Rounding Behavior of Respondents in Household Surveys

1
Rounding Behavior of Respondents in Household
Surveys

• Dr. des. Oliver Serfling
• University of Basel
• Presentation November 11, 2005
• Swiss Statistical Meeting, Zürich

2
Agenda

• Types of Survey Measurement Errors
• The Rounding Phenomenon
• Theoretical Issues Literature
• Research Goals
• Literature on rounding behavior
• Our Data SHP
• Empirical Strategy
• Rounding Patterns
• Conclusion

Survey
Response
Rounding
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Introduction Motivation
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Types of Survey Measurement Errors
Generally, measurement error occur if the
reported value (Z) is not identical with the
true value (X)
INR Item Nonresponse
True value X is not reported, Z?
MME Measurement Error
Continuous X is reported with error as continous
Z ZX?
Continuous X is reported as a discrete interval
with midpoint Z where X lies in ? Rounding
MRE Misreporting Error
MCE Misclassification error
Discrete X is reported as wrong but discrete Z
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The Rounding Phenomenon

• Rounding as a data coarsening
• Loss of information and data quality
• Small changes in the variable become unobservable
• ? Problem for sensitivtiy analysis
• Variance is upward biased
• Rounding as a response phenomenon
• Rounding may indicate motivation of respondent.
  Therefore, it may be a precursor of item or unit
  nonresponse
• Rounding may be a strategy of the respondent to
  avoid/reduce disclosure of privacy

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Literature Rounding as coarsening

• Sheppard (1898)
• Examines grouping effects on normal distribution
• Effect on mean is negligible
• Variance is upward biased by 1/12w with
  wrounding interval
• Sheppards correction calculate unbiased
  estimator of variance
• Eisenhart (1947)
• analyzes the effects of rounding with different
  sample sizes
• Tricker (1984)
• analyzes rounding on non-symmetrical dist.
  gamma, log-normal
• Rounding error in mean and variance is positively
  related to skewness of distribution and rounding
  degree

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Three types of rounding

• Presented literature deals only with same
  rounding behavior on every observed value
• ... but in survey interviews every respondent may
  have its own degree of rounding, which can be
• at random or systematic
• Under the assumption that respondents round
  correctly
• (A1)
• And the rounding error is uniformly distributed
  in the rounding interval
• (A2) e U-w/2 w/2
• 3 types of rounded data can be distinguished
• (R1) every value is rounded to same degree of
  rounding (w)
• Z X e with e U-w/2 w/2
• (R2) degree of rounding (w) differs over
  individuals (i)
• Z X e with e U-wi/2 wi/2
• (R3) degree of rounding (w) is a function of X
• Z X e with e U-w(X)/2 w(X)/2

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R1 effects on distribution

• Simulated right-skewed distribution of money
  amounts

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R1 effects on distribution

• Simulated distribution of money amounts rounded
  to 10s

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R1 effects on distribution

• Simulated distribution of money amounts rounded
  to 100s

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R1 effects on distribution

• Simulated distribution of money amounts rounded
  to 1000s

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R2 effects on distribution

• Simulated distribution, individual rounding
  intensity at random

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R3 effects on distribution

• Simulated distribution, rounding intensity
  dependent on absolute value

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R1-R3 effects on moments

• Deviance () of rounded moments from their
  population counterpart

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Research goals

• Q1.) Find an appropriate rounding intensity
  measure
• Q2.) Occurrence of rounding and correlation of
  rounding with similar respondent behavior
• Q3.) Is there heterogeneity in degree of
  rounding, and how can it be explained?
• Characteristics of respondent (Respondent
  Effects)
• Person of the interviewer (Interviewer Effects)
• Interview type and interview situation (Situation
  Effects)
• Q4.) Is the degree of rounding driven by the
  value of concerned variable?
• Q5.) Is there a panel duration effect?

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Results from literature

• Rounding as respondent behavior

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Literature Rounding as resp. behav.

• Schweitzer, Severance-Lossin (1996)
• 71 of all reported earnings in CPS (Current
  Population Survey) March 1994 are multiples of
  1,000
• Rounding behavior is highly systematic and
  correlated with respondents earnings level
• Systematic nature substantially affects some
  common used measures on earnings data
• Inequaltity summary measures (Gini-coefficient)
• Earnings quantiles
• Kernel density estimates
• In particular, statistics are sometimes altered
  at levels of annual change and/or standard errors.

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Literature Rounding as resp. behav.

• Schräpler (1999)
• Data Gross income question of waves 1-12 of
  GSOEP
• Roundings to 100, 500, 1000 in 67-77 of income
  statements
• Method Multinomial Logit estimation
• categories of dependent var exact, 10, 100,
  500/1000
• Results
• Sex Men have higher rounding propensity (5-7
  higher probability of choosing 500/1000 Female
  interviewers provoque extreme rounding
  intensities (exactness and 500/1000 rounding).
  Male Is provoque middle rounding intensity.
• Age of respondent and precision of statement seem
  to be correlated
• Interview duration positively correlated with
  presicion it takes time to provide exact values
• Interview mode in self administered quest. low
  rounding, higher in face-to-face interviews
• Experience of respondents with interview
  provoques rounding
• Income low roundings in first quartile, high in
  fourth quartile

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Literature Rounding as resp. behav.

