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

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

Implications of flexibility

– Zero nominal change plays no special role– Negative nominal changes result when

negative shocks are greater than inflation

Figure 1Kernel Smoothed Distribution of Percentage Changes

in Reported WagesMales

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

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

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

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

Algorithm from Bai and Perron

1. For each job history, calculate SSR for each possible break

2. Find the break with min SSR

3. Test if break is statistically significant

4. If so, repeat for each sub-period

5. Continue until no further significant breaks

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

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

Probability of Yearly Decline or Increasein Reported and Adjusted Wages

Reported Adjusted Reported Adjusted

Decline 0.157 0.051 0.136 0.043Constant 0.251 0.537 0.228 0.492Increase 0.591 0.412 0.636 0.465

1.000 1.000 1.000 1.000

FemalesMales

Table 4

Table 6Distribution of Changes in Reported

and Adjusted Wages Between Interviews

Reported Adjusted Reported Adjusted

Decline 0.200 0.020 0.180 0.015Constant 0.409 0.858 0.431 0.849Increase 0.391 0.123 0.400 0.136

1.000 1.000 1.000 1.000

Males Females

Figure 2-- Baseline Hazard of Change in Reported Wage

0 5 10 15 20 25 30 35 40duration

hazard

M ale

Female

Figure 3 -- Baseline Hazard of Change in Adjusted Nominal Wage

0 4 8 12 16 20 24 28 32 36 40

duration

hazard

M ale

Female

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

Impact of Non-Classical Measurement Error on Measures

of Inequality and Mobility

Peter Gottschalk and Minh Huynh

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

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

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

Overview

• Review of literature

• Analytical framework

• Empirical application

• Conclusions

Theoretical Literature

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

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

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

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

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)

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

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

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?

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

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