Wage Imputation in the OES Survey: A Model-Assisted Approach 

Jane G. Osburn 

Office of Occupational Statistics and Employment Projections, 

U.S. Bureau of Labor Statistics 

1. Introduction 

Wage imputation in the Bureau of Labor Statistics Occupational Employment Statistics (OES) Survey requires a 

process that matches non-respondent and respondent establishments on characteristics that best predict the wage 

levels of the non-respondent establishments in a given MSA /Industry / Establishment Size cell. The mean wage 

distribution of the establishments in the donor cell is then imputed to the non-respondent. Currently, the OES Survey 

procedures first define the donor cell for a given non-respondent Establishment /Occupation cell by the same semiannual panel /MSA / four/five digit NAICS Industry / Establishment-size (2) as the non-respondent, and cells are 

then collapsed across industry and size groupings in the case of insufficient response. If insufficient response still 

exists after collapsing across industry and size groupings, the base level strata default from MSA to State, the donor 

cell is reformed by State / four/five digit NAICS Industry / Establishment Size (2), and the process repeats as for the 

MSA base-level strata.1

 The base-level strata eventually default to USA in a similar manner. 

In those instances in which State or USA are the base-level strata of the donor cell used in an imputation, the current 

method in effect uses the average wage levels of the State or USA as a proxy for the wage level of the nonrespondent establishment. For those states that contain areas with widely varying wage levels, some of the 

imputation outcomes could be improved. 

A number of experimental wage imputation procedures are examined, the first of which replaces the base-level 

strata currently used in the OES Program with groupings of MSAs based on statistical estimates of area wage levels. 

A linear mixed model is used to estimate the wage level of each area in the U.S., and the estimates are used to guide 

the formation of groupings of MSAs with similar wage levels. Three successively more aggregated groupings are 

formed, including a thirteen-level grouping, ‘MS’ group one, a five-level grouping, ‘MS’ group two, and a threelevel grouping, ‘MS’ group three. ‘MS’ groups one and two take the place of the State, USA base-level strata of the 

current method, and wage imputation otherwise proceeds exactly as in the OES method. ‘MS’ group three adds an 

additional level.2

Five other estimators based on a similar notion are also examined. Three of the estimators use a two-stage estimation 

approach in which the estimates of area wage levels are used as a predictor of the establishment wage level along 

with other predictors including the total employment of the establishment and an OES-data proxy for the 

establishment average wage. Both of these predictors are available from the Quarterly Census of Employment and 

Wage Program, which also provides the basis for the OES sample frame.3

 This approach is then revised for the case 

of the best-performing estimator, in favor of a more efficient approach that uses the proxy QCEW wage as a 

predictor in the linear mixed model. 

Simulation is used to examine the relative performance of the estimators. The results suggest that the best estimator 

predicts the wage level of establishments using a linear mixed model that contains the random effect of areas along 

with the effects of industry, establishment size, occupation, and an OES-data proxy for the establishment average 

wage available from the QCEW Program. 

 

1

 The OES strata include Ownership in NAICs 611, Educational Services, and NAICS 622, Hospitals. 

2

 Note that MSA groups one, two, and three each contain all MSAs. 

3

 BLS Statisticians Polly Phipps and Daniell Toth proposed the use of establishment wage information available 

from the QCEW Program as a predictor of establishment wage levels. 
2 

The following section discusses wage imputation in the OES Survey under the current and experimental procedures. 

Section three discusses the data produced by the Occupational Employment Statistics Survey. Section four outlines 

the estimation of area wage levels using the OES data in a linear mixed model, discusses six experimental estimators 

of the establishment wage level, and describes how the model estimates are used to form donor cells under each 

model. Section five describes a simulation study that examines the relative performance of the estimators. Section 

six examines the results. Section seven offers some conclusions and directions for future research. 

2. Overview of the Current and Proposed Methods of Wage Imputation 

Current OES procedures first identify respondent establishments for a given semi-annual panel and occupation from 

the same MSA/ four/five digit NAICS Industry /Size(2) cell as the non-respondent establishment. If the cell contains 

a sufficient number of respondents for the occupation, the mean wage distribution of the cell is imputed to the nonrespondent Establishment /Occupation cell. In the absence of sufficient response, the cells are combined into 

successively more aggregated industry and size groupings, and the mean wage distribution of the aggregated 

grouping /Occupation cell is used. If cells defined by MSA /All Industries /Occupation still contain insufficient 

response, the base-level strata defaults from MSA to State, the cell is reformed by State /four/five digit NAICS 

Industry / Size (2) /Occupation, and the procedure repeats as for the MSA base-level strata. If cells defined by State 

/All Industries /Occupation still contain insufficient response, the base-level strata defaults to USA, cells are 

reformed by USA /four/five digit NAICS Industry /Size (2) /Occupation, and the procedure repeats as for the State 

base-level strata. 

Each of the experimental estimators replace the base-level strata currently used in the OES Program with three 

successively more aggregated establishment groupings that are based on a statistical model. ‘MS’ group one is a 

thirteen-level grouping, ‘MS’ group two is a five-level grouping, and ‘MS’ group three is a three-level grouping. 

Wage imputation follows the same rules used in the current OES procedures, with the exception that ‘MS’ groups 

one and two take the place of the base-level strata State, USA in the current OES method, and ‘MS’ group three 

adds an additional level to the base-level strata. 

3. Data from the Occupational Employment Statistics Survey 

The Bureau of Labor Statistics Occupational Employment Statistics Survey collects data over a three year cycle on 

the wages and occupational category of each employee in a total of approximately 1.2 million establishments, 

spanning the non-farm private and public sectors in the U.S. For each occupation employed in the establishment, 

survey respondents record the number of employees earning wage rates that fall within each of twelve wage 

intervals. The average wage of an Establishment /Occupation cell is the sum over wage intervals of the product of 

the employment in the interval and the ‘midpoint’, or estimated mean wage of the interval, divided by the sum of 

employment across the wage intervals. The wage interval midpoints that are applied to establishments surveyed 

during different quarters of the three year period are updated using the Employment Cost Index (ECI), such that all 

establishments’ wages reflect the final year /quarter wage levels in the completed dataset.4

 

4. Six Models of the Establishment Wage Differential 

4. 1 A1 Estimator 

The A1 estimator uses an estimate of the area wage differential as a proxy measure of the wage differential of each 

establishment in the area. A nested error linear mixed model containing the effects of industry, occupation, and 

establishment size, and the random effects of area is used to estimate the Empirical Best Linear Unbiased (EBLUP) 

estimator of the area wage effect; 

 

4

 The midpoints of the wage intervals are estimated using data from the Bureau of Labor Statistics National 

Compensation Survey. 
3 

ijkl j k l i ijkl ln w  Industry  Occupation  Establishment size  Area  e

~ ,0( )

~ ,0( )

2

2

ijkl e

i

e N

area N



 

where i indexes areas, j indexes industries, k indexes occupations, and l indexes establishments 

 Industry is a three digit NAICS industry classification 

 Occupation is a six digit Standard Occupational Classification 

 Establishment size is a six category establishment size grouping 

wijkl ln is the log of the mean wage by Establishment /Occupation cell 

The area effects and residual errors are assumed to be iid random variables, independent of each other. 

