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Imputing for Extraordinary Sample Events: A Story of Targeted 

Donor Pools and Administrative Data

Bradley D. Rhein

U.S. Bureau of Labor Statistics, 2 Massachusetts Ave., NE 

Washington, DC 20212

Proceedings of the 2023 Federal Committee on Statistical Methodology (FCSM) Research Conference, 

October 24-26, 2023

Abstract

The Current Employment Statistics (CES) program produces monthly employment estimates by subnational 

geography and industry through a survey of about 666,000 establishments. Occasionally, a large-scale event, such 

as a hurricane, occurs near the survey reference period, significantly affecting data collection for that month, and 

challenging an implicit missing-at-random assumption in the estimator. Several methods have been activated to 

catch the ensuing employment drop, though none of these methods account for the nonresponse directly. This paper 

proposes the potential use of a random cold deck imputation approach, constructing a targeted donor pool from a 

similar circumstance occurring in past administrative data from the Quarterly Census of Employment and Wages 

(QCEW) program. The author explores using a donor pool from an earlier hurricane to impute for missing reporters 

due to hurricanes in 2017 and 2018.

1. Introduction

Large-scale, or extraordinary, events, such as a hurricane, may cause employment movements at the state and area 

level that are difficult to capture in estimation due to increased nonresponse. While the Current Employment Statistics 

(CES) estimators account for missing-at-random (MAR) nonresponse implicitly, increased nonresponse due to an 

extraordinary event challenges the usual assumption of missingness – that is, the increased nonresponse is not missing 

at random because it is a consequence of an extraordinary event.

This paper explores a possible imputation solution to account for the nonresponse caused by an extraordinary event. 

The next section gives a brief background of the survey, followed by brief descriptions of the sampling, estimation, 

and variance methods for the survey. Next, a discussion of the research question, an elaboration of the proposed 

methods, and results follow. Conclusions and future work wrap up the paper.

2. Background Information on CES

The CES program [1] produces detailed industry estimates of employment, hours, and earnings of workers on nonfarm 

payrolls. Each month, the Bureau of Labor Statistics (BLS) collects data through the CES survey, which includes 

about 122,000 businesses and government agencies and represents approximately 666,000 individual worksites. The 

sample is drawn from a sampling frame of unemployment insurance (UI) tax accounts for roughly 12 million 

establishments (covering about 97% of all US jobs).

CES publishes estimates for all 50 states, the District of Columbia, Puerto Rico, the U.S. Virgin Islands, and about 

450 metropolitan areas and divisions. BLS releases these estimates around the third week of the month, along with 

the Local Area Unemployment Statistics (LAUS) estimates. Each publication includes a revision of the previous 

month’s estimates as more sample data becomes available between releases.
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CES benchmarks the state and area employment data on a yearly basis, primarily using information from the Quarterly 

Census of Employment and Wages (QCEW) [2]. The process creates benchmarked employment levels for all months

up through September, with a publication of the updated levels and benchmark revisions to the estimates occurring in 

mid-March the following year.

3. Overview of the CES Sampling, Estimation, and Variance Methods for States and areas 

The CES Handbook of Methods [3] elaborates further on each of the sections below.

Sample Design

The CES draws a stratified, simple random sample of establishments from the QCEW, an administrative data source 

collected quarterly through unemployment insurance accounts and covering about 97% of the jobs in the US economy. 

Stratification is by state, aggregate industry, and employment size class; selection is with optimum allocation.

The North American Industry Classification System (NAICS) [4] defines industries by 6-digit codes. CES may 

combine one or more NAICS industries into a single CES industry code to ensure complete coverage of all nonfarm 

businesses and to prevent disclosure of payroll data for individual establishments.

