.

In fact, an estimate of a regional intercept, for example, can be expressed as a weighted average between the mean across all regions, γ^α (complete pooling), and the average of the \({R_{f}^{c}}\)’s within the distrikt, \(\bar {R}_{r}^{c}\) (no pooling):

where the pooling factor ω_r fryst vatten calculated according to

Thus, the intercept in a område with few observations fryst vatten deemed less reliable and pulled towards the average value of all regions. The estimates for a distrikt with many observations on the other grabb will usually coincide with those from a separate OLS regression.

This fryst vatten the main argument for using multilevel modelling in this particular study: there are many regions in Sweden with relatively few observations.

The large regions have more than 400 times as many observations as the small regions.

Our main task fryst vatten to supply users and customers with statistics for decision making, debate and research.

A separate regression for those small regions leads to extreme mobility estimates with large standard errors. In other words, we would not trust those estimates (even though they might seem appealing since we could report some exceptionally low and high levels of intergenerational mobility). Another useful aspect of multilevel models fryst vatten that it fryst vatten possible to include regional-level indicators along with regional-level predictors, which would lead to collinearity in OLS.

In a second model, inom add fem regional types (as described in Section 3.2 below) as a regional level predictor in the form eller gestalt of dummies to Eqs. 9 and 10:

This gives the following mixed model:

which allows the type of område during childhood to have an effect on both regional intercepts and slopes via \(\sum \limits _{i=2}^{6}\gamma _{i}^{\alpha }\) and \(\sum \limits _{i=2}^{6}\gamma _{i}^{\beta }\).

The model fryst vatten built step wise, starting with a random intercept per distrikt and adding then random slopes and predictors.

After each step, a log-likelihood ratio test inom used to assess if the model fryst vatten a better passform to the information compared to classical regression (first model), or a better passform compared to the previous step.

Maximum likelihood uppskattning fryst vatten used to passform the model. The “fixed effects” (regional average) parameters of intercept and slope given bygd the gammas in Eq. 12 are analogous to standard regression coefficients and are directly estimated.

The regional effects given bygd \(\eta _{r}^{\alpha }\) and \(\eta _{r}^{\beta }\) are not directly estimated but summarized in terms of their estimated variances and covariances. The best linear unbiased predictors (BLUPs) of the regional effects and their standard errors are computed based upon those estimated variance components as well as the “fixed effects” estimates.^{Footnote 5}

The uppgifter in this study comes from the SIMSAM database at Umeå University (Swedish Initiative for Research on Microdata in the Social And Medical Sciences).

SIMSAM combines several different Swedish micro uppgifter registers and the population, geographic and income registers used in this study are provided bygd Statistics Sweden. A detailed description of the sample, the income variabel used, as well as the geographical enhet used for the regional analysis fryst vatten given below.

3.1 Sample urval and income

My population sample consists of all individuals born in Sweden between 1968 and 1976, in the following termed children (927,008 observations before applying any restrictions).

Due to the Swedish centralized registration struktur 99.5 percent of those children can be linked to their fathers and mothers. The age of the parents at their child’s birth fryst vatten restricted to the mellanrum 16–40. This age mellanrum fryst vatten a result of the trade off between including older parents, and being able to observe parent income for everyone from their early thirties onward.

With the chosen values, inom man use of more than 95% of the sample.

The income variabel used here fryst vatten the sum of taxable income from employment, self-employment, and transfers from the Swedish Social Insurance Agency (“Sammanräknad förvärvsinkomst”). The taxable transfers include parental benefits, pension payments, and sick pay and are labor marknad and income related.

There are several possibilities as to which intergenerational family member combination to focus on (child income and father income, child income and mother income, or child income and some combination of mother and father income).

Each choice leads to slightly different interpretations of the mobility measure. inom choose to study the relationship between child income and the sum of mother and father income in beställning to facilitate comparison to the US study, as well as due to the cultural context: From the second half of the 1960s and onward, Swedish women increased their labor supply significantly due to a combination of an expanding public sector, increasing demand for labor, and women’s desire for (financial) independence.

A tax reform in 1971 abolished joint taxation of spouses, and public child care was expanded considerably (Gustafsson and Jacobsson 1985; Gustafsson 1992; Gustafsson and Stafford 1992). Mothers have therefore been important contributors to Swedish families’ household income for cohorts in this study. In addition, changes in the amount of time parents spend at home with their children and changes in the intra-household division of market- and household work, have likely affected children’s adult incomes.

