Cross-country income mobility comparisons under panel attrition: the relevance of weighting schemes



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CROSS-COUNTRY INCOME MOBILITY COMPARISONS UNDER PANEL ATTRITION: THE RELEVANCE OF WEIGHTING SCHEMES Luis Ayala (IEF, URJC) Carolina Navarro (UNED) Mercedes Sastre (IEF, UCM)

  • EPUNet 2006

  • Barcelona 8-9 May 2006


Motivation

  • Longitudinal Data: ECHP

    • Very detailed information
    • Income distribution studies: Static Analysis  Dynamic Analysis
      • Income mobility, poverty dynamics, transitions between economic states (deprivation, unemployment…)
  • Limits:  “sample attrition”

    • Is there attrition in the ECHP?
    • How much?
    • Is it selective?
    • Does if have effects on (dynamic) estimates?
    • How can it be corrected?


Objective

  • Analyse the effect of sample attrition in the ECHP on different measures of income mobility

  • Study the consequences of different weighting schemes used to correct the potential bias introduced by attrition

    • Extension and distribution of sample attrition
    • Estimation of different longitudinal weights based on the inverse selection probability (probit models)
    • International Comparison
      • France, Germany, Italy, Spain, United Kingdom
      • Differential impact of sample attrition and weighting schemes on income mobility
      • Degree in which sample attrition can condition the results of the comparative analysis


Attrition in the ECHP (I)

  • Sample attrition: lost of a percentage of the initial sample as new waves of the survey develop

  • Several studies: Peracchi (2002), Behr et al.(2002), etc.

  • Extension and trends of attrition in the ECHP

    •  Substantial rates over a few years
    •  important differences among countries
  • May prevent to follow up a significant part of the sample and influence the distributive results (if attrition implies a lost of representativeness)



Attrition in the ECHP (II)



Attrition in the ECHP (III)

  • Substantial attrition rates in the ECHP:

    • Attrition: no necessarily affects estimates, only if has a selective character
      • If low income households more exit probability  previsible effect of inequality reduction
      • The estimations of longitudinal processes may be biased


Attrition in the ECHP (IV)

  • Incidence of attrition by socioeconomic categories: % remaining in the ECHP (balanced panel)

    • In general similarities in attrition patterns among countries / some divergences
    • Relevant Variables:
      • Income, household main income source, age, household type, education level and housing tenure
      • Divergences “latin model” vs. Rest of countries


Weighting Schemes (I)

  • Attrition  Not totally ramdom  potential bias

  • Estimation of longitudinal weights for each observation

  • Intuition

    • Probabilistic assesment of how many attriters a particular observation represents
    • Indiv. with greater exit probability  greater weight
  • Estimation

    • Based on the inverse selection probability obtained from different probit models using socieconomic characteristics of individuals and households (Fitzgerald et al., 1998, Gradín et al. 2004)
    • Probit
      • Prob. individual not in the sample in wave 8  Pri (Y=0)
      • Prob. individual remains in the sample in wave 8  Pri (Y=1)
      • For each observation: longitudinal weight  function of the inverse selection probability of remaining in the sample


Weighting Schemes (II)

  • Estimates of longitudinal weights  Alternative Models:

    • Type A  Household and household head characteristics (results sensitivity)
      • Model 1 (1 A): Adjusted income, main income source, household head characteristics (age, sex, marital status and education level (problem)
      • Model 2 (2 A): similar to Model 1 excluding education level
      • Model 3 (3 A): similar to Model 1 + household size, number of children and number of full time workers in the household


Weighting Schemes (III)

  • Tipo B  individual characteristics (adults with completed interview)

    • Model 1 (1 B): : Individual income, activity status, age, sex, marital status and individual education level (problem)
    • Model 2 (2 B): similar to Model 1 + age
    • Model 3 (3 B): similar to Model 2 + health status
  • Type A and type B Models :

  • In general, results confirm descriptive analysis  not random attrition





Weighting Schemes (V)

  • Wave 1 frequency distribution: initial sample vs. balanced panel

    • 1) Initial sample, no weighting
    • 2) Initial sample, cross section Eurostat weights
    • 3) Initial sample (balanced panel), Eurostat longi.tudinal weights
    • 4) Initial sample (balanced panel), estimated longitudinal weights
  • Comparisons: 1) vs 4)  similarities