The model is estimated using Pseudo-Maximum Likelihood, in which each Establishment /Occupation observation

is weighted by a measure of sample-weighted occupational employment that is scaled to account for the dependence 

of the wage distribution on areas.i

 The parameters are estimated using restricted maximum likelihood.5 The EBLUP 

estimator corresponds to the set of parameter values that minimizes the mean squared error of prediction (MSPE) 

ofln w

6

. The EBLUP of the area wage effect is the weighted average residual for the area, discounted by the 

estimated share i

ˆ of between-area variance in the overall variance; 

 

Let 

wtemp = scaled, sample-weighted occupational employment 

eo = Establishment /Occupation cell 

 



















  









eo iArea

ijkl

eo iArea

ijkl ijkl ijkl

i

wtemp

wtemp w x 



ˆ * ln

EBLUParea = ˆ

i

 where 

2 2

2

ˆ ˆ

ˆ

ˆ





 









e

i

 .

7

 

The standard errors are estimated using the delta method as described in Goldstein (Sec.3.24). 

The A1 estimator uses the estimates of the area wage effect (EBLUParea) to assign all establishments in each MSA 

to ‘MS’ groups one, two, and three, where ‘MS’ group one has 13 levels, each of which contains MSAs with very 

similar average wage levels, ‘MS’ group two has five levels, each of which contains MSAs within a broader range 

of wage levels, and ‘MS’ group three has three levels, each of which contains MSAs with wage levels within a 

broad range. 

4.2. Four Experimental Estimators of the Establishment Wage Level 

A variety of additional estimators are based on a two-stage approach that uses a measure of the establishment wage 

differential as the dependent variable and explores the use of predictors including the estimated area wage effect 

 

5

 Unlike maximum likelihood, the REML method of estimating the variance components accounts for the loss of 

degrees of freedom that results from the estimation of β. See discussion in Rao (2003), pp.100-102.

6

 Royal (1976) derived the best linear unbiased predictor for any linear function. 

7

 The estimate 2

ˆ ei in the denominator of i

ˆ is the approximate variance of the mean residual for area i. Thus 

defined, it is a cluster-level variance, on the same scale as the estimated model variance 2

ˆ 

. 
4 

from the model of Section 4.1 (EBLUParea), establishment total employment, and an OES-data proxy for the 

establishment average wage that is available from the QCEW program. 

The dependent variable used in each model is a measure of the establishment wage differential (subsequently 

Estabdiff_v2) formed from residuals obtained from the model of Section 4.1 by differencing the fixed portion of the 

wage estimate from the log wage. The R1A estimator attempts to predict estabdiff_v2 using both the EBLUParea 

and the proxy QCEW wage in conjunction with a measure of establishment employment. The R1B estimator 

incorporates the EBLUParea as a predictor along with a measure of establishment employment. The R1C model uses 

the proxy QCEW establishment wage and establishment employment as predictors; 

R C Estabdiff Intercept qcewdiff emp

R B Estabdiff Intercept EBLUP emp

R A Estabdiff Intercept qcewdiff EBLUP emp

v OES PROXY

v area

v OES PROXY area

1 : * *

1 ;. * *

;1 * * *

2 1 _ 2

2 1 2

2 1 _ 2 3

 

 

  

  

  

   

Each model was estimated by NAICS industry /establishment size using a general linear model.8

 For each model, 

the model-predicted establishment wage differential was used to assign each establishment to groupings similar to 

those described above for the A1 estimator, resulting in three complete sets of establishment groupings that form the 

base level strata under each model. 

A fifth estimator, R1F, uses the OES-data proxy QCEW wage differential directly to assign establishments to the 

groupings. 

4.3 R1A_r1 Model 

The two-stage approach outlined above is quite inefficient. A revised version of the R1A model, R1A_r1, augments 

the model of Section 4.1 to include the proxy QCEW wage differential as a predictor; 

ijkl j k i l l ijkl ln_ wg _ dif  industry  occ  area  estab size  qcew_ dif  e

where 

i indexes areas 

j indexes industries 

k indexes occupations 

l indexes establishments 

ln_wg_dif = the deviation of the log establishment /occupation wage from the grand mean of the log establishment 

/occupation wage 

qcew_dif = the deviation of the log establishment QCEW wage from the grand mean of the log QCEW 

establishment wage. 

The explanatory power of the proxy QCEW wage predictor is most clearly demonstrated by examining its effect in a 

two-fold nested error model (Stukel and Rao, 1999) that accounts for the dependence of wages on both areas and 

establishments; 

ijkl j k i l i l ijkl ln_ wg _ dif  industry  occ  area  estab (area )  qcew_ dif  e

In this model, the effects of area and of establishment conditional on area are each assumed to be iid random 

variables, independent of each other; 

 

8

 The models were estimated at the four, three, and two digit NAICS levels and analyses for detailed groupings were 

replaced with analyses using more aggregated groupings as needed. For the purposes of the simulation discussed in 

Section 6, the models are estimated using data that excludes data from the State for which the simulations are 

conducted. In actual practice, the models should be estimated using all of the data. 
5 

~ ,0( )

~ ,0( )

~ ,0( )

2

2

|

2

ijkl e

il u

i v

e N

Estab N

Area N







The EBLUP of the conditional establishment wage differential in the two-fold model is the average percentage by 

which the wages of occupations in the establishment differ from that predicted by the mixed model, discounted by 

the share of between-establishment variance, (

li  ), in the total (between- plus within-establishment) wage variance; 

 

          

~

ln ~EBLUP i|l estab = 

li li ln li li i i i

u  w  x  w  x

or

        

~

ln ~EBLUP estab l| i = 

li li ln li li li i i i

u  w  x  w  x

where 

 





 

il

li

il

lili

i

w

w







, similarly for i

x

2 2

2

ˆ ˆ

ˆ

ˆ

e u

u

li  









9







il

li

u

v

v

i











2

2

2

ˆ

ˆ

ˆ

ˆ

The EBLUP of the area wage effect is similar to that discussed earlier, with the exception that the shrinkage 

parameter i

ˆ takes into account the lower level random effect. 

The two-fold model was estimated twice, including and excluding the OES-data proxy QCEW wage differential.10 

The inclusion of the proxy QCEW wage reduced the size of the area and establishment variance components by over 

ninety percent and eighty percent, respectively. 

The EBLUP of the establishment wage differential obtained from this model is of limited direct use in the current 

study, because it represents the portion of the (unconditional) establishment wage differential for which we have no 

model. That is, it is the portion of the unconditional establishment wage effect that is not explained by the area wage 

effect and the proxy-QCEW variable together. The establishment wage effect estimated in this model would become 

useful, however, if we were to find an additional predictor that helps explain it. 

The revised estimator, model R1A_r1, uses the estimated parameters of the model to predict the unconditional 

establishment wage differential; 

R1A_r1 = EBLUP of area wage effect + ( β1 × QCEW_wage_differential ) 

The model-predicted establishment wage differentials (R1A_r1) are used in a way similar to the procedures 

discussed earlier. All establishments, non-respondents and respondents, are assigned to groupings on the basis of the 

 

9

 Discussion here assumes equal residual error variances across areas and abstracts away from survey weights . 

