Upper bounds of inequality of opportunity: theory and evidence for Germany and the US

See e.g. Roemer et al. (2003), Dardanoni et al. (2005), Betts and Roemer (2006), Lefranc et al. (2008, 2009), Devooght (2008), Checchi et al. (2010), Checchi and Peragine (2010), Dunnzlaff et al. (2011), Aaberge et al. (2011), Alms et al. (2011) as well as Björklund et al. (2012a).

See, e.g., Katz and Autor (1999) for an overview as well as Autor et al. (2008) and Dustmann et al. (2009) for recent applications to the US and Germany.

An exception is Bourguignon et al. (2007) who simulate the magnitude of omitted variable bias to estimate bounds around the true effect of observed circumstances on income inequality.

There are a number of studies investigating social and economic mobility (see, e.g., Corak and Heisz 1999, Björklund and Jäntti 1997, 2009, Kerm 2004 or Björklund et al. 2012b). However, social or economic mobility is only a partial view on IOp, with only parental education or income level as circumstance variable. In addition, only few measures of social mobility can be directly related to IOp—see Van de gaer et al. (2001). On this, see also the evidence and discussion in Brunori et al. (2013).

According to Alesina and Glaeser (2004), Americans believe that social mobility is important and high in the US, whereas Europeans perceive lower chances to climb the social ladder. Hence, Germans are more in favor of redistribution than Americans (Alesina and Angeletos 2005).

We further discuss—and relax—this assumption in Sect. 5.3. See also Lefranc et al. (2009) for the extension of the EOp framework to explicitly take into account luck.

In contrast, non-parametric methods avoid the arbitrary choice of a functional form on the relationship between outcome, circumstances and effort (e.g. Lefranc et al. 2009, Ferreira and Gignoux 2011 or Aaberge et al. 2011). However, this approach has the drawback that considering more than one circumstance variable is difficult due to practical reasons in the presence of small cell sizes which is usually the case in survey data. Access to large-scale administrative panel data with information on circumstances (family background), which is not available in Germany and rather restrictive in the US, would allow to estimate lower and upper bounds of IOp also non-parametrically.

However, note that when looking at yearly regression of income on observed circumstances, individual coefficients may change but the explained variation does not change (much). In addition, we can usually not reject the null that the respective coefficients are statistically equal at the 5 %-level for any pair of years. These results suggest that neither the effect of (observed) circumstances on the outcome nor the unexplained variation varies a lot over time.

We do this, because the variance of logarithms—in contrast to the MLD and other GE-measures—is not a good measure of inequality because it violates the Pigou–Dalton transfer principle as well as the Lorenz criterion (Foster and Ok 1999).

In principle, it would be possible to provide two lower bounds with and without accounting for the indirect effects—as, e.g., done in Bourguignon et al. (2007).

Note that the estimation of the unit-effect relies on the consistent estimation of coefficients in the FE model. Omitting any effort variables that interact with circumstances biases our results upwards, emphasizing that we should interpret our results as upper bounds of IOp.

A detailed overview of the SOEP is provided by Haisken-DeNew and Frick (2003) and Wagner et al. (2007). Issues concerning sampling and weighting methods or the imputation of information in case of item or unit non-response is well documented by the SOEP Service Group.

Note that the income reference period in both surveys is the year before the interview. Hence, we actually cover the period 1983 until 2008 for Germany and 1981 until 2006 for the US.

Due to the log-linear specification it is not possible to include zero earnings. We decided to only include the longest spell (and not all employment spells) for each individual to focus on EOp in earnings and not to account for selection into and out of employment. It would be possible, and potentially interesting, to apply a two-stage approach by also investigating EOp in labor market participation. We leave this for further research.

This is a rather arbitrary restriction. However, as our robustness checks show the number of time points does not qualitatively change the results. On average, we use 6.9 (7.2) years for Germany (the US).

An even better proxy might be household equivalent disposable income. However, accounting for the household context raises other issues—which have not been addressed in the EOp literature—such as whether an individual is responsible for the choices of her spouse or not. In addition, using net earnings is equivalent to household income for singles and for couples in a collective household model with a sharing rule corresponding to the earnings ratio of the two spouses.

In principle, it would be possible to compute more sophisticated measures of permanent income as, e.g., recently proposed by Aaberge et al. (2011). Comparing the results based on annual and permanent incomes is related to the literature looking at the transitory components to earnings variability (see, e.g., Moffitt and Gottschalk 2012). Looking at permanent incomes is interesting itself because of the possibility for individuals to smooth income shocks over time. In addition, it has the advantage that measurement error [e.g. around 20 % of the total variance according to validation studies of the PSID such as Rodgers et al. (1993)] gets averaged away.

The ‘non-effect’ of race for periodical incomes might be explained with the fact that blacks are more likely to be out of the labor force or even in prison, which leads to underestimated racial wage gaps in cross-sectional data (Chandra 2000).

For brevity, we do not report ‘first-stage’ results for approach (2), i.e. Eqs. (7)–(9), which are qualitatively similar to approach (1) and available upon request.

It should be noted that the upper bounds of IOp decrease if we, e.g., add marital status or number of children, which can be expected to have an indirect impact on annual earnings, in the FE regressions. This provides additional evidence that our results can be interpreted as upper bounds.

This approach is related to approaches estimating what share of inequality can be explained by observable effort variables (see, e.g., Pistolesi 2009). Usually, when measuring the contribution of observable effort, effort is purged from its correlation with observable circumstances. In our approach, effort is purged from both observable circumstances and the individual fixed-effect. Since some (time-invariant) effort possibly belongs to the fixed-effect, inequality due to effort (circumstances) is under(over)-estimated resulting in an upper bound for IOp.

Alms (2008) argues that the ex-post approach treats the unexplained variation as a circumstance which would result in an upper bound. This, however, is only true for a given set of (observed) circumstances. The fact that the ex-post approach gives lower bounds only is also discussed by Aaberge and Colombino (2012). They recognize that for the (ex-post) EOp approach “[...] there might be other exogenous factors that affect individuals’ achievements” which are not captured by the observed circumstances. Hence, the within-type distribution of income might still depend on unobserved circumstances. Their solution (partially) accounts for the within-type inequality and yields an intermediate case with an IOp measure between the lower and the upper bound. Defining the upper bound as in our case (observed vs. unobserved circumstances), gives lower and upper bounds both for the ex-ante and ex-post approaches.

In our application, we have more than 500 types for the lower bound approach. In order to apply the ex-post approach based on percentiles of the earnings distribution, we would need at least 100 observations per cell, i.e. in total more than 50,000 observations per year. Unfortunately, we do not have access to such a large panel data set.

Contrary to Germany, the majority of respondents in the US thinks that larger income differences are necessary as incentives, while 40 % of the respondents think that the most important reason why people live in need is laziness—the numbers are only half as high in Germany.