Alexander Silbersdorff is a research associate at the Department of Statistics, University of Göttingen, Germany, where he predominantly works on the development and application of regression techniques to economic contexts. Previously, he served at the Department of Economic History at the University of Bielefeld, Germany, where he investigated the development of historical income structures.

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Inequality and Earnings Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 A Brief Glance at the History of Income Inequality Analysis . . . . . . 7

2.2 Preliminaries on the Income Distribution and Inequality Measures . 9

2.2.1 Income variables, units and data . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Distributional measures and informational complexity . . . . . 13

2.3 The Development of German Earnings Distributions, 1988-2013 . . . 17

References . . . . . . . . . . . . . . . . . . . . . . .

3 Estimating and Assessing Distributional Regression . . . . . . . . . . . . . . . . 25

3.1 On Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 The linear model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Structured Additive Distributional Regression . . . . . . . . . . . . . . . . . . . 32

3.2.1 Structured additive regression . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2.2 Parametric distributions and SADR . . . . . . . . . . . . . . . . . . . . . 34

3.2.3 Differentiating with respect to covariates . . . . . . . . . . . . . . . . 38

3.3 Other Methods for Estimating Conditional Distributions . . . . . . . . . . 40

3.3.1 A

3.3.2 A contrast with distribution regression and conditional

transformation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.4 A Note on Panel Data and Individual-Specific Effects . . . . . . . . . . . . 45

3.5 A Note on State Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 The Distributional Perspective and Labour Markets . . . . . . . . . . . . . . . 59

4.1 The Market Equilibrium Price and Mean Regression . . . . . . . . . . . . . 59

4.2 Market Places and Market Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.1 On the ideal-typical modern labour market model . . . . . . . . . 61

4.2.2 Five problems of t

4.2.3 Conceptualising a labour market space . . . . . . . . . . . . . . . . . . 64

4.3 Towards a distributional perspective of labour markets . . . . . . . . . . . . 72

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5 Applications of SADR in Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.1 First Steps in Analysing Conditional Earnings Distributions . . . . . . . 77

5.2 Taking a Bayesian Perspective and Proposing SADR . . . . . . . . . . . . . 82

5.3 Gender, Earnings and SADR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.4 Health Effect Assessment based on SADR . . . . . . . . . . . . . . . . . . . . . 92

5.5 Unemployment, Inequality and SADR . . . . . . . . . . . . . . . . . . . . . . . . . 95

References . . . . . . .

6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.1 The Distributional Perspective and SADR . . . . . . . . . . . . . . . . . . . . . . 103

6.2 Possible Directions for Future Research . . . . . . . . . . . . . . . . . . . . . . . . 105

6.3 Some last words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

This book seeks new perspectives on the growing inequalities that our societies face, putting forward Structured Additive Distributional Regression as a means of statistical analysis that circumvents the common problem of analytical reduction to simple point estimators. This new approach allows the observed discrepancy between the individuals' realities and the abstract representation of those realities to be explicitly taken into consideration using the arithmetic mean alone. In turn, the method is applied to the question of economic inequality in Germany.