10 A nested error model containing a single random effect of area was estimated first using a large dataset. The 2-

fold model was then estimated using a sample of residuals from this estimation, holding the area variance 

component constant at the level of the first estimation. 
6 

model-predicted establishment wage differential, and these are used to form the successively more aggregated, 

three-tier base-level strata in the same way as discussed earlier. 

Wage imputation then proceeds as in the previously discussed method. Non-respondent Establishment /Occupation 

cells from a given panel are wage-imputed using the mean wage distribution of the panel respondents in the same 

model-defined group /Industry /Size /Occupation cell or appropriately collapsed cell. 

5. The Simulation 

Simulation is used to test the various model alternatives against the OES method. The main elements of the 

simulation include the establishment groupings (‘MS’ groups one, two, and three) under each model, the simulated 

sample, the simulated non-respondents, and the simulated respondents. 

The simulation uses data from the May 2009 OES survey round for all size four establishments located in Louisiana, 

and all size seven establishments located in New York. The simulated sample for a given State is comprised of all of 

the respondent establishments from the State /Size cell. Stratified random samples from the simulated sample are 

used to identify a set of simulated non-respondent establishments that makeup a similar proportion of establishments 

and a similar Industry /Size composition of establishments to the set of actual non-respondent establishments in the 

OES sample. The simulated respondents include all units in the simulated OES sample not identified as simulated 

non-respondents. 

The simulation for each model is guided by the ‘Imputation dataset’, which contains the simulated non-respondent 

establishment data stripped of all wage distributions but retaining identifiers including a non-respondent indicator, 

industry and establishment size identifiers, establishment total employment, the occupational employment of each 

occupation employed in the establishment, and the ‘MS’ group one, two, and three assignments under each of the 

models A1, R1A, R1A_r1, R1B, R1C, and R1F. 

For each model, the identifiers are used to match recipients and donor cells such that the units included in the donor 

cell are drawn from the same semi-annual panel, Occupation, Industry, and ‘MS’ group one, two, or three as the 

non-respondent Establishment /Occupation cell. The mean wage distribution of the donor cell is then used to 

apportion the recipient cell occupational employment among the OES wage intervals.11

For each simulation and for each of the six experimental models and the OES method, the mean imputed wage by 

Establishment /Occupation is calculated using the wage interval means in conjunction with the apportioned 

occupational employment. 

Performance measures including 1) average relative error , 2) average relative bias and 3) variance are 

calculated by averaging over the simulations for a cell; 

Let 

wsim = mean imputed wage by Sim /MSA /Establishment /Occupation 

wactual = mean “true” wage by MSA /Establishment /Occupation 

nocc = number MSA /Establishment /Occupation cells in summary cell 

t = un-weighted occupational employment by MSA /Establishment /Occupation 

 

   

 















 





























nocc

sim

actual OCC

sim

nocc w

w

t

t

ERA

1

100

1

1

* 1

100

1

)(

1

 

11 In the actual OES procedures, non-respondent establishments are first employment-imputed and then wage 

imputed. The simulation by-passes the employment-imputation step in favor of using the actual occupational 

employment totals of the simulated non-respondents that are available by virtue of the simulation design. 
7 

  































 





























nocc

sim

actual

sim

nocc w

w

t

t

BRA

1

100

1

1

* 1

100

1

)(

1

Let 

wmod,sim = unweighted mean wage of a FIPS /MSA /Occupation cell for a given simulation, calculated using 

dataset S, the union of the imputed non-respondent and respondent Estab /OCC cells in the simulated sample 

wmod = unweighted mean of wmod,sim , calculated over all simulations 

  





S

sim

w sim

s 1

mod,

1

The simulation variance is 

  









S

sim

w sim w

S

SV

1

2

mod, mod ( )1

1

6. Results 

Table 1 contains the results by State /OCC2 (two digit Standard Occupational Classification code) and by State 

/MSA for the relative error and bias measures. 

In New York overall, the weighted average relative error for the A1, R1B, and R1C estimators is about .25, and the 

similar measures for the R1A, R1A_r1, R1F and OES estimators are .23, .22, .24 and .28, respectively. The R1A_r1 

estimator has lower error than the OES estimator in 20 of the 22 occupational groups, while the A1, R1A, r1B, r1C, 

and r1F estimators have lower relative error in 13, 18, 15, 15, and 17 occupational groups, respectively. 

The R1A_r1 estimator is biased downward about one percent in New York, while the R1B, R1C, R1F, and OES 

estimators over-predict wages to some extent. The R1C and OES estimators are biased upward about three percent, 

the R1B estimator is biased upward about four percent, and the R1F estimator is biased upward about two percent. 

The A1 and R1A estimators are biased downward about five percent and six percent, respectively. The R1B and 

R1F estimators are less biased than the OES estimator in 11 of the 22 occupational groups, while the A1, R1A, 

R1A_r1, and R1C estimators are less biased than the OES estimator in 17, 13, 14, and 12 occupational groups, 

respectively. 

In Louisiana overall, the weighted average relative error is .22 for the A1 estimator, .18 for the R1A estimator, .17 

for the R1A_r1 estimator, .25 for the R1B and OES estimators, and .20 for the R1C and R1F estimators. The R1A 

estimator has lower error than the OES estimator in the case of 17 of the 22 occupational groups, the R1A_r1 

estimator has lower error than the OES estimator in the case of 21 of the 22 occupational groups, and the A1, R1B, 

R1C, and R1F estimators have lower relative error than the OES estimator in 14, 12, 18, and 20 occupational 

groups, respectively. 

The R1A and A1 estimators are biased upward about three percent in Louisiana overall, the R1A_r1 estimator is 

biased upward about four percent, the R1B, R1C, and R1F estimators are all biased upward about six percent, and 

the OES estimator is biased upward about ten percent. The R1A and R1A_r1 estimators have lower bias than the 

OES estimator in the case of 19 of the 22 occupational groups, and the A1, R1B, R1C, and R1F estimators have 

lower bias than the OES estimator in 20, 17, 14, and 18 of the 22 occupational groups, respectively. 

One source of upward bias in the OES estimator is the use of the ‘State’ base level imputation strata. In States that 

contain one or more large, high-wage areas in addition to numerous smaller, lower wage areas, the mean wages of 

the ‘State’ donor cell are dominated by the large, high-wage area(s) in the cell, causing upward bias in the imputed 

wage for most areas. One would expect this effect to be stronger for New York, due to a somewhat larger median 
8 

wage gap between NYC and other areas (about 25% versus 19% between New Orleans/Baton Rouge and other areas 

in LA) and its larger share of State employment.12

 

The results do not confirm this expectation. Looking at two digit SOC occupational groups, the results show that, on 

average, the OES estimator over-predicts the wages of 16 of the 22 occupational groups in the New York data, while 

it over-predicts the wages of 19 of the 22 groups in the OES data for Louisiana. All of the experimental estimators 

exhibit a more balanced pattern of over- and under-prediction for both states. In New York, the A1 and R1F 

estimators each overpredict the wages of 7 groups, while the R1A, R1A_r1, R1B, and R1C estimators over-predict 

the wages of 6, 12, 11, and 8 groups, respectively. In Louisiana, the R1A estimator over-predicts the wages of 14 

groups, and the R1B, R1C, A1, R1A_r1, and R1F estimators over-predict the wages of 18, 17, 15, 19, and 18 

groups, respectively. 

