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## Rounding Behavior of Respondents in Household Surveys

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**Rounding Behavior of Respondents in Household Surveys**Dr. des. Oliver Serfling University of Basel Presentation November 11, 2005 Swiss Statistical Meeting, Zürich**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 Swiss Statistical Meeting, Zürich**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: Z=X+ 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 Swiss Statistical Meeting, Zürich**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 Swiss Statistical Meeting, Zürich**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 w=rounding 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 Swiss Statistical Meeting, Zürich**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] Swiss Statistical Meeting, Zürich**R1 effects on distribution**Simulated right-skewed distribution of „money“ amounts Swiss Statistical Meeting, Zürich**R1 effects on distribution**Simulated distribution of „money“ amounts rounded to 10s Swiss Statistical Meeting, Zürich**R1 effects on distribution**Simulated distribution of „money“ amounts rounded to 100s Swiss Statistical Meeting, Zürich**R1 effects on distribution**Simulated distribution of „money“ amounts rounded to 1000s Swiss Statistical Meeting, Zürich**R2 effects on distribution**Simulated distribution, individual rounding intensity at random Swiss Statistical Meeting, Zürich**R3 effects on distribution**Simulated distribution, rounding intensity dependent on absolute value Swiss Statistical Meeting, Zürich**R1-R3 effects on moments**Deviance (%) of rounded moments from their population counterpart Swiss Statistical Meeting, Zürich**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? Swiss Statistical Meeting, Zürich**Results from literature**Rounding as respondent behavior**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. Swiss Statistical Meeting, Zürich**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 I‘s 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 Swiss Statistical Meeting, Zürich**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. Swiss Statistical Meeting, Zürich**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! Swiss Statistical Meeting, Zürich**Our Data**The Swiss Household Panel**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) Swiss Statistical Meeting, Zürich**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 Swiss Statistical Meeting, Zürich**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? Swiss Statistical Meeting, Zürich**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: αt =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, (R*I) are the interaction of both and εit is white noise Swiss Statistical Meeting, Zürich**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: Rounding–Quotient = rounding digit / number of digits (discrete relative measure) • RSM: Rounding strain measure = NRD-(NSD-1) • Relative rounding error (%)(continous relative measure) Swiss Statistical Meeting, Zürich**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 Swiss Statistical Meeting, Zürich**Correlation Rounding <-> Nonresponse**• large autocorrelations of rounding measures • small positive correlation of rounding with Item-Nonresponse Swiss Statistical Meeting, Zürich**Respondent Effects**… on Rounding Intensity (NRD): Swiss Statistical Meeting, Zürich**Interviewer Effects**Weak but significant effects, since SHP is conducted via CATI (telephone interviews) No significant Interviewer-Respondent Interaction / Social Distance effects! Swiss Statistical Meeting, Zürich**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 Swiss Statistical Meeting, Zürich**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 Swiss Statistical Meeting, Zürich**The End**Thank you for your attention ! Paper will soon be available at: http://www.wwz.unibas.ch/stat/team/serfling Swiss Statistical Meeting, Zürich