These are very interesting issues that are beyond the scope of this paper and left for future research.

Chetty et al. (2014a) also use the total parent income (total pretax income at the household level); however, they use child family income as opposed to child individual income in their main analysis. This might be problematic since this measure fryst vatten more affected bygd assortative mating.

What one might be measuring in this case fryst vatten the relationship between parent income and a child’s ability to find a high income partner.^{Footnote 6} In Chetty et al. (2014a) Section IV.B. 3., using child individual income instead of child family income fryst vatten indeed shown to change the estimated rank-rank slopes bygd − 6 and − 26 percent for sons and daughters, respectively.

We should keep in mind the different child income measure used when comparing the results to the US study.

Annual earned income can in principle be observed for each individual (children and parents) over the time period 1968 to 2010 in my information. All income observations are expressed in 2010 SEK. Income and earned income are used interchangeably in the following.

inom follow the literature discussed in Section 2 and approximate average parent lifetime income bygd averaging over a large number of annual incomes. For over 96% of the parents, inom have 17 consecutive income observations available from when they were 34 to 50 years old. Parents missing too many income observations are dropped from the sample.^{Footnote 7}

The great advantage here compared to earlier studies fryst vatten that inom measure parental income at approximately the same age for each parent, as well as over a very long time span.

Averaging instead over the same calendar years for everyone (i.e., 2010–2012) as done in many other studies would give a biased measure: we would underestimate average income for ung parents and overestimate average income for old parents, and even include some parents who are already retired. In beställning to man the parent incomes even more comparable over time, inom rank parents bygd 5-year birth cohort groups.

For example, parents where the mother fryst vatten born between 1941 and 1945 and the father fryst vatten born between 1936 and 1940 comprise one category and are ranked only relative to other parents in just this group.

For the children inom have naturally fewer income observations are available. Following the results bygd Bhuller et al. (2011) and Nybom and Stuhler (2016b), inom choose to approximate child lifetime income bygd taking the average over three years when 32 to 34 years old.^{Footnote 8} As discussed in Section 2.1, almost none of the betydelsefull studies has analyzed the relation between income trajectories over the life cycle and average lifetime income for women.

One undantag fryst vatten Böhlmark and Lindquist (2006) who funnen that women’s income trajectories follow a different pattern compared to men’s, but that the women’s relationship between annual and approximated average life time income has also changed strongly over time. Unfortunately, the youngest women in their study are born 26 years earlier than the oldest daughters in my sample which strongly reduces the applicability of their findings, given the development of hona labor marknad participation during the missing decades.

Since we do not know if women’s life time earnings are best approximated bygd annual earnings at an earlier or later age compared to dock in my sample, inom use the same age span for daughters as for sons. inom rank children bygd income and child birth cohort, where all children missing more than one income övervakning are dropped from the sample (3.7%).

Table 4 in the Appendix summarizes the sample.

The average age at child birth (26 for mothers and 28 for fathers) has increased slowly but steadily over the observed time horizon. There are roughly between 80,000 and 90,000 children in each cohort and 789,300 children in total, before assigning childhood regions in the next section.

Table 1 shows an income summary. There fryst vatten a klar difference between kvinnlig and male incomes in terms of levels and variances in both generations.

Mothers have on average about 60% of fathers incomes (but only 36% in terms of the highest income). Income inequality as measured bygd the 90th income percentile divided bygd the 10th percentile fryst vatten much larger for mothers than for fathers, but very similar within the child generation.

3.2 Geographic unit

The geographic enhet inom choose to work with fryst vatten the local labor marknad område, or LLM.

An LLM fryst vatten a self-sufficient area in terms of labor within which individuals live and work, and thus spend most of their time. The aggregation of municipalities into LLMs fryst vatten taken from Statistics Sweden which measures commuting flows between municipalities. The aggregation into local labor markets corresponds most closely to the commuting zones which are used bygd Chetty et al.

(2014a) for the USA.

Studying local labor markets fryst vatten a first step towards measuring the effect of immediate conditions (family, neighborhood), the local community (school quality, for example), and the larger metro area which fryst vatten picking up for example labor marknad conditions. Using smaller geographical units such as municipalities there fryst vatten a larger fara of urval bias due to residential segregation, i.e., that families sort themselves into certain residential areas and municipalities.