Industry codes and employment size class definitions appear below:

Table 1: Industry codes and employment size classifications [3]

Estimation

CES features two types of estimators for private industry employment series: sample-based and a model. As a time

series, CES relies on a weighted link relative - the ratio of current month employment to prior month employment -

to estimate the over-the-month (OTM) change, building off the prior month’s employment level. The employment 

estimate also includes a series-level forecast of the net business births and deaths [5] and an adjustment for noncovered employment for religious organizations (part of the other services industry). The equation for the samplebased estimator is below:

Equation 1: Sample-based Estimator
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Many series do not qualify for a sample-based estimator due to small sample sizes, low average response rates, or 

modest employment levels. For these series, a model estimator determines the current month employment level using 

information from a variety of sources, including the sample, the relevant group’s state/area/series/month trends, staterelated effects, industry effects, and historical state/area/series information. The model [6] employs a regression tree 

to determine state/area/series groupings, an unsupervised clustering mechanism to add industry (aka domain) effects, 

and variances to establish the influence of each component. The small area model equation is below:

Equation 2: Small Area Model Estimator
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All estimators feature outlier detection, non-sample events, seasonal adjustment, and key non-respondent (KNR) 

imputation.

A routine identifies outliers during the estimation process. Depending on the degree of outlierness, a sample unit

either becomes self-representative or significantly downweighted, dampening its influence on the estimate. Selfrepresentative outliers are not included in the weighted link relative.

Unique business closures, strikes, or layoffs not caught by the sample can be added as non-sample event adjustments. 

CES verifies the occurrence of the event, the number of employees affected, and the timing by collaborating with state 

partners. Non-sample events must occur during the survey reference period. 

CES uses X-13ARIMA-SEATS software [7], developed and maintained by the U.S. Census Bureau, to seasonally 

adjust estimates. Seasonal adjustment eliminates the piece of the series that is attributable to normal seasonal variation, 

allowing for the observation of the underlying employment trend [8]. Seasonally adjusted series are published for 

selected nonfarm payroll employment series.

On occasion, large, seasonal, in-sample reporters fail to submit data for a month that, historically, has a seasonal 

movement. Such reporters, or key non-respondents (KNRs), have important seasonal movements that would be 

noticeable if missing from estimation. To account for these movements, should any KNRs fail to submit data, CESimputes the over-the-month employment change using administrative values from the previous year.

Variance Estimation

Reliability measures for CES employment estimates are published on the BLS website for statewide aggregate 

industries and MSA total nonfarm employment [9]. Many estimates have small domains, causing variance estimates 

to be quite unsettled. To stabilize the variances, CES uses a model-based Generalized Variance Function (GVF) to 

calculate a measure of error for employment estimates [10]. 

4. Overview of the Research Question

Occurrences of extraordinary events near the reference period tend to increase nonresponse rates and challenge the 

missing at random assumption inherent to statistical surveys – that is, the extraordinary event directly causes some of 

the nonresponse. While this paper focuses on hurricanes, there are other types of extraordinary events as well. Future 

work could investigate solutions to floods, wildfires, tornados, snowstorms, and other extreme weather. 

There are plenty of circumstances that could challenge an establishment’s ability to submit data in a month where an 

extraordinary event occurs. Some storefronts could be boarded up and temporarily closed. Retail, leisure, and 

hospitality businesses tend to fall into these scenarios. Areas may have been evacuated. Construction projects could 

be delayed or postponed. However, some industries may add jobs, such as relief workers or cleanup crews belonging 
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to the administrative, support, and waste services industry. For CES, if employees were paid during the reference 

period, even if the business closes temporarily, they are considered employed.

Currently, CES takes the following actions in the case of an extraordinary event:

• Monitoring response rates

• Watching for last-minute microdata submissions

• Altering the state/area/industry groupings used in model estimation (perhaps)

• Relying on the sample more (or entirely) in modeled series

Response rates tend to decrease in a month with an extraordinary event. Economists that monitor data collection may 

detect changes in response rates at the county level. Matching low response rates at a county level with areas 

designated as disaster zones may help identify geographic areas to monitor. Meanwhile, the monthly production cycle 

allows for a brief window to include additional microdata submittals before the Wednesday after calculating estimates 

(shown below). Estimates must be finalized by Wednesday (week 2) to ensure that seasonal adjustment and 

publication activities finish in time for the release.

Table 2: Example Production Cycle Calendar

While the model estimator usually determines state, area, and industry groupings by using a regression tree, allowing 

small domains to borrow information from similarly trending domains, a model feature permits special groupings of 

state, area, and industry data if desired. In the case of an extraordinary event, affected states and areas may benefit 

from an isolated grouping, away from state, area, and industry combinations that are not experiencing such an event. 

Isolated groups could depend on county-level information, designated disaster areas, or simply states and areas near 

the site of the extraordinary event.

