Business Births and Deaths

 28 Monthly Labor Review May 2006

Business Births and Deaths

Impact of business births and

deaths in the payroll survey

The CES probability-based sample redesign accounts

for most business birth employment

through the imputation of business deaths,

with the remaining portion estimated by a net birth/death model

Kirk Mueller

Kirk Mueller is a

supervisory

statistician in the

Division of Current

Employment

Statistics, Bureau of

Labor Statistics.

E-mail:

mueller.kirk@bls.gov

T

he Current Employment Statistics (CES) survey, conducted by the Bureau of Labor Statistics (BLS), is a monthly survey of more than

400,000 business establishments. The CES program

provides estimates on employment, hours, and earnings by industry detail for the Nation, States, and

metropolitan areas. The CES is widely considered

one of the most timely and accurate economic indicators published by the Federal Government.

The CES sample-based employment estimates

for March of each year are benchmarked, or reanchored, annually to the March universe count

derived principally from the Quarterly Census of

Employment and Wages (QCEW) program. These

QCEW population counts are much less timely than

sample-based estimates and are used to provide

an annual point-in-time census for employment.

For national series, only the March sample-based

estimates are replaced with the population counts.1

BLS completed a comprehensive redesign of the

CES sample in 2003, changing the survey from a

quota-based sample to a probability-based sample.2

The probability-based sample redesign addressed

one of the major limitations of the previous quotabased sample: the absence of a method to directly

measure new business births. The new probability-based sample accounts for most business birth

employment through the imputation of business

deaths, with the remaining portion estimated by a

net birth/death model that calculates the effect of

the imputation, measures the imputation error, and

generates a forecast of this error to adjust the current estimate.

With the introduction of the redesign, many

questions have arisen with respect to the new

model-based estimation of the net of births and

deaths. This article discusses the underlying assumptions of the model and the rationale behind

them. It also discusses the reasons why the total

accounting for business births is cyclically sensitive, in spite of the use of the forecast net birth/

death values. Lastly, it draws comparisons between the bias adjustment model of the quota

sample design and the net birth/death model of the

probability sample design. The models differ in

the portion of the population that they are meant

to measure.

Probability sample design

From its inception in the 1930s until the redesign,

the payroll survey was collected as a quota-based

sample. A bias adjustment model was used to account for the employment movement each month

not captured by the sample, including employment

growth because of the birth of new establishments.

Over time, both internal and external reviews of

the CES program concluded that a probabilitybased sample would benefit the program by introducing a more standard survey design and decreasing the reliance of model-based adjustments. After several years of research, BLS began in June

2000 to implement in the CES a probability-based

sample, phased in by industry. This process was
Monthly Labor Review May 2006 29

completed with the 2002 benchmark release in June 2003,

when the last industry was converted to a probability basis.

During the redesign phase in period, BLS conducted production tests of the new sample design and made parallel

estimates each year for industries prior to their official implementation with the subsequent benchmark. The new survey

design includes both the new sample composition and the

use of a two-step process to account for the employment associated with business births. This process first imputes a

portion of the birth employment from the employment associated with business deaths. The second step models the historical difference between the imputation and the actual relationship between business birth and business death employments; this step is referred to as the net birth/death model.

 The establishments that make up the population of interest for the CES can be broken up into three segments relative

to a benchmark month. Those segments are 1) establishments

that continue to employ workers after the benchmark, 2) establishments that go out-of-business after the benchmark, and

3) establishments that begin to employ workers after the

benchmark. With the probability sample implementation, the

entire population of establishments that are in business in the

benchmark month is appropriately represented for the period from which the sample is selected. As a result, the

sample accounts for the first two segments—establishments

that are continuing in nature and establishments that go out

of business. The population employment for these units is

moved forward through the use of weighted link relative estimation. If it is assumed that there is little difference in the

response rates between the continuing units in the sample

and the units that go out of business in the sample, then the

monthly estimate based on the establishments in the sample

should appropriately capture the employment movements

within these two segments of the universe of establishments.

(The accuracy of the assumption of similar response rates is

addressed later in the article.) Accounting for the third segment—establishments that are births—still requires additional steps.

To understand how the employment estimates are moved

forward with the weighted link relative, it is necessary to

consider the form of the estimator. The basic formula for

estimating all employees is:

( )

( )

























×

×

= ×

∑

∑

i

i p i

i

i c i

p

c

w ae

w ae

AE AE

,

, ^ ^

where

ÂEc = estimate of all employees for the current month

ÂEp= estimate of all employees for the previous month

i = the i-th sample unit

wi= the weight for the i-th sample unit

aec,i = i-th sample unit that reports for the current month

aep,i = i-th sample unit that reports for the previous month

The estimator requires that the business reports data for

both the previous and current months if its data are to be

used. This is referred to as a matched sample. This estimator uses the trend in the matched sample to move the previous month’s estimated employment forward.

