On the Magnitude of Income Mobility in Germany

Van Kerm, Philippe Article On the Magnitude of Income Mobility in Germany Schmollers Jahrbuch – Zeitschrift für Wirtschaftsund Sozialwissenschaften. Journal of Applied Social Science Studies Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Van Kerm, Philippe (2003) : On the Magnitude of Income Mobility in Germany, Schmollers Jahrbuch – Zeitschrift für Wirtschaftsund Sozialwissenschaften. Journal of Applied Social Science Studies, ISSN 1865-5742, Duncker & Humblot, Berlin, Vol. 123, Iss. 1, pp. 15-25, https://doi.org/10.3790/schm.123.1.15 This Version is available at: https://hdl.handle.net/10419/292035 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ On the Magnitude of Income Mobility in Germany* By Philippe Van Kerm Abstract This paper documents the magnitude of income mobility in Germany and its distribution across different income positions, using data from the German Socio-Economic Panel. The suggested graphical approach makes it straightforward to identify the portions of the distribution that have the largest impact on aggregate ‘income movement’ indices a `la Fields & Ok, and hence offers a starting point to help account for income mobility levels. It appears that most of the contribution to mobility is made by the poorest 10% of the initial distribution. Average relative income changes are much lower and generally constant for the rest of the population. JEL Classification: C 14; D 31; I 32 1. Introduction The measurement of income mobility, when one is concerned with the movements of individuals within the income distribution over time forms a body of vivid theoretical and empirical literature. Awide array of indices have been proposed to capture the extent of mobility in a given society, and empirical analyses commonly use a variety of such mobility indices to help intertemporal or cross-country comparisons. 1 This analysis is an attempt to document in greater detail the magnitude of income mobility in Germany between 1984 and 2000 and its distribution across different income positions, using an intuitive graphical approach. The suggested graphical approach makes it straightSchmollers Jahrbuch 123 (2003) 1 Schmollers Jahrbuch 123 (2003), 15–26 Duncker & Humblot, Berlin * Paper presented at the 5 th German Socio-Economic Panel conference, Berlin, July 3–4 2002. Comments by Jennifer Hunt are gratefully acknowledged. This paper is part of a research project supported by the European Commission under the Transnational Access to major Research Infrastructures programme (Contract No. HPRI-CT-2001– 00128) hosted by IRISS at CEPS/INSTEAD Differdange (Luxembourg). 1See Maasoumi (1998), Fields/Ok (1999a) and Fields (2000) for a comprehensive survey of existing approaches. Recent examples of applied analysis can be found in Burkhauser/Poupore (1997), Schluter (1998), Canto-Sanchez (2000) or Maasoumi/ Trede (2001) among others. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 16 Philippe Van Kerm forward to identify the portions of the distribution that have the largest impact on aggregate ‘income movement’ indices a `la Fields & Ok (Fields/Ok 1996, Fields/Ok 1999b), and hence offers a starting point to help account for income mobility levels. 2. Methodology The paper concentrates on income movement indices a `la Fields & Ok. These mobility measures are population averages of ‘distance’ statistics capturing the degree of income change experienced by individuals over a given time interval. Common ‘distance’ functions are the income difference (Fields/Ok 1996), and the log-income difference (Fields/Ok 1999b), either taken in absolute value or not. I focus here on log-income difference, and hence look at relative income changes: two individuals experience equal amounts of mobility if their percentage income changes over time are the same. 2 The mobility index of interest is therefore M  X ; Y  ZZ d  x ; y  f  x ; y  dxdy  1  where Xand Yare two random variables representing the distribution of income in an initial and a final time period, and fis their joint probability density function. d(x,y) is the distance function, i.e. either (log (y) – log (x)) for an assessment of expected income increases (losses offset gains), or |log (y) log – (x)| for an assessment of the overall variability of incomes (losses add to gains). The cornerstone of this paper is estimating separate mobility levels for different points in the initial income distribution, and expressing the mobility index as a functional of a conditional mobility function as follows: M  X ; Y  ZZ d  x ; y  fY j x  y  dy  fX  x  dx  2   Z m  X ; Y j X  x  dFX  x  3  where fXis the marginal probability distribution function of X, FXis the cumulative distribution, and f Y|X is the probability distribution function of Yconditional on X  x.m  X ; Y j X  x  is the resulting conditional mobility function that can be plotted to obtain an evocative picture of the distribution of mobility levels across different parts of the distribution. 3 Schmollers Jahrbuch 123 (2003) 1 2At least for small percentage change when log-difference approximates percentage change closely. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 On the Magnitude of Income Mobility in Germany 17 I use the locally weighted regression (LOESS) technique introduced by Cleveland (1979) to estimate m  X ; Y j X  x  without imposing any parametric restriction. This method is easily implemented, solves the boundary effect problem of kernel regression and permits a ‘robust’ estimation that guards against deviant points affecting estimation of m  X ; Y j X  x  . 4 Indirect estimation of M  X ; Y  by integration of the robust estimate of m  X ; Y j X  x  makes it robust to outlying observations, in contrast to standard direct estimation based on unit record data. 5 Similarly to M  X ; Y  , the conditional mobility function is decomposable by population subgroups. If A  A1 ; ... ; AK  is a partition of the population into Kmutually exclusive states, and P  Ak j X  x  denotes the probability that an individual belongs to state k(conditionally on X=x), then m  X ; Y j X  x  X K k  1 P  Ak j X  x  m  X ; Y j X  x ; Ak  4  where m  X ; Y j X  x ; Ak  is the conditional mobility function estimated for individuals of state k. This property allows an assessment of the impact of exogenous attributes on the level of mobility, and helps identify differential roles of individual characteristics at different points of the income distribution. Defining population subgroups by using the experience (or absence of experience) of a set of mutually exclusive events also permits closer investigation of the effects on income mobility of potential ‘triggering events’, as has been done in the analysis of poverty transitions. 3. Data Income mobility assessment requires repeated income observations over time for a sample of individuals. Such data are available for Germany in the Cross-National Equivalent File (CNEF), which contains constructed annual income variables directly derived from the German Socio-Economic Panel (GSOEP) survey data. 6 These data allow me to study patterns of income mobiSchmollers Jahrbuch 123 (2003) 1 3This methodology is closely related to the procedures presented in Schluter /Trede (1999) and Schluter/Van de Gaer (2002). The same objective is indeed shared, but the approach is applied here in the different and greatly simplified context of ‘distancebased’ mobility measures. 4See Cleveland (1979) or Hastie/Loader (1993). 5See Cowell/Schluter (1998) on estimation of income mobility measures with dirty data. 6See Wagner et al. (1993) for a presentation of the English-Language Public Users German Socio-Economic Panel, and Burkhauser et al. (2001) for more information on the Cross-National Equivalent File. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 18 Philippe Van Kerm lity over the period 1984–2000. Focus is put on disposable income as a proxy for an individual’s living standard. The measure of income adopted is therefore real annual post-government household income converted to a ‘single adult equivalent’ using the ‘modified OECD’ scale. 7 Household income is the pooled income of all family members, including labour earnings, asset flows, private transfers, and public transfers minus total household taxes. The latter are not directly available, but simulated and provided with the data (Schwarze 1995). Most of the results pertain to pooled data for West Germany 1984– 1992, West Germany 1992–2000, and East Germany 1992–2000. 4. Income mobility in Germany, 1984–2000 Expected annual income increases – measured by M  X ; Y  with the change in log-income as underlying distance function (the ‘directional’ index) – have been near 4% in all three samples: 0.037 for West Germany 1984–1992, 0.030 for West Germany 1992–2000 and 0.038 for East Germany 1992– 2000. (These estimates were obtained by numerical integration of the robust LOESS estimates of the conditional mobility function.) However, gains have offset losses, and these figures conceal much income mobility. The expected annual income changes – measured by the absolute change in log-income (the ‘non-directional’ index) – have been near 20%: 0.187 for West Germany 1984–1992, 0.195 for West Germany 1992–2000, and 0.173 for East Germany 1992–2000. Surprisingly, the samples with the lowest expected income increases have the highest expected income changes and vice versa. Time series of mobility indices for 1984–2000 are not reported, but are available from the author. No clear trends emerge, except an overall reduction of income variability in East Germany since 1992. It is interesting to note that the ‘directional’ and ‘non-directional’ indices measure empirically distinct phenomena, since the correlation between these indices across the different regions and time periods is only 0.13. The underlying conditional mobility functions are plotted in Figure 1. The curves for the three separate subsamples are very similar and can be distinguished only at the tails. One clear pattern emerges from both pictures. The highest contribution to aggregate mobility is made by the poorest individuals. Expected income change reaches 80% or more for approximately the poorest 5%. The decline is steep, however, and at about the first decile point the curves stabilise and remain flat until the upper decile of the initial distribution. Between 32% (in East Germany) and 38% (in West Germany 1992–2000) of total expected income change are contributed by the poorest 10%. Schmollers Jahrbuch 123 (2003) 1 7Total household income is divided by an adjusted household size where the first adult counts for one person, other adults count for 0.5 and children count for 0.3 (see e.g. Eurostat Task Force 1998). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 On the Magnitude of Income Mobility in Germany 19 Figure1: Conditional mobility functions for d  x ; y j log  y ÿ log  x j (top) and d  x ; y  log  y ÿ log  x  (bottom). Pooled data for year tto year t  1 changes. Schmollers Jahrbuch 123 (2003) 1 West. Germany 1984-1992 East. Germany 1992-2000 West. Germany 1992-2000 West. Germany 1984-1992 W East. Germany 1992-2000 est. Germany 1992-2000 West. Germany 1984-1992 East. Germany 1992-2000 West. Germany 1992-2000 Initial percentile Initial p ercentile Expected income change Expected income increase OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 20 Philippe Van Kerm Comparing the pictures for the two different distance concepts helps describe the patterns of income mobility in greater detail. For example, according to the plot for the non-directional distance concept, the majority of individuals (those between the 20 th and 80 th percentiles) experience on average absolute income changes of about 15%. But it appears from the plot for the directional distance that their expected net gain is close to zero: the absolute changes are a mixture of income gains compensated by income losses of the same average magnitude. It is at the tails of the distribution that the expected net gains depart from zero, reflecting the phenomenon of regression to the mean, with the richest 10% expecting income losses and the poorest 20% expecting (substantial) income increases. I also consider longer term mobility patterns using a time interval of five years and using three-year moving average incomes to smooth out transitory income fluctuations. With these definitions, expected income increases were about 7% for West Germany 1984–2000 and East Germany 1992–2000, but were nil for West Germany 1992–2000. Overall income changes remain at about 0.20, so that smoothing out transitory income fluctuations offsets the increase in mobility expected from the increase in time interval to five years. The underlying conditional mobility functions are reported in Figure 2. Note that the axis scales are the same as in Figure 1 to allow direct comparison of the two pictures. The shape of the conditional mobility functions remains the same. 8 However, the peak at the bottom of the distribution is greatly reduced. The expected income increases have been higher in East Germany than in West Germany in the 1992–2000 period for almost all percentiles of the distribution (compare the two dashed curves in the bottom panel of Figure 2). As a final illustration, I now present a rudimentary inspection of the effect of a potential mobility-triggering event: the change in the labour market participation of the household head. 9 Individuals are classified into three groups according to the change in the declared labour market participation of the household head between two consecutive interviews: (i) individuals with no change in the labour market participation of the household head, (ii) individuals living in a household whose head increased participation (i.e. either moved from inactive to working or moved from part-time to full-time work), and (iii) individuals living in a household whose head reduced participation (i.e. either moved from working to inactive or moved from full-time to partSchmollers Jahrbuch 123 (2003) 1 8The constancy of the ‘flat base U shape’ of the conditional mobility functions is also observable across different countries in the 1990s, although aggregate levels of mobility may differ substantially between countries. International comparisons based on a beta release of the Consortium of Household Panels for European Socio-economic Research (CHER) data are available from the author. 9The person identified as household head in the GSOEP is “the person who knows best about the general conditions under which the household acts” (Haisken-De New/ Frick 2001). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 On the Magnitude of Income Mobility in Germany 21 Figure 2: Conditional mobility functions for d  x ; y j log  y ÿ log  x j (top) and d  x ; y  log  y ÿ log  x  (bottom). Pooled data for year tto year t  5 changes using three-year moving average incomes. Schmollers Jahrbuch 123 (2003) 1 0.1 .2 .3 .4 .5 .6 .7 .8 .9 1 0 .2 .4 .6 .8 1 1.2 1.4 1.6 1.8 West. Germany 1984-1992 W East. Germany 1992-2000 est. Germany 1992-2000 West. Germany 1984-1992 W East. Germany 1992-2000 est. Germany 1992-2000 Initial per centile Initial per centile Expected income change Expected income incr ease OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12 22 Philippe Van Kerm Figure 3: Subgroup conditional mobility functions according to labour market participation, for d  x ; y j log  y ÿ log  x j (top) and d  x ; y  log  y ÿ log  x  (bottom). Pooled data for Germany 1984–2000. Schmollers Jahrbuch 123 (2003) 1 0.1 .2 .3 .4 .5 .6 .7 .8 .9 1 0 .4 .8 1.2 1.6 2 2.4 No change Reduced participation Increased participation No change Reduced participation Increased participation Initial percentile Expected income change Initial percentile Expected income increase OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.123.1.15 | Generated on 2023-04-04 12:31:12