• Hanisch (2003)
• Data Finish sample of ECHP
• Roundings after 1 or 2 significant digits
• 80 of gross wage statement
• 95 of net disposable income question
• Method ordered probit on number of significant
  digits
• Results
• Sex males provide higher precision (scandinavian
  artifact)
• Foreigners have lower roundings
• Interview mode CAPI leads to highest precision,
  longer interview duration produced more precision
• Job effects some professions are more precise
  than others
• Panel participation does not have a monotone
  effect on rounding behavior.

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Literature Rounding as resp. behav.

• Kroh (2004)
• analyses interview effects on rounding with
  self-reported body weight
• Data body weight of GSOEP 2002
• Method Binary Probit on the event of rounded
  weight statement
• Results
• Sex Women provide rounded weights more often
• Lower educated interviewees and singles provide
  rounded weights more frequently
• Overweighted people tend to stronger roundings!

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Our Data

• The Swiss Household Panel

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The Swiss Houeshold Panel (SHP)

• SHP is an annually collected comprehensive survey
• Comprises information on
• housing, living standard, income and ist
  components
• socio-demographics, education, employment,
• politics, values, and leisure.
• Three separate questionnaires
• grid
• personal
• household
• Personal questionnaire has to be answered by
  every household-member who reached the age of 14
• SHP is completely surveyed by CATI (Computer
  Assisted Telephone Interviews)
• Sample size 7,799 persons (1999) to 5,220
  (2003), (refresh 2004)

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SHP Interviewer Survey

• Additionally, in second wave (2000) survey of
  the interviewers with 24 questions on
• Socio-demographics
• Interviewer experience and occupation
• Opinions towards the survey
• From 53 interviewers worked for SHP in 2000
• 45 participated
• 41 filled in questionnaire completely
• No information on interviewers in 1999, and
  2001-2003
• Therefore, missing interviewer information on
• 1,211 out of 7,799 cases in 1999
• approx. 700 cases in 2001, 2002 and 2003

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Own analysis
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Research goals revisited

• Q1.) Find an appropriate rounding intensity
  measure
• Q2.) Occurrence of rounding and correlation of
  rounding with similar respondent behavior
• Q3.) Is there heterogeneity in degree of
  rounding, and how can it be explained?
• Characteristics of respondent (Respondent
  Effects)
• Person of the interviewer (Interviewer Effects)
• Interview type and interview situation (Situation
  Effects)
• Q4.) Is the degree of rounding driven by the
  value of concerned variable?
• Q5.) Is there a panel duration effect?

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Rounding Decision Model

• Hypothesis
• The respondent is free to decide about his
  rounding intensity (RI)
• which is determined by the costs and benefits
  of precision
• i.e. cognitive burden, disclosure of privacy
• The respondent chooses the RI which maximizes his
  utility
• If the cost and benefit components are attributed
  to the characteristics of the respondent, his
  interviewer and the interactions thereof, the
  latent rounding intensity (RI) is
• With at baseline cost-surplus in answering the
  question at time t, Rit are the characteristics
  of the respondent i, Ij are the characteristics
  of the interviewer j, (RI) are the interaction
  of both and eit is white noise

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Rounding measures

• Which measure reflects the latent rounding
  intensity?
• NRD Number of rounded digits (discrete absolute
  measure)
• NSD Number of significant digits (discrete
  absolute measure)
• RQ RoundingQuotient rounding digit / number
  of digits (discrete relative measure)
• RSM Rounding strain measure NRD-(NSD-1)
• Relative rounding error ()(continous relative
  measure)

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Empirical strategy

• Regression of rounding measure on possible
  determinants
• Respondent characteristics sex, age, education,
  employment status, satisfaction, health status,
  language, experience, nationality
• Interviewer characteristics and interview
  experience
• Interviewer-Respondent interactions
• Interview situation effects panel duration
• The value of rounded variable, log
  amount-splines, higher polynomials of variables
  value
• Using
• Ordered Probit modelwith a set of fully
  interacted covariates (RHS Var NoD-dummies)
• Dependent variable
• Number of Rounded Digits for the first income
  statement in the SHP questionnaire

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Correlation Rounding lt-gt Nonresponse

• large autocorrelations of rounding measures
• small positive correlation of rounding with
  Item-Nonresponse

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Respondent Effects

• on Rounding Intensity (NRD)

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Interviewer Effects
Weak but significant effects, since SHP is
conducted via CATI (telephone interviews)
No significant Interviewer-Respondent Interaction
/ Social Distance effects!
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NoD or Income Effect?

• Model is augmented with log-income splines for
  2,3,5, and 6 digits (4 digits as reference)
• (robustness check estimation of 5th order income
  polynomial)
• We find different slopes of the income effect by
  NoD
• with a negative effect for 6-digit incomes
• no log-linear income effect
• or
• additional NoD-Effect

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Conclusion

• Rounding in income data of the SHP is a rule,
  rather than an exception
• Rounding intensity differs over respondents
• There are robust patterns of influences on
  rounding behavior by respondents characteristics,
  interviewers characteristics, but non for
  interviewer-respondents interactions
• Rounding intensity is also driven by the amount
  of considered variable, but its magnitude seems
  to be relatively decreasing

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The End
Thank you for your attention !
Paper will soon be available at http//www.wwz.un
ibas.ch/stat/team/serfling