Reference Income Effects in the Determination of Equivalence Scales Using Income Satisfaction Data Melanie Baroh Andreas Knabe Carina Kuhställer

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1 David Johnson Universy of Michigan Reference Income Effects in the Determination of Equivalence Scales Using Income Satisfaction Data Melanie Baroh Andreas Knabe Carina Kuhställer

2 What are Equivalence Scales? They represent the cost ratio required to equate the wellbeing or utily for households wh different sizes and composions. S Key is U 0 = max U(x,A,K) subject to px T That is, U 0 solves T = E(p,U 0,A, K). This will only hold for U 0 and is not a general equivalence scale. And scale could be different for different levels of U 0. E p, Uo; A, K p, U ; A, K E p, U ; A, K o, o R R S A K

3 Equivalence Scales impact both inequaly and poverty Scale elasticy creates U-shape relationship Gini Poverty 3

4 Types of equivalence scales (Deaton 1999) The analysis of behavior -- using the consumption patterns of families to estimate the scale economies. Arbrary but transparent formulas -- using the two-parameter scale. Asking people -- using subjective responses related by family size.

5 Parametric equivalence scales Linear scales aa + ck (OECE a=.5; c=.3) One-parameter scale (M) e = (M) 0.5 M = household size Two-parameter scale (A+dK) e = (A+0.7K) 0.7 A = # of adults, K = # of children Modified elasticy (Schwarze) (A+K) e a-bk = (A+K) K A = # of adults, K = # of children

6 Scale relative to single Equivalence Scales Equivalence Scales and Economies of Scale Per-capa Two-parameter Household Ea k*ec elasticy OECD Square root 0

7 Subjective Equivalence Scales

8 Other Scale Estimates using Income Satisfaction method Estimation using income satisfaction data Lerature review 2 nd Adult 1 st Child 2 nd Child Expert Scale OECD Equivalence Scales using Income Satisfaction Data (SOEP) Schwarze (2003) Schwarze (2003) FE Biewen & Juhasz (2014) OECD-type Van Praag & Ferrer-i-Carbonell (2004) Deutschland Bollinger (2102), BHPS

9 Why do we care about scales Motivation Adults receive higher weights than children. Weights for children are very low. Income satisfaction may be influenced by a variety of factors Satisfaction of genuine needs Income comparisons (Clark et al. 2008) interpersonal or intertemporal Equivalence Scales intend to capture differences in needs

10 Subjective Equivalence Scale Methods Basic Approach: Regressing income satisfaction on household income and family size/structure to calculate income compensation needed to hold satisfaction constant Schwarze (2003, RoIW) Model specification including children: S Y ln X 0 1 lny 1aln h 1bk ln h X e 2 h lny eln h X e e/ 1 1 Y S 0 1 ln X abk 2 h 1a 1b a,b 1 1

11 Some examples of relative income The role of relative income: An intuive illustration Example 1: A partner joins the household of a previously single adult Suppose the income required to satisfy addional consumption needs increases by 60 % The reference income is now twice as large Income satisfaction will be kept constant only if household income increases by something between 60% and 100% Example 2: A couple has a child Suppose the income required to satisfy addional consumption needs increases by 60 % again The reference income increases by only 10% An income compensation of something between 10% and 60% will be estimated Equivalence weight estimates will be biased, depending on whether an individual s contribution to the household s needs is above or below the contribution s reference income

12 The impact of relative income The role of relative income: A formal illustration Assuming that income satisfaction depends addively on the household s equivalence and relative income: Y Y S 1 ln 2 ln r HHeq Y needs satisfaction status satisfaction Illustration using the linear model (Schwarze (2003)) Y Y S ln ln h ah 1 e 2 e ln a 1 2 lny 1e1 2e2 ln h const. e e e e

13 The role of relative income: A formal illustration Illustration using the linear model accounting for children (Schwarze (2003)) Y Y S ln ln 1 a b k 2 a b k h ah ln a lny a a ln h b b k ln h const. The impact of relative income a b a a a ; b b b for a 1 < a 2 : Overestimation of addional adults needs for b 1 > b 2 : Underestimation of children s needs

14 SOEP, Data Data Dependent variable: Satisfaction wh household income (on a scale from 0 to 10) net monthly household income, adjusted for intertemporal and regional price level differences The first and last percentile of household in each year s income distribution have been dropped Every person below the age of 18 is considered a child Only one- and two-adult households wh or whout minor children have been included in our sample The second adult has to be the head of household s partner. Households wh adults children are thus ignored.