The existing sample-based estimator routinely captures current labor market trends due to a combination of sample 

design, cooperation of businesses in submitting data, coordination of field offices, and rigorous analysis and cleaning 

of microdata by economists working both in the region and at the BLS national office in Washington, DC. 

Models, however, tend to perform well during “normal” times when there are no shocks to the system. To counteract 

this tendency during an extraordinary event, CES may alter the model to increase the reliance on the sample. While 

the model estimator may decrease the influence of the sample in a month containing an extraordinary event, a CES 

analyst may review the microdata, consider the sample to be representative, and choose to place more emphasis on 

the sample data (or rely on the sample entirely). As another fallback, the analyst may revisit that choice for the revised 

release of estimates, after several more weeks of data collection have taken place.

There can be cases that are longer term or have especially significant shocks to the labor market, such as the COVID19 pandemic or Hurricane Katrina. In these cases, there are more severe solutions available for use, including the use 

of reported zeros, excess zeros, manual adjustment factors, UI claims, and modifying the business birth-death

methodology temporarily.

Establishments that report zero employment in the current month or prior month do not contribute to the calculation 

of estimates since the birth-death forecast captures these movements. However, when Hurricane Katrina made 

landfall, reported zeros were used in estimation. Post-Katrina analysis revealed the method overstated the employment 

drop [11].
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Since using reported zeros in estimation risks a too heavy-handed intervention, using “excess zeros,” which account 

for a baseline frequency of reported zeros, became available as an upgrade in methodology. The use of Excess Zeros

(EZ) involves including establishments that report zero in the current or prior month, but then downweighting the 

effect of such a movement by applying the following ratio for each state, area, series, and month combination. 

Calculations occur separately for a reported zero in the current month and prior month. The ratio accounts for the 

number of zeros in excess of historical averages for a given state, area, series, and month combination.

Equation 3: Excess zero downweight formula

EZ Downweight =

(number of reported zeros − historical average number of reported zeros)

number of reported zeros

The use of manual adjustment factors and alterations to the business birth-death forecast were explored in a Monthly 

Labor Review article written by Steven Mance [12].

Note that current methods do not address the scenario of not missing at random, which the author assumes is causing 

at least some of the nonresponse when an extraordinary event occurs. To clarify, the assumption is that the 

extraordinary event affects the act of submitting data for some non-respondents. So, the nonresponse may be due to 

numerous factors (too busy, evacuated, closed, or temporarily closed) that may or may not be related to the number 

of employees on the payroll during the reference period in a month with an extraordinary event. The proposed method, 

described in the next section, targets both non-respondents and donor pools to help ensure that the imputation solution 

applies to nonresponse that is not missing at random.

5. Exploring an Imputation Solution

Due to the nature of extraordinary events, selection of both the recipients of imputation and the donors providing the 

imputed values would ideally reflect the unique circumstance. 

Defining the recipients of imputation

The last section notes that during an extraordinary event some nonresponse is not missing at random. One strategy 

for determining recipients that are not missing at random depends on whether the non-respondent “usually” submits 

data in time for preliminary estimates. Define these Usuals as establishments that have provided data for at least five 

out of the last six months in time for preliminary estimates (the earliest release of CES data). Such a definition 

strengthens the assumption that The Usuals’ failure to submit data was due to the occurrence of an extraordinary event.

Before imputing values for recipients at the establishment level, a couple modifications must occur. CES samples by 

UI account (stratified by state, aggregate industry, and size), assigning sample weights and employment size classes. 

Many establishments could fall under one UI account. Since imputation is set to occur at the establishment level, 

there is a need to modify the sample weights and employment size classes for all Usuals. As a result, The Usuals

receive a substitution of appropriate sample weights and a reclassification of employment size class based on the 

individual establishment’s employment level. 

Determining the donor pool

For the donor pool, consider historical data from the source of the CES sampling frame: the Quarterly Census of 

Employment and Wages (QCEW). This administrative data source contains monthly microdata, reported quarterly, 

for establishment employment and wages (based on total payroll). Establishments in the QCEW have NAICS 

designations, state, county, and various other business characteristic information. The QCEW also covers about 97% 

of the jobs in the US economy. These features make the QCEW an excellent data source for donor pools.
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Since The Usuals were selected with the assumption that their act of submitting data was affected by the extraordinary 

event, the donor pool must be targeted in a similar way – by determining which historical events are similar to the

extraordinary event affecting The Usuals. Upon finding an appropriate match in circumstances, the administrative 

data from the past forms a targeted donor pool from which to determine values for imputation.

