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Two Applied Papers on Measurement Error in Wages

Two Applied Papers on Measurement Error in Wages. Downward nominal wage flexibility– real or measurement error? Impact of Non-Classical Measurement Error on Measures of Inequality and Mobility. Downward nominal wage flexibility– real or measurement error?. Peter Gottschalk.

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Two Applied Papers on Measurement Error in Wages

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  1. Two Applied Papers on Measurement Error in Wages • Downward nominal wage flexibility– real or measurement error? • Impact of Non-Classical Measurement Error on Measures of Inequality and Mobility

  2. Downward nominal wage flexibility– real or measurement error? Peter Gottschalk

  3. Question and Relevance • How flexible are nominal wages in the US? • Nominal versus real wage • Relevance • Possible explanation for lower unemployment in US • Claim in literature • US -- flexible labor market • Other OECD countries--institutional constraints

  4. Implications of flexibility • Zero nominal change plays no special role • Negative nominal changes result when negative shocks are greater than inflation

  5. Summary of Studies • Summary of studies • PSID studies • Substantial spike at zero– 7-10% • Substantial nominal decline– 15-20% • Firm specific studies • Negligible nominal decline – 0-2% • Acknowledge role of measurement error • Issue-- How to separate signal from noise • Requires identifying assumption

  6. Identification • Use weaker identifying assumptions • No functional form assumption on measurement error • Use well developed techniques from Bai and Perron (1998) to find wage changes • Originally developed to find structural breaks in macro data

  7. Identifying Assumption • Nominal wages adjust at discrete break points • Work for same employer from t=1…T • Wages adjust at T1 …. Tm • yt = β1+ut t=1...T1 • = β2+ut t=T1+1..... T2 • = βm+1+ut t=Tm+1..... T • No assumption on number of breaks (i.e. Tm >=0) • Weak restriction on frequency of break • Assume wages do not adjust continuously • No assumption on size of wage change

  8. Algorithm from Bai and Perron • For each job history, calculate SSR for each possible break • Find the break with min SSR • Test if break is statistically significant • If so, repeat for each sub-period • Continue until no further significant breaks

  9. Data--Survey of Income and Program Participation (SIPP) • 1986-93 Panels • Each is 24-40 months long • Monthly data collected every four months • Detailed questions on • Employer • Wages

  10. Empirical Specification • Sample • Hourly workers • Males and females while not in school • 18 to 55 • Within firm wage changes • Includes changes to new jobs or assignments • Includes transitions between full and part-time

  11. Conclusions • Offer new way to correct for measurement error based on weak identifying assumption • wages change at discrete break points • Reconciles firm studies with PSID studies • Nominal wage declines rare • Tend to occur around 12 month

  12. Impact of Non-Classical Measurement Error on Measures of Inequality and Mobility Peter Gottschalk and Minh Huynh

  13. Motivation • Common presumptions: • Inequality is overstated due to measurement error • Some cross-sectional variation reflects measurement error • Mobility overstated due to measurement error • Some cross-sectional variation reflects measurement error

  14. Motivation • Measures of inequality and mobility • Often based on self-reported earnings • Reflect joint distribution of • earnings • measurement error • Measurement error in • Earnings • Lagged earnings

  15. Motivation • Classical measurement error • Independent measurement error • Impliciations • Inequality overstated • Mobility overstated • Non-classical measurement error • Key properties • Mean reversion in earnings and lagged earnings • Correlated measurement errors • Implications • Can’t sign bias • But can derive impact

  16. Overview • Review of literature • Analytical framework • Empirical application • Conclusions

  17. Theoretical Literature

  18. Theoretical Literature • Classical measurement error in bivariate regression • Measurement error in x (lagged ln earnings) leads to • Attenuation bias • Under-estimate of correlation in earnings • Over-estimate mobility • Measurement error in y (ln earnings) • No effect on elasticity

  19. Theoretical Literature • Bound, Brown and Mathiowitz (2001) • Non-classical measurement error • impact of mean reversion • Impact in standard regression (not mobility) • Measurement error in y or x but not both • Findings– mean reversion in measurement error • in x offsets attenuation bias • in y introduces attenuation bias

  20. Theoretical Literature • Bound, Brown and Mathiowitz (2001) con’t • Not applicable to our problem • y and x potentially suffer from same source of measurement error • Measurement errors potentially correlated • with each other • with e

  21. Empirical Literature • Validation studies • Compare • Reported wages • Wages from admistrative records or firm’s payroll data • Findings-- Measurement error • Large • Var(error)/var(payroll)=.30 • Mean reverting • Positively correlated across time

  22. Data • Detailed Earnings Records (DER) • Yearly earnings from tax records (W2 forms) • More complete than FICA tax records • Social Security maximum • Uncovered sectors • SIPP • Exclude self-employment to match W2 • 1996 panel • Aggregate to yearly earnings • 12 months of valid earnings (including zeros)

  23. Data • SIPP • Top-codes yearly earnings >$150,00 • Replaces by demographic specific mean earnings • We impose same top-coding on DER • Imputes earnings • 31 percent of yearly earnings have at least one month imputed • Introduces other source of error that can be avoided • Show results for all and non-imputed

  24. Data • Matched on basis of Social Security number • Match rate .77 • Analysis Sample • Males 25-62 • Not attending school • Valid earnings in t and t-1

  25. Role of Linearity • Mobility is measured as • Linear correlation • Elasticity from linear projection • Decomposition is based on linear decomposition • Mean reversion-- • Linear projection of errors on y or x • Correlated errors • Are these relationships linear?

  26. Conclusion • Analytics • Common assumption that measurement error leads to overestimates of inequality and mobility • Based on classical measurement error assumption • Assumption is wrong • Impact of measurement error depends on • Mean reversion • Correlation in measurement error

  27. Conclusions • Empirical Findings • Measurement error in earnings in SIPP, PSID and CPS is • large • far from classical • Leads to • under estimate of inequality • little impact on correlation and elasticity • Large but offsetting bias

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