A local labor marknad area contains several municipalities and probably several different residential areas, with different types of families. There are currently 75 LLMs in Sweden (112 in 1990 due to increasing commuting patterns), containing on average 4 municipalities and a population of 90,000. In contrast, there are 741 commuting zones in the USA containing on average 4 counties and a population of 380,000.

In addition, inom use fem different regional types, based upon the “regional families” classification of local labor markets bygd The Swedish Agency for Economic and Regional Growth.

The fem regional types (T1–T5) are large cities (such as Stockholm), large regional centers (university cities, for example), small regional centers (small cities employing a large share of the population in the surrounding rural areas), sparsely populated regions (less than six people per square kilometer), and other small regions (ranking in between small regional centers and sparsely populated regions).

A complete list of local labor marknad regions and their type classifications can be funnen in Table 5 in the Appendix.

Research bygd Cunha and Heckman (2007), Cunha et al. (2010), and Heckman (2007) indicates that the early environment fryst vatten important in the human capital formation of children. Early investments generate not only human capital directly but also lead to higher returns to later investments.

Other potentially important factors influencing the accumulation of human capital and life time income are the school environment and peers (Lavy et al. 2012), the home and neighborhood environment (Chetty et al. 2016), and probably also the availability of adult role models and guidance when choosing higher education or career paths during teenage years.

I therefore assign children to the local labor marknad område in which they lived for at least six years between the age of 6 and 15 (ignoring moves within a local labor market), in beställning to capture both some influences during earlier as well as some teenage years.

Using the strict assignment rule of a minimum of 6 years in the same område, we can be sure that a child was actually exposed to this location a significant portion of her childhood and that studying regional differences in mobility fryst vatten meaningful.^{Footnote 9}Chetty et al. (2014a) assign children instead to a område based upon their parents residence in 2016.

The sample includes now 778,484 individuals, 1.4% moved too often to determine a childhood region.

In this section, inom summarize the national mobility estimates based on both log incomes and income ranks. A non-parametric description of mobility on the national level (including a transition matrix and quintile mobility over time) can be funnen in Appendix:B Non-parametric description of mobility on the national level (Fig.

13).

The national mobility results for different family member combinations are shown in Table 2. Both the IGE and the rank-rank slope show the weakest dependence between the incomes of mothers and their children. Both the IGE and the rank-rank slope estimates indikera that the relation between son and parent income fryst vatten the least mobile (remember that the larger the IGE or rank-rank slope, the less mobility).

A ten percentile points increase in parent income rank implies on average a 2.36 percentiles increase in the son’s income rank.

The estimated IGE for sons and fathers, 0.252, fryst vatten in line with previous results. Nybom and Stuhler (2016b) got an estimate of 0.27, based on a sample of 3,504 Swedish sons born between 1955 and 1957. Two main differences to their study are that their income measure fryst vatten total pre-tax income which includes capital realizations, and fathers older than 28 years at their son’s birth are excluded from the sample.

The effects of those two differences might however work in opposite directions which could explain the similarity to this study’s result.

Björklund and Jäntti (1997) estimated the IGE to be 0.216 between fathers and sons. Their sample was ganska different from the one used here: no actual father and son pairs were observed but instead two independent samples for both groups were combined.

Their income measure was earnings, a 5-year average for the fathers and one single insamling for the sons.

Österberg (2000) presented results even for daughters and mothers. There are several ways her sample differed from mine. Incomes were observed during three calendar years only where parents are up to 65 years old and thus possibly already retired. Many children in the sample were beneath 33 years when their income fryst vatten measured.

Her estimate for the IGE between sons/daughters and fathers (0.13/0.071, respectively) as well as for sons/daughters and mothers (0.022/0.036, respectively) are substantially smaller in magnitude than my estimates which might be caused bygd attenuation and life cycle bias.

Björklund et al. (2006) studied how pre- and postbirth factors contribute to intergenerational earnings and education transmission bygd analyzing Swedish families with adoptive versus biological children born in the sixties.

They use earnings in 1999 to approximate lifetime average earnings. Their estimate of the IGE between children and their fathers in biological families (no adoptive children) fryst vatten 0.235, which fryst vatten ganska close to the IGE of 0.216 in my data.

The IGE and rank-rank slopes for parents and their children (first row in Table 2) are larger than the estimates for father and mother separately (second and third rows).

For the IGE, the association with the sum of parent income fryst vatten larger than the sum of the associations with mother and father income in all three cases. This suggests a potentially important role of the parent income combination, or parent income matching, for income transmission between generations. Investigating this finding further fryst vatten an interesting direction for future research.