Hurricanes could be measured and compared in various ways. The National Hurricane Center and the Central Pacific 

Hurricane Center [13], divisions of the National Weather Service that track and predict tropical weather systems, 

classify hurricane intensity along the path of the storm using the Saffir-Simpson Scale [14]. News reporting on 

hurricanes mention areas along the path and the location of where the storm makes landfall. Affected areas could be 

mined for population density (number of workers by county), industry composition (number of workers for each 

aggregate industry), geographic details (flood plains, mountains, forest areas, gulf, or ocean coast), and disaster 

designations. Using this information, for example, the effects of a past hurricane (e.g., Hurricane Irma on Naples, FL) 

could serve as a donor pool for a set of Usuals from a more recent hurricane (e.g., Hurricane Ian on Punta Gorda, FL).

The following table lists viable donor pools from recent hurricanes. Note that Hurricane Ian, from October of 2022, 

would be a good future addition to the list.

Table 3: Donor Pool Examples

Since the donor pool source is administrative, the number of available donors is vast and includes all employment 

sizes, NAICS designations, and county information. Actual behavior, on an establishment level, from a past 

extraordinary event is available for use as a direct donor to a non-respondent of interest. With this setup, the author 

suggests that there is no need to synthesize or model imputed values.

Narrowing the imputation method

There still needs to be a method to match a donor to a recipient. Consider two imputation methods used frequently in 

practice: random cold deck (RCD) and nearest neighbor (NN) from a cold deck. Since the donors arrive from an 

outside data source, the QCEW, the “deck,” or list of potential donors, is a cold deck. Both methods utilize donor-torecipient matching, transferring actual values from a donor establishment to an establishment-level recipient. The use 

of a specific imputation cell establishes the assumption that the donor and recipient are similar and behave similarly 

under similar circumstances. In this case, both donors and recipients have similar establishment characteristics and 

are subject to similar extraordinary events.
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Effective cold deck imputation methods rely on a strict definition of the imputation cell, a sufficiently large donor 

pool, a modest need for imputed values, and the use of multiple imputation to avoid bias [15]. The setup for an

extraordinary event arguably meets these qualifications due to a vast number of donors available (administrative data) 

for relatively few recipients (The Usuals), one missing value of interest (establishment employment), and a specific

imputation cell definition consisting of the affected area, full 6-digit NAICS designations, and eight employment size

classes. If zero donor-to-recipient matches exist under the initial imputation cell definition, a potential fallback could 

use the 4-digit NAICS designation and potentially a more aggregate grouping of employment size. There is some 

debate in the literature over how many multiple imputations to perform; the author briefly investigates a couple 

scenarios.

Using nearest neighbor imputation involves specifying an additional measure to compare the “distance” between a 

recipient and potential donor establishment. Note that the imputation cell ensures that the matching process already 

narrows the available donors by area, NAICS designation, and employment size class. However, size class is a range 

of “distances” – finding the closest match in employment level is one measure that could determine the nearest 

neighbor. For example, both the donor and recipient could be establishments with exactly 18 employees in the month 

prior to the month of interest. Again, the assumption is that similarly sized establishments behave the same under 

similar circumstances.

Since the donor pool is an administrative source, there could be many donors qualifying as nearest neighbors, perhaps 

with the same exact employment as the recipient. For these cases, a random number becomes the deciding factor, 

leaving the recipient with just one nearest neighbor. As a precaution against biasing the variance by using a single 

donor many times, each donor establishment may only contribute imputed values to only one recipient regardless of

how many times the process chooses a given donor as the nearest neighbor for various recipients. 

Examples of imputed values for some Usuals appear below, using Corpus Christi, TX from Hurricane Harvey as the 

donor pool. Ten and twenty-five multiple imputations tended to produce very similar results in terms of imputed value 

distribution and variance for all test cases. Multiple imputation results with high volatility were examined further for 

issues with donor values and were removed from consideration when necessary.