In both New York and Louisiana, all estimators are least biased for most of the largest occupations and those 

earning close to the minimum wage, including Office and Administrative Support (43), Food Service and 

Preparation (35), and Personal Care and Service (39) occupations. In Louisiana, all estimators are generally more 

biased for the professional occupations that contain much lower employment in Louisiana, including Managers (11), 

Business and Financial Operations (13), Computer and Mathematical Science (15), Architecture and Engineering 

(17), and Life, Physical, and Social Science (19), Community and Social Service (21), Legal (23), and Education, 

Training, and Library (25) occupations. The OES estimator is severely upward biased (.50+) for both Business and 

Financial Operations (13) and Sales (41) occupations. In New York, the estimators generally had low amounts of 

bias for all occupations with the exception that all estimators over-predict the Healthcare Practitioner and Technical 

(29) Occupations, most models under-predict Arts, Design, Entertainment, Sports and Media (27) occupations, and 

most models seriously over-predict the wages of Building and Grounds workers (37). In addition, all of the 

experimental estimators under-predict the wages of Healthcare Support occupations (31) in both the Louisiana and 

New York data. 

The results also seem to reflect the sensitivity of wages of many local-level public sector occupations to a 

combination of fiscal and political pressures. All estimators over-predict the wages of Education, Training, and 

Library occupations and Social and Community Service occupations in Louisiana, whose public school systems rank 

in the fourth quartile on spending per student and whose fiscal commitment to anti-poverty measures is similar.13

 

Turning to the results by area, in New York the OES estimator is clearly upward biased in most of the lower wage 

areas including all of the Balance of State areas, Glen Falls, Utica, Syracuse, Buffalo, and Binghamton, while it is 

downward biased in NYC. In Louisiana, the pattern of biases of the OES estimator is similar, and the A1, R1A, and 

R1A_r1 estimators are all significantly less biased than the OES estimator in all areas. 

 

Table 2 contains, for each estimator, the value (S) of the simulation variance at which MSA /Occupation cells that 

together account for a given percentage of total sample employment have values of simulation variance less than or 

equal to S. For example, in the New York simulation of the R1A model, MSA /Occupation cells that together 

account for ninety eight percent of New York, size-seven-establishment sample employment have simulation

variance less than or equal to 5.65. The R1A_r1, R1A, R1C, and R1F estimators all have lower variance than the 

OES estimator at all points in the distribution except for the last .5%, and the R1B and A1 estimators have lower 

variance than the OES estimator at all but three points. 

7. Conclusions and Directions for Future Study 

Overall, the results suggest that the R1A_r1 estimator outperforms the other estimators, showing that an estimator 

that augments information about area wage levels with auxiliary information about the average wage of the 

establishment can outperform an estimator that utilizes either one of these alone. The analyses are currently being 

re-run using the actual QCEW wage in place of the OES data proxy. 

 

12 BLS statisticians Polly Phipps and Daniel Toth have identified a second source of wage bias resulting from nonresponse patterns of large establishments. 

13 Auxiliary analyses show that the average magnitude of the wage bias for the detailed occupations in each group, 

for each model, mirrors the results for the more aggregated groups. 
9 

References 

Asparouhov, Tihomir 2005. “Sampling Weights in Latent Variable Modeling,” Structural Equation Modeling, Vol. 

12., No.3., pp.411-434. 

Eltinge, John L. and Jeffrey M. Gonzalez 2009. “Sensitivity of Inference Under Imputation,” Federal Committee on 

Statistical Methodology Research Conference, Washington, DC. 

Firebaugh, Glenn 1978. “A Rule for Inferring Individual-Level Relationships from Aggregate Data,” American 

Sociological Review, Vol.43., No.4., pp.557-572. 

Goldstein, Harvey 2011. Multilevel Statistical Models, 4th Edition, John Wiley and Sons, Ltd., 

Chichester, West Sussex, UK. 

Greene, William H. 2000. Econometric Analysis, Fourth Edition. Prentice Hall Press, New Jersey. 

Grilli, Leonardo and Monica Pratesi. 2002. “Weighted Estimation in Multilevel Models to Allow for 

Informativeness of the Sampling Design,” Working Paper 2002 /01, Dipartimento di Statistica, Università degli 

Studi di Firenze. 

Hox, Joop. 2002. Multilevel Analysis: Techniques and Applications, Lawrence Erlbaum Associates, Mahwah, NJ. 

Pfeffermann, D., C.J. Skinner, D.J. Holmes, H. Goldstein, J. Rasbach “Weighting for Unequal Selection Probability 

in Multilevel Models,” Journal of the Royal Statistical Society, B, 1998 Vol.60., Part 1. pp.23-40.

Prasad, N.G.N and J.N.K.Rao. 1990. “The Estimation of Mean Square Error of Small Area Estimators,” Journal of 

the American Statistical Association, Vol.85., pp.163-171. 

Rao, J.N.K. 2003. Small Area Estimation, John Wiley and Sons, New Jersey 

Royal, R.M. 1976. “The Linear Least-Squares Prediction Approach to Two-Stage Sampling,” Journal of the 

American Statistical Association, Vol.71.,pp.657-664.

Shoemaker, Owen and William Johnson. 1999. “Estimation of Variance Components for the U.S. Consumer Price 

Index,” Proceedings of the Section on Business and Economic Statistics, American Statistical Association.

Snijders, Tom and Roel Bosker. 1999. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel 

Modeling, Sage Publications, Thousand Oaks, CA.

Stukel, D.M. and Rao, J.N.K. 1999. “Small Area Estimation Under Two-fold Nested Error Regression Models,” 

Journal of Statistical Planning and Inference, Vol.78., pp. 131-147.
10 

Endnotes 

 

i

 See Pfeffermann, et.al (1998). Weighting is not needed in a linear mixed model that includes as covariates each of 

the strata components of a self-weighting survey, in which the probability of selection is the same for all units within 

a stratum. The parameter estimates of the linear mixed model are biased if units at any level (i.e. individual 

establishment/occupation observations at level 1, MSAs at level 2) are selected with unequal probabilities in ways 

that are not accounted for by the linear mixed model. While the OES Survey is self-weighting within 

MSA/Industry/Size strata, the model used here includes these strata components as covariates only at somewhat 

aggregated levels. For example, a three digit Naics industry is included rather than the four or five digit Naics 

industry used in sampling. 