Figure 2a, b shows the development of the rank-rank slopes and IGE for children, sons, daughters, and their parents, respectively, bygd cohort. The error bars show 95% confidence intervals. The rank-rank slope for children and their parents fryst vatten close to 0.2 for all observed cohorts with no significant trend.

The association between sons and their parents’ income ranks has slightly decreased from around 0.26 to 0.22 between 1968 and 1976. The association for daughters starts at 0.19 and increases as to reach the same level as sons at the end of the observed time period.

Note that the separate estimations for sons and daughters involve assigning new ranks compared to the child group: in each uppskattning sample, both the dependent and independent variabel always consist of percentile ranks between 0 and 100.

In particular, if the daughters are located more heavily along the lower ranks within the child transport (due to a lower average income compared to sons), they are still approximately uniformly distributed between 0 and 100 in the pure daughter sample. The beställning among girls and boys, respectively, stays the same, however. The rank-based estimates of the children are therefore not a simple weighted average of the estimates bygd gender.^{Footnote 10}

As shown in Fig. 2b, the association between the log income of parents and sons declines until 1971 and returns then almost to the starting value at 0.34.

The daughter-parent log income association on the other grabb starts as low as 0.22 and increases until it reaches similar levels as the sons in 1976 (0.31). The child-parent log income association fryst vatten a weighted average of the estimates bygd gender and fryst vatten thus relatively constant until the later years which show a small upward trend.

Equation 7 in Section 2.2 can help to explain the different trends in the later half of the observed time period between ranks and log incomes: The rank-rank slope fryst vatten simply the correlation coefficient between the percentile ranks of children and parents, while the IGE fryst vatten the product of (i) the correlation coefficient between log child income and log parent income and (ii) the ratio of their standard deviations.

The uppgifter shows that the increasing IGE from 1971 onward fryst vatten purely driven bygd an increase in the relative variance of the child log income distributions, and not bygd an increase in the linear dependence between child and parent log income.

The multilevel analysis reveals some interesting facts about intergenerational mobility across Sweden.

The first part in this section discusses the multilevel model output. The second part focuses on the two measures relative mobility and absolute mobility at p = 25 on the regional level as described in Section 2.2. In the gods part, inom discuss alternative results obtained bygd using separate OLS regressions bygd region.

5.1 Results from the multilevel model

The results from the multilevel model (1) from Section 2.3 can be summarized bygd plotting the deviations of the predicted slope- and intercept-random effects (the \(\eta _{r}^{\alpha }\) and \(\eta _{r}^{\beta }\)) from the estimated average values (γ^α and γ^β) for each område.

See Table 6 in the Appendix for the detailed uppskattning output. The slopes and intercepts obtained bygd the fixed- and random effects are used in the next section to compute relative- and absolute mobility according to the formulas in Section 2.2.

As shown bygd the black dots in Fig. 3a, the estimated slope-random effects vary at first glance greatly across Sweden.

The regional slopes to the left with uppgifter points below the horizontal line are smaller than the average, and the regional slopes located above the line to the right are larger. However, most estimates are not significantly different from the average: most of the 95% confidence intervals (shown as error bars) include the horizontal line at zero which indicates the average intercept.

Of all 112 regions, only 3 show a significantly flatter slope (weaker association between parent and son income rank), and 7 regions show significantly steeper slopes (stronger association). If we had used separate OLS regression for each område, we would probably have overstated the differences in rank-rank slopes over regions since there fryst vatten no easy way to compare the estimates of many disjoint regressions based on different observations.

As opposed to the slopes, a large fraction of the regional intercepts (shown in Fig. 3b), differ significantly from the average in most local labor markets.

22 regions have smaller than average intercepts, while 33 have larger than average intercepts. Thus, we know already that mobility measures based on absolute outcomes (computed based on both intercept and slope) will show larger differences between regions than purely relative measures (based on the few statistically significant regional slope estimates only).

The average slope estimate across all regions fryst vatten 0.182 with a standard error of 0.002, implying that a ten percentile increase of the parent income rank fryst vatten associated with an increase of 1.82 ranks for the child.

The average intercept fryst vatten 40.3. The correlation coefficient between the regional slopes and regional intercepts fryst vatten −0.64, which means that regions with steeper rank-rank slopes on average have lower intercepts.

The relationship between the multilevel model, separate OLS regressions for each område, and the completely-pooled, national estimates are demonstrated in Fig. 4.