Graph 1: Multiple Imputation Results for Usuals in Punta Gorda, FL
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Establishment 1 falls into size class 2 (10 to 19 employees) and had a tight dispersion of imputed values as illustrated 

by the narrow quartile range. There was at least one extreme outlier found in 25 multiple imputations, having a 

weighted over-the-month (WOTM) change of -1,500. Note that while this outlier has little effect on the mean of 25 

imputations, such an outlier could lead to larger-than-desired volatility if chosen by the nearest neighbor approach. 

Establishment 2 falls into size class 4 (50 to 99 employees) and had a slightly larger quartile range. Both companies 

have narrow distributions of imputed values that support the use of a mean as the final imputed value.

Graph 2: Multiple Imputation Results for Usuals in Cape Coral, FL

Nine Usuals in the leisure and hospitality industry were evaluated for Cape Coral, FL in the month of Hurricane Ian, 

October 2022. While there were some outliers, and most outliers were decidedly negative, the twenty-five multiple 

imputations seem to find means with small overall deviations for each Usual. 

Once imputation is complete for all recipients in a series, the WOTM values become the input for a calculation of an 

estimate adjustment. Estimate adjustments are applied directly and account for the estimator, sample circumstances, 

and model inputs (if appropriate). 

Implementation of the methodology

To illustrate the implementation of this methodology, consider the real-time runup to Hurricane Idalia, an

extraordinary event that made landfall in Florida at the writing of this paper (October 2023). The category 3 hurricane 

made landfall near Perry, FL on August 30, 2023, causing significant damage to northern Florida. Along the way to 

Perry, FL, there was notable damage due to a storm surge near Tampa, FL where the hurricane reached its peak 

strength as a category 4 hurricane [16].

While August 30 is well past the reference period for August, the effects of the hurricane could possibly show up in 

the September job numbers for parts of Florida and perhaps Georgia. As a result, CES began monitoring microdata 

reports for the September reference period. Preliminary estimates for September were set to be run on October 4, so 

by the last week of September the following actions were taken:

• Monitored response rates
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• Read news reports

• Checked for FEMA disaster designations

• Scanned for any Usuals

Although National Guard members were deployed and a federal emergency declaration was issued for the state of 

Florida, the response rates and microdata monitoring did not turn up any collection abnormalities compared to recent 

months. A search for Usuals came up empty as well. 

If significant Usuals had been found, a search of donor pools would be the next step. After determining a donor pool, 

the imputation method and estimate adjustment calculations would produce results for consideration.

6. Analysis of the Empirical Results

The following test cases were explored, using the imputation methodology described above. Performance of the 

imputation methodology was evaluated by measuring the improvement (or worsening) in the percent revision – the 

percent difference between the CES published estimate and the benchmarked employment. CES published estimates 

can be found in archived news releases [17] while CES benchmarked employment can be found using the BLS data 

tool [18]. The equation for calculating the percent revision appears below.

Equation 4: Calculating the percent revision

Percent Revision =

(CES Published Estimate − Benchmarked Value)

Benchmarked Value

Circumstances with both large and small revisions were of interest, as the imputation method ideally must not only 

improve the capture of employment drops when such drops occur (i.e., Irma), but also avoid exaggerating employment 

drops that did not happen (i.e., Elsa). Note that revisions for Hurricane Ian are preliminary (based on published data 

by QCEW), as CES has not yet benchmarked employment for October 2022. All other revisions could be found using 

archived press releases and the BLS data tool.

Table 4: Hurricane Test Cases

In September 2017, Hurricane Irma made landfall near the Naples, FL metropolitan area, causing considerable damage 

and a temporary decline of about 10,000 workers in various industries [19]. Job losses at the total private industry 

level appear below, illustrating the noticeable difference between the CES estimate – a drop of 2,000 jobs [20] – and 

the benchmark value for September of 2017. A downward revision of about 6.7% was found after completing the 

benchmark. Note that the confidence intervals are crudely calculated – prior month CES published values are assumed 

correct - and were added to give the reader a sense of the variance.
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Graph 3: Effect of Hurricane Irma on Naples, FL

At the industry level, consider the following examples.

Graph 4: Effect of Hurricane Irma on Retail Trade in Naples, FL

Retail trade had a noticeable downward revision of about 5% for September 2017. The sample-based estimator 

operated below the benchmark level for most of the year, up until August 2017. Some employment drop was captured 

in September. Could the imputation method provide a more accurate result?