15 Satisfaction and Income in the Data Descriptive Statistics Average Satisfaction wh Household Income and Average Household Income by Household Type 7, , , , ,00 2, , ,00 1 adult no children (30.7%) 1 adult 1 child (2.3%) 1 adult 2 children (1.1%) 1 adult 3 children (0.3%) 2 adults no chiildren (38.3%) 2 adults 1 child (11.5%) 2 adults 2 children (11.8%) 2 adults 3 children (3.1%) 0 satisfaction wh household income real net monthly household income N = 305,976

16 Estimation Model Estimated Models Linear model including reference income effects Y Y S 1 ln a bk 2 ln r h Y Estimation using Ordered Log Nonlinear model including reference income effects Y Y S 1 ln 2ln r 1 a ( adults 1) c ( children ) Y Estimation using Nonlinear Least Squares

17 How to construct Reference Incomes Reference Income Construction Two approaches to constructing an individual s reference income: Average income of people /households wh the same characteristics (e.g. Ferrer-i-Carbonell 2005, JPubE) Number of adults, age group, education, east/west, wh/whout children, year Estimation via an earnings regression (e.g. Senik 2008, Economica) Linear regression wh the following explanatory variables: number of adults and children, age, education, east/west, labor market status, gender, year Extension: Taking the partner s characteristics into account

18 Dependent Variable: ln Household Income (β 1 ) ln Household Members (β 1 a) Children * ln Household Members (β 1 b) Results: Linear Model No Reference Effect 2.016*** (0.020) *** (0.030) *** (0.009) ln Relative Income - Satisfaction wh Household Income Cell averages 1.548*** (0.072) *** (0.073) (0.017) 0.640*** (0.069) Individual Mincer 1.708*** (0.027) *** (0.035) (0.010) 0.504*** (0.028) Household Mincer 1.678*** (0.030) *** (0.034) (0.010) 0.599*** (0.036) N 316, , , ,472 Pseudo R e = a bk Results Linear model k k k k Wh addional control variables, e = k

19 Results Results: non-linear Nonlinear Model model Dependent Variable: Scale Parameter Adult Scale Parameter Child ln Equivalent Income No Reference Effect 0.352*** (0.015) 0.234*** (0.009) 2.268*** (0.021) ln Relative Income - Satisfaction wh Household Income Cell averages 0.214*** (0.051) 0.295*** (0.027) 1.570*** (0.095) 0.908*** (0.092) Individual Mincer 0.240*** (0.018) 0.262*** (0.011) 1.835*** (0.030) 0.654*** (0.032) Household Mincer 0.263*** (0.019) 0.277*** (0.012) 1.798*** (0.034) 0.774*** (0.041) N 316, , , ,472 adj. R * p < 0.10, ** p < 0.05, *** p < 0.01 Standard errors in parentheses, clustered by households. Standard errors in column 2 clustered by reference groups. Column 3 and 4 report bootstrapped standard errors based on 1000 replications.

20 Summary Summary One approach to estimate equivalence scales is to use income satisfaction data Results in the related lerature so far: Weights assigned to addional household members are generally low Children are assigned much lower weights than adults Possible explanation: reference income effects When reference income effects are taken into account, the estimated needs of adults and children converge However: overall weights remain que low Examining by age of child older children have larger scale

21 Comments Summary As in previous lerature, scales are low how can we reconcile? Demonstrate why these differences matter to poverty or inequaly Can you include all families wh more than two adults Intra-household distribution who responds to the lifesatisfaction questions and are there differences between mothers and fathers? Estimate consumption-based scales using GSOEP and compare to satisfaction-based (needs and life satisfaction) Estimate life-cycle scales scales change depending on the place in life-cycle Do scales, economics of scale, change over time

22 Results Robustness Robustness Tests Results reported for the nonlinear model using two-stage regression using household Mincer earnings Specification weight assigned to addional adults weight assigned to children observations Prob-adjusted (0.019) (0.013) 296,472 Including mean relative income (0.019) (0.012) 296,472 Excluding households making payments to children outside the household (0.019) (0.012) 267,581 Asymmetric reference effects (0.019) (0.012) 296,472 Age-dependent weights for children (0.019) (0.016) (0.014) (0.019) 296,472 Standard errors in column 3 clustered by reference groups. Bootstrapped standard errors based on 1000 replications in parentheses, clustered by households.

23 Equivalence Scales reflect the differences in expendures of households of different sizes and composion, when all these households attain the same level of utily or standard of living (Lewbel and Pendakur, 2008) Applied to make household income comparable whenever welfare is of greater importance than absolute level of income Income inequaly and poverty analysis Design of redistributive policies E.g. German social secury system provides children wh benefs of 60% (under 15) and 80% (above and including 15) of a single s benefs Different approaches to determine equivalence scales: Expert scales Estimation using objective data Estimation using subjective data