A correction offered by Pfeffermann, et.al (1998) involves scaling the level 1 sample weights such that the naïve 

estimate of MSA employment, Ni

ˆ

, equals actual total reported employment for the area. With this scaling, the 

variance of the cluster-level latent variable is determined by the true sample size of level 1 units (see Asparouhov 

(2005 ). Goldstein (2011) also provides a discussion of the approach. Grilli and Pratesi (2002) conducted extensive 

simulations demonstrating that the approach outlined above works well, minimizing both bias and the increase in 

variance that results from the use of survey weights. 
Table 1 

 OES Wage Imputation Simulation Study: Results of Six Experimental Models and the OES Estimator 

1. New York, size seven establishments 

OCC Title

Number

Estab/

OCC Cells

Average Relative Error 

( Simple average over sims of 

MEAN( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL )

Weighted Average Relative Error

 Simple average over sims of 

∑( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMPぶ 

Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

Weighted Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES

ALL 117735 0.27 0.24 0.23 0.26 0.25 0.25 0.30 0.25 0.23 0.22 0.25 0.25 0.24 0.28 -0.02 -0.04 0.00 0.05 0.03 0.03 0.07 -0.05 -0.06 -0.01 0.04 0.03 0.02 0.03

Managers 5030 0.25 0.19 0.19 0.19 0.19 0.22 0.23 0.24 0.19 0.19 0.18 0.19 0.21 0.22 -0.07 -0.02 0.02 0.00 -0.03 -0.05 0.10 -0.08 -0.03 0.01 0.00 -0.04 -0.07 0.08

Bus.&Fin. Operations 5952 0.31 0.28 0.23 0.29 0.29 0.22 0.42 0.31 0.27 0.22 0.28 0.29 0.22 0.42 0.11 0.03 0.03 0.15 0.04 0.06 0.28 0.13 0.05 0.05 0.17 0.08 0.07 0.30

Computer & Math 6073 0.27 0.26 0.21 0.25 0.27 0.22 0.25 0.25 0.24 0.20 0.24 0.25 0.21 0.23 0.00 -0.03 0.05 0.11 0.00 0.01 0.08 -0.02 -0.05 0.04 0.11 -0.01 0.00 0.06

Architecture and Eng. 6452 0.35 0.27 0.26 0.28 0.27 0.23 0.28 0.30 0.24 0.28 0.26 0.28 0.23 0.29 0.19 0.04 0.08 0.13 0.05 0.03 0.04 0.07 -0.03 -0.04 0.02 -0.06 -0.06 -0.07

Life, Physical, and Social Science 6893 0.27 0.21 0.20 0.24 0.27 0.37 0.25 0.25 0.19 0.19 0.22 0.27 0.35 0.22 -0.01 0.01 0.03 0.09 0.08 0.20 0.07 -0.03 0.02 0.02 0.10 0.10 0.19 0.04

Community and Social Service 3096 0.18 0.14 0.15 0.15 0.16 0.15 0.20 0.17 0.14 0.15 0.15 0.16 0.14 0.19 -0.06 -0.03 -0.01 -0.02 -0.03 -0.05 0.06 -0.06 -0.02 -0.01 -0.01 -0.04 -0.06 0.06

Legal 1227 0.23 0.17 0.21 0.44 0.16 0.15 0.18 0.20 0.15 0.16 0.45 0.10 0.10 0.18 0.03 0.10 0.14 0.17 0.09 0.06 0.07 0.03 0.10 0.13 0.19 0.07 0.05 0.08

Education, Training, and Library 27476 0.28 0.25 0.26 0.29 0.27 0.26 0.33 0.27 0.25 0.24 0.28 0.26 0.24 0.30 -0.03 -0.07 -0.02 0.07 0.06 0.05 0.07 -0.08 -0.09 -0.04 0.05 0.05 0.03 0.02

Art, Design, Entertain., Sprts, Media 5170 0.38 0.36 0.32 0.44 0.33 0.36 0.39 0.42 0.38 0.33 0.48 0.33 0.38 0.41 -0.13 -0.19 -0.02 -0.06 -0.15 -0.16 -0.15 -0.11 -0.16 -0.03 0.03 -0.17 -0.13 -0.15

Healthcare Prac. and Tech. 10551 0.41 0.42 0.33 0.28 0.44 0.47 0.41 0.42 0.42 0.34 0.28 0.45 0.48 0.42 0.28 0.28 0.20 0.13 0.28 0.33 0.29 0.29 0.29 0.21 0.14 0.30 0.35 0.30

Healthcare Support 3208 0.13 0.18 0.16 0.14 0.19 0.17 0.17 0.13 0.19 0.16 0.13 0.19 0.18 0.16 -0.04 -0.07 -0.03 -0.02 -0.07 -0.07 0.02 -0.06 -0.08 -0.03 -0.03 -0.08 -0.08 0.01

Protective Service 3342 0.16 0.16 0.18 0.18 0.18 0.17 0.29 0.15 0.14 0.17 0.17 0.16 0.15 0.29 0.06 0.00 0.07 0.03 0.02 -0.04 0.15 0.05 -0.02 0.06 0.02 0.01 -0.04 0.15

Food Preparation and Serving 1422 0.26 0.22 0.18 0.14 0.22 0.20 0.24 0.26 0.21 0.18 0.13 0.21 0.19 0.23 -0.15 -0.10 0.04 -0.04 -0.13 -0.09 0.06 -0.13 -0.08 0.04 -0.03 -0.12 -0.08 0.08

Building and Grounds, Cleaning and Main 567 0.55 0.36 0.32 0.50 0.35 0.38 0.21 0.55 0.36 0.32 0.50 0.35 0.39 0.21 0.37 0.19 0.22 0.30 0.16 0.02 0.01 0.37 0.19 0.23 0.30 0.16 0.02 0.01

Personal Care and Service 2376 0.10 0.13 0.15 0.18 0.09 0.12 0.12 0.10 0.13 0.14 0.17 0.08 0.11 0.12 -0.03 -0.09 0.09 -0.12 -0.01 -0.06 0.06 -0.03 -0.09 0.09 -0.12 -0.01 -0.06 0.05

Sales and Related 1500 0.45 0.33 0.23 0.33 0.28 0.25 0.65 0.24 0.28 0.23 0.30 0.21 0.20 0.36 0.22 -0.16 -0.11 -0.07 -0.18 -0.19 0.30 0.05 -0.25 -0.18 -0.21 -0.17 -0.15 -0.11

Office and Administrative Spt. 5874 0.20 0.16 0.15 0.15 0.17 0.21 0.20 0.19 0.16 0.14 0.15 0.16 0.20 0.20 0.00 0.02 -0.02 0.03 0.00 0.05 0.05 0.00 0.03 -0.02 0.03 0.00 0.06 0.05

Farming, Fishing, and Forestry 218 0.24 0.21 0.20 0.29 0.24 0.27 0.34 0.22 0.20 0.19 0.29 0.22 0.27 0.33 -0.10 -0.05 0.00 -0.07 -0.21 -0.18 -0.22 -0.08 -0.04 -0.01 -0.06 -0.19 -0.17 -0.21

Construction and Extraction 4160 0.25 0.19 0.15 0.15 0.22 0.20 0.33 0.25 0.19 0.15 0.15 0.22 0.20 0.33 -0.04 -0.03 0.02 -0.02 -0.13 -0.12 0.18 -0.04 -0.02 0.02 -0.02 -0.13 -0.11 0.18

Installation, Maint., and Repair 4253 0.19 0.14 0.11 0.19 0.17 0.13 0.15 0.19 0.14 0.10 0.18 0.17 0.14 0.14 -0.04 -0.04 -0.03 -0.08 -0.08 -0.05 -0.05 -0.04 -0.03 -0.02 -0.08 -0.08 -0.06 -0.05