Using Panama City, FL, an MSA near the landfall of Hurricane Michael (October 2018, category 5), as a donor pool, 

three Usuals were imputed for, and an estimate adjustment was calculated and added, as illustrated below. Panama 

City during Hurricane Michael was selected as the donor pool due to its employment size, similar location traits, and 

hurricane intensity at the time of landfall.
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Graph 5: Imputation Results for Retail Trade, Naples, FL

With 25 multiple imputations for each of the three Usuals, the random cold deck (RCD) method captured a further 

drop in employment for September 2017, decreasing the downward revision from 5% to 3.3%. The nearest neighbor 

(NN) method did not provide any results for retail trade.

As another example, consider the education and health services industry in Naples, FL. By August there was already 

a slight downward revision, which expanded notably to about 5.4% in the month affected by Hurricane Irma. In 

Naples, FL, this industry typically has seasonal movements, and the CES model estimate captured the customary 

seasonal increase in September 2017, as shown by the upward movement in the green line below. 

Graph 6: Effect of Hurricane Irma on Education and Health Services in Naples, FL
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Both imputation methods were able to catch more of the employment drop in September, imputing for four Usuals 

and continuing the use of Panama City during Hurricane Michael as the donor pool. Revisions improved to about 

3.5% and 3.8% utilizing the random cold deck and nearest neighbor imputation methods, respectively.

Graph 7: Imputation Results for Education and Health Services, Naples, FL

It is worth noting, for the purpose of the next example, that most hurricanes tend to strike between August and October, 

a time of the year that is furthest from the annual benchmark for CES at the state and area level. While the estimates 

and benchmark values line up perfectly in the previous September, by the time the hurricane season approaches, the 

estimates have been potentially deviating from the benchmark level for ten to twelve months. Such deviations are 

realized and measured as percent revisions once the employment has been benchmarked.

The next example illustrates the complications of attempting to capture an employment drop while operating under a 

notable pre-existing revision. Leisure and hospitality had about a 7% revision (see the red bracket below, the 

difference between the black and green line) in August of 2017, and this pre-existing revision “helped” the CES 

estimator nearly perfectly capture the benchmarked employment level after the drop caused by Hurricane Irma.

Graph 8: Effect of Hurricane Irma on Leisure and Hospitality in Naples, FL
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There were four Usuals in leisure and hospitality, and the estimate adjustment calculated from the imputed values 

drove the revision to increase significantly. However, considering the capture of the over-the-month change, using 

the imputation method was quite an improvement. Notice how the slope of the benchmark line (arrow) compares to 

the slope of the circled, imputed over-the-month change. CES reports over-the-month changes, and so while the postimputation employment level is noticeably lower than the benchmark value for September, the over-the-month change 

has been captured quite accurately.

Graph 9: Imputation Results for Leisure and Hospitality, Naples, FL
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All results for Naples, FL appear below. Only four industries had non-negligible imputation effects, three of which 

notably improved revisions and one that did not (though, as discussed above, the over-the-month change was captured 

more accurately). The state of Florida had 1,265 Usuals but zero imputation effects due to estimate adjustments 

offsetting each other. A statewide revision of 1.2% (yellow highlight) is notable - about 116,000 workers - and well 

outside the 95% confidence interval for September 2017. An improvement in estimates at the MSA level could filter 

up to aid the statewide estimate values.

Table 5: Imputation Results for Industries affected by Hurricane Irma in Naples, FL

Other results appear below. Cells highlighted in yellow identify cases with somewhat small revisions where there 

may be no need for further imputation effects (and none were found). Hurricane Ian was recent enough that CES 

benchmark data was not yet available – revisions shown here are preliminary, based on fourth quarter data published 

by the QCEW. Blue highlights identify series with model estimators that were plausibly switched to sample-based 

estimators as a result of sufficient sample representation, response rates, and conflicting historical trends that the 

model happened to prioritize (much like the education and health services example in Naples, FL). In a couple of 

cases, multiple donor pools were used, each finding similar results.