    • Estimated longitudinal weights  some “guarantees”
    • Comparisons: 2) vs 3)  high divergences
    • Categories with greater attrition rates  less adjustment due to the use of longitudinal weights


Weighting Schemes (VI)

  • Summary:

    • Several attrition adjustment possibilities  longitudinal weights
    • Frequency distribution  important differences according to the weighting scheme
    • Implications for dynamic analysis


Attrition and Income Mobility (I)

  • Income Mobility Analysis

    • Results may be affected by the possible “balanced panel” lack of representation of the population
      • Greater exit of low income individuals  possibly ascending mobility indicators greater than real
      • Lower attrition of high income individuals  potential effect on wage mobility analysis
  • Preliminary Analysis

    • Differential impact of attrition among countries
    • Not random attrition (selective)


Attrition and Income Mobility (II)

  • What are the extent and type of income mobility in a society?

    • The answer depends greatly on how well panel data represent the population
  • Does attrition introduce bias on income mobility estimations?



Attrition and Income Mobility (III)

  • Does attrition introduce bias on income mobility estimations? (Fitzgerald et al. 1998, Behr et al. 2003)

    • Split the sample according to attrition behaviour of individuals on future waves and compare the mobility results for the two subsamples
  • Estimating medium-term income mobility : Wave 1 to Wave 4

    • ECHP  8 waves
    • Subsample P balanced panel  individuals remaining all waves (from wave 1 to wave 8)
    • Subsample K  individuals remaining in the sample at least the four first waves
          • Np < Nk


Attrition and Income Mobility (IV)

  • Income mobility indices  summarize changes in economic status from one time period to another

  • Fields y Ok 1999:

    • Mobility as a normative concept / value judgments
    • Various approximations  different dimensions  No consensus
      • Mobility as inequality reduction as the accounting period is extended  Shorrocks Rigidity Index
      • Mobility as origin independence of last period income (statistic associación)  Hart Index
      • Mobility as transition among different classes on the income distribution (matrices)  Shorrocks Index, Bartholomew Index
      • Mobility as income movement (Fields and Ok Index)


Attrition and Income Mobility (V)

  • Effect of attrition on income mobility measures: compare the mobility results of subsample P and subsample K

    • Attrition: no bias on international comparisons  No country rerankings.
    • Comun pattern: subsample P shows lower mobility than subsample K  greater mobility of attriters


Attrition and Income Mobility (VI)

  • Mobility decomp. = Growth Mobility + Transfer Mobility

    • Changes in the relative contribution of each component
  • Mobility decomposition by population subgroups

    • Important differences in group mob. measures and mobility contribution between subsample p and subsample k


Mobility and weighting schemes (I)

  • Attrition adjustment schemes:

    • No adjustment : li=1
    • Eurostat longitudinal weights: l i= Ei
    • Estimated longitudinal weights: l i= A2i
  • Does the weighting scheme affect the estimations?

    • Correlation among different weights questions the robustness of analysis
      • ECHP Mobility from wave 1 to wave 8


Mobility and weighting schemes (II)

  • ECHP Mobility Wave 1 to wave 8

  • Hart Index  sensitive to the weighting scheme

    • Country rerankings
  • Shorrocks Rigidity Index/Transition Matrices  sensitive to the weighting scheme (moderate)

    • Country rerankings
  • Fields and Ok Index Decomposition  sensitive to the weighting scheme

    • Growth mobility and transfer mobility
    • Descomp. by population subgroups  highly sensitive
  • Income mobility measures sensitive to the weighting scheme, specially on the disaggregated analysis



Main Results

  • Attrition in the ECHP  certain non-randomness

  • Estimation of longitudinal weights to adjust for selective attrition (probit models)

    • Estimated longitudinal weights  dif. with Eurostat weights
  • Results Sensitiviness

    • Attrition  no high effect on income mobility indices
    • Income mobility decomposition  Greater sensitivity to the weighting scheme  “Correction”  Adjustment throught longitudinal weights
  • Adjustment with longitudinal weights

    • Some degree of sensitiviness: especially important for some population subgroups


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