Production 9815 0.18 0.18 0.16 0.15 0.20 0.19 0.24 0.17 0.18 0.15 0.15 0.20 0.18 0.24 -0.08 -0.02 0.04 -0.02 -0.03 -0.06 0.01 -0.07 -0.02 0.03 -0.02 -0.03 -0.07 0.01

Transportation and Mat. Moving 3080 0.22 0.22 0.26 0.28 0.28 0.29 0.27 0.22 0.22 0.25 0.28 0.27 0.29 0.26 -0.05 -0.08 -0.10 -0.15 -0.16 -0.19 -0.09 -0.03 -0.09 -0.10 -0.13 -0.13 -0.16 -0.06

1. New York, size seven establishments 

Area 

Name

Number

Estab/

OCC Cells

Average Relative Error 

( Simple average over sims of 

MEAN( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL )

Weighted Average Relative Error

 Simple average over sims of 

∑( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMPぶ 

Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

Weighted Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES

Balance of 

State 

Areas

6568 0.16 0.14 0.15 0.14 0.17 0.14 0.23 0.16 0.138 0.14 0.14 0.16 0.14 0.235 0.02 -0.03 0.02 0.06 -0.02 -0.02 0.11 0.02 -0.02 0.03 0.06 -0.02 -0.02 0.11

1547 0.20 0.25 0.20 0.20 0.25 0.23 0.35 0.2 0.251 0.2 0.2 0.25 0.23 0.355 0.12 0.08 0.05 0.13 0.04 0.04 0.35 0.12 0.08 0.05 0.13 0.04 0.04 0.35

5839 0.28 0.12 0.15 0.17 0.16 0.18 0.23 0.27 0.117 0.14 0.17 0.15 0.18 0.228 0.19 0.02 0.06 0.03 0.06 0.09 0.12 0.19 0.02 0.05 0.03 0.06 0.08 0.12

9604 0.23 0.22 0.20 0.19 0.22 0.20 0.39 0.22 0.215 0.18 0.2 0.21 0.18 0.389 0.04 0.13 0.14 0.07 0.14 0.07 0.28 0.06 0.12 0.12 0.06 0.13 0.04 0.26

5920 0.29 0.25 0.20 0.28 0.23 0.25 0.37 0.22 0.224 0.19 0.28 0.19 0.23 0.27 0.05 -0.12 -0.07 -0.06 -0.13 -0.20 0.06 0.00 -0.15 -0.09 -0.10 -0.13 -0.19 -0.07

Albany-Schenectady-Troy, NY 7056 0.23 0.17 0.20 0.19 0.18 0.18 0.25 0.2 0.159 0.18 0.18 0.16 0.15 0.25 -0.03 0.01 0.06 -0.02 -0.02 0.03 0.06 -0.04 -0.01 0.04 -0.02 -0.04 0.02 0.06

Binghamton, NY 434 0.10 0.14 0.16 0.12 0.22 0.17 0.29 0.1 0.141 0.16 0.12 0.22 0.17 0.293 -0.02 0.02 0.08 0.06 0.11 0.08 0.27 -0.02 0.02 0.08 0.06 0.11 0.08 0.27

Buffalo-Niagara Falls, NY 8500 0.31 0.18 0.19 0.31 0.23 0.24 0.39 0.29 0.182 0.18 0.3 0.23 0.25 0.368 0.03 0.04 0.06 0.03 0.08 0.13 0.21 -0.02 0.04 0.04 0.03 0.08 0.13 0.16

Elmira, NY 637 0.26 0.25 0.16 0.15 0.29 0.24 0.26 0.26 0.254 0.16 0.15 0.29 0.24 0.258 -0.10 -0.21 -0.15 -0.10 -0.27 -0.20 -0.24 -0.10 -0.21 -0.15 -0.10 -0.27 -0.20 -0.24

Glens Falls, NY 5315 0.08 0.16 0.14 0.12 0.18 0.18 0.27 0.08 0.157 0.14 0.12 0.18 0.18 0.268 0.02 -0.09 0.09 0.00 -0.06 -0.13 0.17 0.02 -0.09 0.09 0.00 -0.06 -0.13 0.17

Ithaca, NY 12588 0.23 0.24 0.25 0.30 0.34 0.30 0.27 0.23 0.242 0.25 0.3 0.34 0.3 0.27 -0.22 -0.22 -0.20 0.18 0.10 0.04 0.09 -0.22 -0.22 -0.20 0.18 0.10 0.04 0.08

Kingston, NY 1028 0.20 0.20 0.15 0.22 0.17 0.16 0.11 0.2 0.205 0.15 0.22 0.17 0.16 0.105 -0.18 -0.11 -0.05 -0.21 -0.06 -0.04 -0.04 -0.18 -0.11 -0.05 -0.21 -0.06 -0.04 -0.04

Nassau-Suffolk, NY Metro Div 9756 0.31 0.23 0.24 0.22 0.20 0.19 0.30 0.26 0.2 0.23 0.21 0.18 0.17 0.246 0.21 0.09 0.11 0.07 0.02 0.01 0.06 0.16 0.08 0.12 0.05 0.02 0.01 -0.01

New York-Wayne-White Plains, NY-N 13120 0.36 0.30 0.30 0.33 0.31 0.31 0.32 0.35 0.287 0.29 0.32 0.3 0.3 0.323 0.05 0.05 0.06 -0.03 0.00 0.03 -0.06 -0.02 0.01 0.00 -0.07 -0.05 -0.03 -0.12

Poughkeepsie-Newburgh-Middletown, 2271 0.17 0.11 0.17 0.14 0.11 0.13 0.15 0.18 0.113 0.16 0.15 0.11 0.12 0.151 0.07 -0.02 0.08 0.02 -0.04 -0.05 0.07 0.08 -0.01 0.09 0.03 -0.04 -0.05 0.07

Rochester, NY 8081 0.24 0.27 0.24 0.22 0.17 0.22 0.32 0.26 0.275 0.19 0.2 0.17 0.17 0.244 -0.11 -0.11 0.11 0.06 0.02 0.06 0.07 -0.17 -0.12 0.08 0.04 0.06 0.06 -0.03

Syracuse, NY 11489 0.24 0.27 0.22 0.18 0.28 0.31 0.26 0.23 0.255 0.21 0.17 0.27 0.31 0.256 0.09 0.07 0.05 0.01 0.11 0.13 0.14 0.09 0.07 0.05 0.01 0.12 0.12 0.15

Utica-Rome, NY 7982 0.10 0.14 0.14 0.15 0.13 0.11 0.21 0.1 0.135 0.14 0.15 0.13 0.12 0.215 0.00 -0.07 0.05 -0.07 -0.02 -0.04 0.15 -0.01 -0.07 0.05 -0.07 -0.03 -0.03 0.15
Table 1 

 OES Wage Imputation Simulation Study: Results of Six Experimental Models and the OES Estimator 

Louisiana, size four establishments 

OCC Title 

Number

Estab/

OCC Cells

Average Relative Error 

( Simple average over sims of 

MEAN( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL )

Weighted Average Relative Error

 Simple average over sims of 

∑( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMPぶ 

Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

Weighted Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES

ALL 67467 0.23 0.18 0.17 0.25 0.20 0.20 0.25 0.22 0.18 0.17 0.25 0.20 0.20 0.25 0.02 0.02 0.04 0.06 0.06 0.05 0.09 0.03 0.03 0.04 0.06 0.06 0.06 0.10

Managers 4089 0.39 0.30 0.32 0.38 0.30 0.33 0.41 0.39 0.30 0.32 0.38 0.31 0.33 0.41 0.05 0.02 0.09 0.11 0.11 0.13 0.15 0.05 0.02 0.10 0.12 0.11 0.13 0.13

Bus.&Fin. Operations 3270 0.54 0.33 0.39 0.63 0.39 0.49 0.72 0.54 0.32 0.39 0.64 0.38 0.49 0.73 0.30 0.17 0.25 0.43 0.21 0.32 0.50 0.31 0.16 0.26 0.44 0.21 0.34 0.52

Computer & Math 1029 0.37 0.43 0.40 0.32 0.40 0.46 0.46 0.34 0.44 0.38 0.33 0.41 0.43 0.47 0.10 0.24 0.20 0.06 0.21 0.34 0.25 0.09 0.30 0.18 0.08 0.27 0.32 0.26

Architecture and Eng. 5257 0.27 0.26 0.27 0.28 0.32 0.27 0.34 0.27 0.26 0.26 0.30 0.32 0.27 0.34 0.02 0.08 0.08 0.06 0.13 0.09 0.15 0.05 0.10 0.10 0.10 0.16 0.11 0.17

Life, Physical, and Social Science 1097 0.38 0.29 0.28 0.37 0.40 0.31 0.24 0.36 0.28 0.25 0.37 0.38 0.28 0.25 0.11 0.01 0.13 0.09 0.17 0.12 0.06 0.14 0.02 0.08 0.09 0.16 0.07 0.05

Community and Social Service 1938 0.35 0.30 0.25 0.37 0.38 0.33 0.36 0.40 0.32 0.27 0.41 0.43 0.32 0.38 0.16 0.12 0.02 0.22 0.22 0.15 0.25 0.23 0.17 0.06 0.28 0.29 0.18 0.28

Legal 1018 0.26 0.38 0.26 0.41 0.44 0.37 0.18 0.26 0.38 0.26 0.41 0.44 0.37 0.18 -0.05 0.20 0.16 0.25 0.33 0.25 0.04 -0.04 0.20 0.16 0.25 0.33 0.25 0.04

Education, Training, and Library 1152 0.28 0.10 0.15 0.39 0.17 0.17 0.33 0.28 0.10 0.15 0.39 0.17 0.17 0.33 0.26 0.06 0.10 0.35 0.13 0.13 0.26 0.26 0.06 0.10 0.35 0.13 0.13 0.26

Art, Design, Entertain., Sprts, Media 2380 0.34 0.21 0.22 0.33 0.29 0.36 0.37 0.34 0.20 0.21 0.33 0.28 0.36 0.37 0.07 -0.05 0.06 0.12 0.12 0.13 0.21 0.07 -0.06 0.06 0.13 0.11 0.12 0.21

Healthcare Prac. and Tech. 3528 0.25 0.25 0.24 0.24 0.26 0.24 0.32 0.25 0.25 0.25 0.24 0.26 0.24 0.32 0.11 -0.01 0.06 0.08 0.08 0.09 0.16 0.12 0.00 0.06 0.08 0.08 0.09 0.16

Healthcare Support 1476 0.21 0.17 0.17 0.22 0.18 0.19 0.24 0.21 0.17 0.18 0.21 0.18 0.19 0.24 -0.09 -0.05 -0.06 -0.12 -0.04 -0.06 -0.13 -0.09 -0.07 -0.07 -0.12 -0.04 -0.07 -0.13

Protective Service 1430 0.19 0.18 0.17 0.20 0.24 0.26 0.34 0.21 0.20 0.17 0.23 0.25 0.28 0.35 0.07 0.02 0.01 0.07 0.02 0.07 0.19 0.10 0.04 0.02 0.10 0.04 0.09 0.20

Food Preparation and Serving 4620 0.07 0.06 0.07 0.09 0.08 0.08 0.09 0.07 0.06 0.07 0.08 0.08 0.07 0.10 0.01 0.01 0.03 0.02 0.04 0.04 0.04 0.01 0.02 0.03 0.02 0.04 0.04 0.04

Building and Grounds, Cleaning and Main. 1003 0.18 0.10 0.09 0.18 0.09 0.12 0.17 0.18 0.10 0.10 0.18 0.09 0.12 0.17 0.09 -0.02 0.03 0.04 0.00 0.04 0.06 0.09 -0.02 0.03 0.04 0.00 0.04 0.07

Personal Care and Service 2435 0.18 0.14 0.11 0.20 0.14 0.14 0.17 0.18 0.15 0.11 0.21 0.14 0.14 0.17 0.00 0.00 0.01 0.03 0.02 0.02 -0.01 0.00 0.00 0.01 0.04 0.03 0.02 -0.01

Sales and Related 2463 0.44 0.23 0.22 0.50 0.26 0.24 0.67 0.46 0.22 0.22 0.51 0.24 0.24 0.75 0.14 -0.08 0.01 0.17 -0.04 -0.01 0.45 0.17 -0.08 0.02 0.17 -0.06 -0.01 0.51

Office and Administrative Spt. 6089 0.19 0.16 0.17 0.21 0.18 0.21 0.22 0.19 0.16 0.17 0.22 0.18 0.21 0.23 -0.05 0.00 0.02 -0.05 0.04 0.04 0.05 -0.05 0.00 0.03 -0.04 0.04 0.04 0.06

Farming, Fishing, and Forestry 322 0.35 0.71 0.15 0.23 0.28 0.18 0.20 0.35 0.71 0.15 0.23 0.28 0.18 0.20 -0.06 0.57 -0.02 -0.13 -0.15 -0.08 -0.10 -0.06 0.57 -0.02 -0.13 -0.15 -0.08 -0.10

Construction and Extraction 6636 0.24 0.22 0.20 0.24 0.22 0.21 0.22 0.24 0.22 0.20 0.24 0.21 0.21 0.22 -0.04 0.03 0.07 0.01 0.06 0.03 0.04 -0.04 0.04 0.08 0.01 0.06 0.03 0.05

Installation, Maint., and Repair 5411 0.29 0.20 0.17 0.35 0.22 0.22 0.32 0.29 0.20 0.17 0.35 0.22 0.21 0.31 0.02 0.02 0.01 0.07 0.06 0.04 0.12 0.02 0.02 0.01 0.07 0.07 0.04 0.12

Production 7187 0.27 0.22 0.19 0.29 0.22 0.23 0.25 0.26 0.21 0.18 0.29 0.22 0.22 0.25 -0.03 -0.04 -0.03 -0.01 -0.02 -0.02 0.08 -0.03 -0.04 -0.03 -0.02 -0.03 -0.02 0.07