Table 6: Imputation Results for Other Hurricane Test Cases

Note that all imputation effects improved revisions, though effects were only found for some industries. Overall, the 

random cold deck found more results due to the stability of using an average among multiple imputations. Nearest 

neighbor results tended to be much more volatile and often found that the nearest neighbor donor selected had zero 

over-the-month change.

6. Summary of the Results

There appears to be some reduction in revisions with the use of the proposed imputation methods. The random cold 

deck provides more imputation effects compared to the nearest neighbor method, mostly due to the use of multiple 
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imputations that have a habit of centering nicely around a mean imputed value. More time, practice, and additional 

donor pools will likely improve results.

Future work could focus on finding more statistically sound methods for choosing a donor pool, further analysis of 

the variance effects, both for imputed values and post-adjusted estimate values, addressing the concern of capturing 

the recovery in the months after an extraordinary event, and investigating the use of imputation for other events, such 

as wildfires, tornados, flooding, snowstorms, and other extreme weather events.

References

[1] CES State and Area, www.bls.gov/sae

[2] Quarterly Census of Employment and Wages (QCEW), www.bls.gov/cew

[3] CES-SA Handbook of Methods, www.bls.gov/opub/hom/sae/

[4] North American Industry Classification System, https://www.census.gov/naics/

[5] Mueller, Kirk, “Impact of business births and deaths in the payroll survey,” Monthly Labor Review, May 2006, 

https://www.bls.gov/opub/mlr/2006/05/art4full.pdf.

[6] Gershunskaya, Julie, Savitsky, Terrance D, “Bayesian nonparametric joint model for point estimates and 

variances under biased domain variances,” November 2019, https://www.bls.gov/osmr/researchpapers/2019/st190020.htm.

[7] The X-13ARIMA-SEATS software is available on the U.S. Census Bureau website at 

https://www.census.gov/data/software/x13as.html

[8] More information on the seasonal adjustment process for CES National can be found at this link -

https://www.bls.gov/web/empsit/cesseasadj.htm. CES-SA uses a 2-step process, Stuart, Scott, Stamos, George, 

Sullivan, Thomas, Chester, Paul, “Seasonal Adjustment of Hybrid Economic Time Series,” 

https://www.bls.gov/osmr/research-papers/1994/pdf/st940350.pdf

[9] CES reliability information, https://www.bls.gov/sae/additional-resources/reliability-of-state-and-areaestimates.htm

[10] Gershunskaya, Julie, Dorfman, Alan H., “Calibration and Evaluation of Generalized Variance Functions,” 

October 2013, https://www.bls.gov/osmr/research-papers/2013/pdf/st130050.pdf.

[11] Garber, Molly, Unger, Linda, White, James, Wohlford, Linda, “Hurricane Katrina’s effects on industry 

employment and wages,” Monthly Labor Review, August 2006, https://www.bls.gov/opub/mlr/2006/08/art3full.pdf

[12] Mance, Steven, “Estimating state and local employment in recent disasters – from Hurricane Harvey to the 

Covid-19 pandemic,” Monthly Labor Review, April 2021. 

https://www.bls.gov/opub/mlr/2021/article/pdf/estimating-state-and-local-employment-in-recent-disasters-fromhurricane-harvey-to-the-covid-19-pandemic.pdf

[13] National Hurricane Center and Central Pacific Hurricane Center, https://www.nhc.noaa.gov/

[14] Saffir-Simpson Hurricane Scale, https://www.nhc.noaa.gov/aboutsshws.php
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[15] Discussion in section 7.3, conclusion in section 9; Andridge, Little. 2010. A Review of Hot Deck Imputation for 

Survey Non-response. International Statistical Review, April 2010, 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3130338/

[16] NOAA report on Hurricane Idalia nearing landfall, 

https://www.nhc.noaa.gov/archive/2023/al10/al102023.public.015.shtml

[17] CES News Release archive, https://www.bls.gov/bls/news-release/metro.htm

[18] CES data tool, https://www.bls.gov/sae/data/

[19] This drop could be found using the CES data tool (https://www.bls.gov/sae/data/) or QCEW data tool 

(https://www.bls.gov/cew/data.htm)

[20] CES News Release for September 2017, https://www.bls.gov/news.release/archives/metro_11012017.htm

Note: Any opinions expressed in this paper are those of the author(s) and do not constitute policy of the Bureau 

of Labor Statistics.