As mentioned previously, the third segment of the CES

population of interest is establishments that open after the

benchmark, orbusiness births. Like many establishment surveys, the CES has difficulty with obtaining and developing a

timely sample frame for business births. This is because a

lag exists between an establishment opening for business and

its appearance on the universe frame, where it would be available for sampling. This lag currently is about 7 months. In

contrast, the lag from the reference month to the CES first

publication of the employment estimates for that reference

month is 3 weeks. Absent a sample, some form of modeling

of this employment is necessary to account for the business

births and their associated employment growth.

Early research associated with the redesign efforts indicated a strong relationship between the employment associated with business births and that associated with business

deaths. This relationship can be seen in the Business Employment Dynamics (BED) data when a comparison is made

between the employment associated with quarterly business

openings and that associated with quarterly business closings.3

 (See chart 1.) The primary difference between the BED

data and the CES concepts is that the BED data track births over

a quarter. The birth employment relevant to the CES is the

employment associated with births since the last benchmark.

Imputation of deaths

As was mentioned earlier, the probability sample with the

weighted link relative estimator will accurately represent the

movement of the population. However, as a practical matter,

units that have gone out of business generally do not report

their data for the month in which they go out of business.

There are two primary reasons. First, the CES is a voluntary

survey and not all firms respond. Second, companies by definition have no employees once they are out of business, and

there may be no one to report their data.4 As a result, these

unreported sample events are not included in the calculation

of the weighted link relative and are counter to the assumption discussed earlier that there were no large differences

between the response rates of continuous units and those that

go out of business.
Business Births and Deaths

 30 Monthly Labor Review May 2006

To resolve this, a rather intensive followup with all

nonresponders would be required each month to attempt to

distinguish between nonrespondents and business deaths.

Even if this could be accomplished successfully, a model

would still be needed for all of the employment associated

with business births.

Instead, BLS decided to use the underlying relationship

between business birth employment and business death employment that was described in the previous section to at least

partially account for the employment associated with business births. Rather than identifying all the deaths for the estimation process, the logic is adjusted to exclude all business

deaths from the sample link. Deaths that are nonrespondents

are automatically excluded from the matched sample as they

have no current month data, and establishments that report that

they are out of business are treated as nonrespondents for the

current month and are also excluded from the link. As a result, the link calculation is based solely on continuing units.

While this first step accounts for a large portion of the birth

employment, it does not account for it all.

To understand what is occurring with this first step, it is

helpful to break down the estimation process. Conceptually,

the previous month’s employment can be broken into two

parts: 1) the previous month’s employment for firms that continued to employ workers in the current month, and 2) the

previous month’s employment for firms that go out of business, that is report zero employment, in the current month.

Next, consider the application of the weighted current-to-previous month employment ratio for sample units to the previous month employment level for each of the two pieces. This

weighted ratio is the same used in the weighted link relative

estimator. The employment at establishments that employed

workers the prior month and continue to employ workers

during the current month is moved forward by the link of the

continuous sample units. Applying the link of the continuous units to the employment associated with business deaths

effectively imputes a level of birth employment and the

growth of previous births for the current month.

Based on the relationship shown in the BED data, this imputation should account for a large portion of the business

birth employment. The degree to which this imputation is

different from the birth employment is left to be modeled

and represents the second step in the accounting for business

birth employment.

Modeling residual birth employment

The business birth employment not accounted for by the imputation of business deaths in the sample is modeled as an

AutoRegressive Intergrated Moving Average (ARIMA) time

Chart 1. Private sector components of gross job gains and gross job losses, Business Employment

Dynamics data, September 1992–June 2005, seasonally adjusted

Millions Millions

Contractions

Openings

Expansions

Contractions

Openings

Closings

1992 93 94 95 96 97 98 99 2000 01 02 03 04 05

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8
Monthly Labor Review May 2006 31

series.5 This model is referred to as the net birth/death model.

The Bureau’s Longitudinal Database (LDB) is the basis for

developing the historical relationship to be modeled. The

LDB links establishments over time, which allows for the identification of the continuous establishments, establishments

that go out of business, and births of establishments. To develop the history for modeling, the same handling of business deaths as described for the CES sample data is applied to

the population data. Establishments that go out of business

have employment imputed for them based on the rate of

change of the continuous units. The employment associated

with continuous units and the employment imputed from

deaths are summed. The difference is compared with the actual population level to create the series modeled by the birth/

death models.6

To date, the residual net birth/death component has shown

to be a relatively stable portion of the population employment regardless of the point in the business cycle. This may

seem counterintuitive until the impact of the imputation of

the business deaths is considered in more detail. However,

the BED data show that the majority of the employment change

in the population is explained by changes in the continuing

units rather than the relationship between the employment

associated with business births and that associated with business deaths. Furthermore, the BED birth/death relationship is

somewhat cyclical like the continuous unit population. The

CES application of this relationship takes a step further with

the application of the continuous unit link to the employment

associated with business deaths. This imputation of employment from business deaths does not provide an exact one-toone relationship between employment from establishment

births and deaths; rather, it is dependant upon the movement

of the continuous units.