Transportation and Mat. Moving 3637 0.28 0.19 0.18 0.31 0.22 0.21 0.33 0.23 0.20 0.18 0.28 0.23 0.22 0.30 0.08 0.10 0.08 0.13 0.11 0.09 0.13 0.03 0.10 0.08 0.09 0.11 0.09 0.10

Louisiana, size four establishments 

Area

Name

Number

Estab/

OCC Cells

Average Relative Error 

( Simple average over sims of 

MEAN( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL )

Weighted Average Relative Error

 Simple average over sims of 

∑( ABS ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMPぶ 

Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

Weighted Average Relative Bias

Simple average over sims of 

∑( ( WAGE_EST - WAGE_ACTUAL ) / WAGE_ACTUAL ) * EMP

∑ふEMP ぶ 

A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES A1 R1A R1A_r1 R1B R1C R1F OES

 | 2638 0.14 0.11 0.12 0.14 0.13 0.14 0.18 0.14 0.11 0.12 0.14 0.13 0.14 0.18 0.04 0.05 0.08 0.05 0.09 0.11 0.11 0.04 0.05 0.07 0.05 0.10 0.11 0.11

Balance of State Areas 3480 0.21 0.16 0.18 0.23 0.18 0.19 0.30 0.22 0.16 0.18 0.23 0.18 0.19 0.30 0.07 0.02 0.07 0.11 0.07 0.07 0.22 0.07 0.02 0.06 0.11 0.07 0.07 0.23

 | 5268 0.22 0.24 0.16 0.30 0.25 0.24 0.28 0.22 0.24 0.15 0.31 0.25 0.24 0.29 0.04 0.07 0.04 0.18 0.12 0.09 0.18 0.05 0.08 0.05 0.19 0.12 0.10 0.19

 | 6103 0.30 0.25 0.25 0.34 0.29 0.26 0.28 0.31 0.25 0.24 0.35 0.30 0.25 0.28 0.07 0.06 0.08 0.10 0.13 0.11 0.09 0.08 0.07 0.08 0.11 0.15 0.10 0.09

Alexandria, LA 3295 0.14 0.11 0.13 0.24 0.14 0.15 0.15 0.13 0.11 0.12 0.24 0.14 0.15 0.15 0.02 -0.01 0.03 0.12 0.04 0.04 0.08 0.02 0.00 0.03 0.13 0.04 0.05 0.08

Baton Rouge, LA 8771 0.22 0.19 0.17 0.25 0.20 0.20 0.26 0.22 0.19 0.17 0.26 0.20 0.20 0.26 0.01 0.01 0.03 0.07 0.04 0.03 0.10 0.01 0.00 0.03 0.07 0.03 0.02 0.10

Houma-Bayou Cane-Thibodaux, LA 6091 0.20 0.18 0.15 0.22 0.21 0.18 0.21 0.20 0.18 0.15 0.22 0.22 0.19 0.21 0.00 0.06 0.04 0.03 0.07 0.08 0.10 0.00 0.07 0.05 0.03 0.08 0.08 0.10

Lafayette, LA 6487 0.24 0.17 0.18 0.24 0.21 0.21 0.24 0.22 0.18 0.18 0.22 0.21 0.21 0.23 0.09 0.05 0.07 0.09 0.11 0.09 0.13 0.07 0.05 0.08 0.07 0.11 0.10 0.12

Lake Charles, LA 6163 0.18 0.12 0.12 0.19 0.15 0.17 0.21 0.18 0.12 0.12 0.19 0.14 0.17 0.22 -0.02 -0.05 0.00 -0.02 0.02 0.02 0.07 -0.01 -0.05 0.00 -0.01 0.02 0.02 0.07

Monroe, LA 3328 0.14 0.13 0.12 0.15 0.12 0.13 0.14 0.14 0.13 0.12 0.15 0.12 0.13 0.13 0.00 -0.04 0.01 0.00 0.02 0.01 0.03 0.00 -0.04 0.01 0.00 0.02 0.01 0.04

New Orleans-Metairie-Kenner, LA 9084 0.30 0.20 0.20 0.31 0.22 0.22 0.34 0.30 0.19 0.20 0.32 0.21 0.22 0.34 -0.01 0.01 0.02 0.01 0.02 0.01 0.05 0.00 0.01 0.02 0.01 0.02 0.01 0.05

Shreveport-Bossier City, LA 6759 0.21 0.19 0.18 0.23 0.19 0.20 0.22 0.21 0.19 0.19 0.23 0.20 0.20 0.22 0.05 0.05 0.06 0.06 0.07 0.08 0.07 0.05 0.06 0.07 0.07 0.08 0.09 0.07
Table 2 

OES Wage Imputation Simulation Study: Results of Six Models and the OES Estimator 

Simulation Variance 

1. New York, size seven establishments 

Percentage Employment Model

for which simulation 

variance is <= table entry A1 R1A R1A_r1 R1B R1C R1F OES

20 0.00 0.00 0.00 0.00 0.00 0.00 0.00

25 0.00 0.00 0.00 0.00 0.00 0.00 0.00

30 0.00 0.00 0.00 0.00 0.00 0.00 0.00

40 0.00 0.00 0.00 0.00 0.00 0.00 0.00

50 0.00 0.00 0.00 0.00 0.00 0.00 0.00

70 0.00 0.00 0.00 0.00 0.00 0.00 0.00

75 0.00 0.00 0.00 0.00 0.00 0.00 0.00

85 0.01 0.01 0.01 0.01 0.01 0.01 0.02

90 0.12 0.16 0.10 0.15 0.14 0.15 0.20

95 2.00 0.60 0.81 1.41 0.75 0.78 1.59

98 5.65 3.30 3.94 5.02 3.53 4.55 8.98

99 11.02 8.58 9.63 9.80 7.35 10.32 16.89

99.5 20.21 14.99 15.22 16.54 14.63 15.15 30.82

100 1110.34 1790.14 1513.22 1513.22 1824.61 1841.19 1267.13

2. Louisiana, size four establishments 

Percentage Employment Model

for which simulation 

variance is <= table entry A1 R1A R1A_r1 R1B R1C R1F OES

20 0.00 0.00 0.00 0.00 0.00 0.00 0.00

25 0.00 0.00 0.00 0.00 0.00 0.00 0.00

30 0.00 0.00 0.00 0.00 0.00 0.00 0.00

40 0.00 0.00 0.00 0.00 0.00 0.00 0.00

50 0.00 0.00 0.00 0.00 0.00 0.00 0.00

70 0.00 0.00 0.00 0.00 0.00 0.00 0.00

75 0.00 0.00 0.00 0.00 0.00 0.00 0.00

85 0.11 0.08 0.08 0.15 0.08 0.11 0.17

90 0.48 0.36 0.32 0.58 0.37 0.41 0.64

95 2.38 1.53 1.31 2.39 1.72 1.74 2.60

98 9.03 5.99 4.95 10.03 7.98 7.57 9.70

99 20.94 13.00 11.89 23.80 17.50 14.31 22.66

99.5 34.78 24.42 25.39 40.60 35.87 25.32 47.30

100 2207.65 1620.61 1701.49 2083.04 1622.91 1184.54 673.38