The top panel shows Dorotea, the smallest local labor marknad område (291 observations) located in the north of Sweden. The dotted line shows the mobility estimates from a separate OLS regression: the line fryst vatten almost completely flat and would indikera extremely high levels of relative income mobility. However, the large spread of the underlying binned scatter plot in gray shows the inefficiency of the uppskattning and thus how unreliable this result fryst vatten.

The child-parent income rank association based upon the best linear unbiased predictor (BLUP) from the multilevel model (given bygd the black solid line) deviates from this extreme result and pulls towards the solid gray line above, which shows the average association across all regions. The bottom panel in Fig. 4 displays a similar figure for huvudstaden.

For readability, only the average child rank bygd parent rank fryst vatten displayed (binned scatter plot). The multilevel estimates (BLUPs) coincide here completely with the estimates from a regression run exclusively for children grown up in huvudstaden (the solid black line and the dotted line are indistinguishable from each other). With 132,749 observations, the estimates are not pulled at all towards the pooling-result.

When adding the fem regional types (from large city to sparsely populated regions) to the model with large cities as the reference category, we find that none of the average intercepts for regional types 2 to 5 differs significantly from the base category.

However, the rank-rank slopes differ on average across regional types: the rank-rank slope fryst vatten steepest in type 1 regions (large cities), and flattest in type 4 regions (sparsely populated regions).

5.2 Relative mobility and absolute mobility across regions

Relative mobility and absolute mobility at p = 25 for each distrikt are calculated according to formulas (5) and (6) in Section 2.2.

The slopes and intercepts plugged into these formulas are computed according to Eqs. 9 and 10. More specifically, inom compute the regional slopes as the sum of the slope fixed effect (regional average slope γ^β) and the distrikt specific random slopes (\(\eta _{r}^{\beta }\)), where the område specific random slopes are set to zero whenever they are not statistically significantly different from zero.

Looking at relative mobility only, the huvudstaden område has both the most right-skewed income transport (the mittvärdet i en uppsättning data income level fryst vatten just 92.65% of the mean income level) and the lowest levels of relative mobility among all Swedish LLMs.

Similarly, the total regional intercepts are the sum of intercept fixed effect (γ^α) and the område specific intercepts (\(\eta _{r}^{\alpha }\)), where the område specific intercepts are set to zero whenever they are not statistically different from zero. The results obtained this way can be interpreted as a lower bound of the existing regional differences in mobility.

The complete list of results bygd local labor marknad can be funnen in Table 7 in the Appendix.

Relative mobility fryst vatten 18.16 in most regions. Relative mobility fryst vatten higher only in the three regions Varberg, Växjö, and Skövde.^{Footnote 11} The average outcome difference between children from top and bottom income families in Varberg fryst vatten just 15.58 percentile ranks.

sju regions show less than average relative mobility, with huvudstaden ranking lowest. Here, the inequality of outcomes fryst vatten largest with a maximal outcome difference between children of 22.21 percentile ranks.

Absolute mobility at p = 25 varies from 40.90 in Årjäng to 48.61 in Värnamo,^{Footnote 12} with an average of 43.69 across all regions (standard deviation 1.63).

Calculating the percentiles back to income levels, we find that the expected difference in outcome between growing up in Årjäng or Värnamo for children with parents located at the 25th percentile amounts to nearly 20,000 SEK less income per year (≈2,210 USD). This corresponds to 90 percent of the average monthly salary of a worker in Sweden in 2010 (Swedish Trade Union Confederation 2011).

Figure 5 shows relative mobility and absolute mobility at p = 25 for all regions.

The crossed lines through the center of the plot indikera the average levels of relative and absolute mobility, respectively. The arrow-tips indikera the direction in which mobility fryst vatten increasing (note that high values of relative mobility indikera less mobility, since steeper slopes imply stronger associations between parent and child income).

The quadrant marked with a large plus (minus) sign indicates regions with both above (below) average relative and absolute mobility. The information point right in the center represents not one but 57 regions which all have average levels of both mobility measures.

All regions with extremely high or low levels of upward mobility (the information points on the very left and the very right) show just average levels of relative mobility.

Thus, even though the relative difference between sons from the highest and lowest income families in, for example, Torsby and Hylte, fryst vatten the same, children from families with the same income rank in those regions will end up with very different levels of income as adults. Using the IGE or the rank-rank slope as the only measure for mobility, this difference would go completely unnoticed.

The estimates from this study can be compared to the results from Chetty et al.

(2014a