To complete the estimation formula for the entire population, a net birth/death value must be added to the weighted

link relative described earlier. The final formula is as follows:

( )

( )

























×

×

= ×

∑

∑

i

i p i

i

i c i

p

c

w ae

w ae

AE AE

,

, ^ ^

 + net birth/death

Cyclical sensitivity

The total business birth employment is accounted for by both

the imputation of business deaths and the net birth/death

value. While the net birth/death value is a fixed, projected

value, the imputation of deaths is dependent upon current

sample information.

The impact of the imputation is best seen in the following

series of examples. (See table 1.) For the examples, assume

that there is full response associated with the sample. This

allows for the evaluation of the imputation process, without

the complication of nonresponse. In these examples, the

sample is broken down to illustrate the impact of the imputation of business deaths and the estimate of total business birth

employment. For each of these examples, assume that the

previous month’s employment level is 20,000 and the net

birth/death factor for the cell is 0.

In each of the examples, a table shows the previous month

reported employment for each sample reporter in column 1,

the current month reported employment for each sample reporter in column 2, the sample weight for each sample reporter in column 3, the previous month weighted employment (weight times the previous month employment) for each

sample reporter in column 4, and the current month weighted

employment (weight times the current month employment)

for each sample reporter in column 5. The last two rows in

each table show the weighted previous and current month

employment totals for the sample both including the sample

member that went out-of-business and excluding the sample

member.

For each example, three calculations are computed.

1) An estimate including the sample member that goes

out of business (report zero employment)

2) An estimate excluding the sample member that goes

out of business (this estimate is the CES estimate based

upon the existing estimation algorithm)

3) A calculation of the employment associated with the

imputation of business deaths (it is the difference between the two estimates listed above)

The differences in the total birth employments in the three

examples illustrate the impact of the imputation of business

deaths. They also indicate that the total accounting for business birth employment is sensitive to current business cycle

information. The first example provides a case where the

continuous units are relatively flat. (See table 1, example a.)

Applying the link relative estimation formula with the

sample death included results in an employment estimate of

(20,000*7,590.10/7,840.90) = 19,360. Applying the link

relative estimation formula with the sample death excluded

results in an employment estimate of (20,000*7,590.10/

7,502.00) = 20,235. In this case, the imputation of the death

added 875 in employment associated with business births.

In the second example, the continuous units are expanding. (See table 1, example b.) Applying the weighted link

relative estimation formula with the sample death included

results in an employment estimate of (20,000*8,425.40/

7,840.90) = 21,491. Applying the weighted link relative estimation formula with the sample death excluded results in
Business Births and Deaths

 32 Monthly Labor Review May 2006

an employment estimate of (20,000*8,425.40/7,502.00) =

22,462. In this case, the imputation of the death added 971

in business birth employment.

In the last example, the continuous units are contracting.

(See table 1, example c.) Applying the link relative estimation formula with the sample death included results in an employment estimate of (20,000*7,054.56/7,840.9) = 17,994.

Applying the link relative estimation formula with the sample

death excluded results in an employment estimate of

(20,000*7,054.56/7,502.00) = 18,807. In this case, the imputation of the death added 813 in employment.

In other words, the employment level from the imputation

differs depending upon the movement of the continuous

sample. This is important when considering how the CES acCurrent month

sample employment

Sample

weight

Previous month

weighted employment

Current month

weighted employment

Previous month

sample employment

100 103 7.20 720.00 741.60

70 71 11.12 778.40 789.52

400 411 6.80 2,720.00 2,794.80

8 9 68.78 550.24 619.02

4 7 1.00 4.00 7.00

3 2 11.12 33.36 22.24

11 8 6.80 74.80 54.40

35 38 32.00 1,120.00 1,216.00

70 63 11.12 778.40 700.56

65 58 11.12 722.80 644.96

5 0 67.78 338.90 .00

... ... ...

17,840.90 17,590.10

... ... ...

27,502.00 27,590.10

100 108 7.20 720.00 777.60

70 76 11.12 778.40 845.12

400 416 6.80 2,720.00 2,828.80

8 14 68.78 550.24 962.92

4 12 1.00 4.00 12.00

3 7 11.12 33.36 77.84

11 13 6.80 74.80 88.40

35 43 32.00 1,120.00 1,376.00

70 68 11.12 778.40 756.16

65 63 11.12 722.80 700.56

5 0 67.78 338.90 .00

... ... ...

17,840.90 18,425.40

... ... ...

27,502.00 28,425.40

100 98 7.20 720.00 705.60

70 65 11.12 778.40 722.80

400 405 6.80 2,720.00 2,754.00

8 4 68.78 550.24 275.12

4 2 1.00 4.00 2.00

3 1 11.12 33.36 11.12

11 8 6.80 74.80 54.40

35 37 32.00 1,120.00 1,184.00

70 58 11.12 778.40 644.96

65 63 11.12 722.80 700.56

5 0 67.78 338.90 .00

... ... ...

17,840.90 17,054.56

... ... ...

27,502.00 27,054.56

Table 1. Example a: continuous units are relatively flat

Example b: continuous units are growing

Example c: continuous units are declining

1 Total with business death included. 2 Total without business death included.
Monthly Labor Review May 2006 33

counts for business births and their employment. While the

net birth/death figure is a forecasted value, there is current

information being used through the imputation of business

deaths. As a result, there is sensitivity to current economic

conditions in the assumptions for accounting for business

birth employment.

If each of these examples is changed to assume that there

are sample nonrespondents, then the total amount of birth

employment accounted for by each example’s imputation is

a lower bound for the total births employment in the population. This is because some of the nonrespondents may be

deaths with employment imputed for them. For the

nonrespondents that are still in business, the link from continuous units is appropriate. If some of the nonrespondents

are out of business, then in the estimation process, they also

have employment imputed for them.

Bias adjustment vs. net birth/death

Historically, the CES has relied on modeling of some segment

of the population to complete the most accurate and current

employment picture possible. Under the old quota-based

design, which was discontinued in 2003, this modeling was

referred to as bias adjustment. A comparison between the

bias adjustment and the birth/death adjustment is frequently

made by CES data users. However, there are several distinctions between the two models. Both models account for the

only nonsample-based adjustment to the CES estimates; however, the birth/death model is not simply an improved bias

adjustment model. Bias adjustment was a total error correction model that was used to account for several deficiencies

in the quota sample including a nonrandom sample and response errors. As a result, the bias adjustment models were

directly driven by revisions to the estimates with the previous benchmark and assumed all error and variability in the

estimate should be corrected by the model.

Under the current probability-based design of the CES survey, only the business births are not directly accounted for

through the sample design. The residual net birth/death

model can have error associated with it that is not directly

tied to benchmark revisions. The model values are affected

by defined portions of the population—business births and

business deaths. Benchmark revisions can be attributable to

nonresponse error, reporting error, sample error or simple

sample variability, and the error associated with the modeling for the net of births and deaths. With the new design,

each of these components can be examined separately and

corrected as the need arises. As a result, it is possible for net

birth/death factors to increase in industries with downward

benchmark revisions or in industries with upward revisions.

The bias model and the birth/death model are expected to

capture different portions of the population movement and,

under the current survey, more of the population movement

is captured over time through the sample and less is captured

through modeling. With the introduction of the new design,

parallel estimates were made for a 12-month period in each

division. Official quota-based estimates and the probabilitybased estimates performed similarly; however, generally less

birth/death adjustment was applied to the probability estimates than was applied by the bias adjustment model used

with the quota-based sample. (See table 2.)

Birth/death model performance

With the full conversion of the CES sample to a probability

and NAICS basis, an analysis of the performance of the birth/

death model against population data can be performed with

the refitting of the models each year. While benchmark revisions have been small in recent years, it is possible that the

small revisions could be a result of offsetting errors within

the CES-estimation process rather than the quality of the birth/

death model. An examination of the forecasted net birth/

death factors compared with the actual net of business births

and deaths shows that the two did not differ greatly for the

April 2002–March 2004 period at the total private level. (See

chart 2.)

Industry

implemented

12-month

bias total

12-month

 birth/death total Industry

Mining ..................................................... June 2001 0 –8,000

Construction ............................................ June 2001 144,000 119,000

Manufacturing .......................................... June 2001 96,000 17,000

Wholesale trade ....................................... June 2000 153,000 37,000

Retail trade .............................................. June 2002 221,000 87,000

Transportation and public utilities ................ June 2002 90,000 23,000

Finance, insurance, and real estate ............ June 2002 25,000 9,000

NOTE: Services estimates were not produced in parallel because of the conversion to NAICS in June 2003.

Table 2. Bias and birth/death factors for parallel estimation periods
Business Births and Deaths

 34 Monthly Labor Review May 2006

Additional research

The complete accounting of business birth employment does

contain a cyclical component that results from the imputation process, and analysis of both the benchmark revisions

and the comparisons of the birth/death factors with population data indicates that the imputation and model combination are performing well. However, there are no variables in

the net birth/death model that provide information that is

more current than the most recent benchmark. Future research with respect to the birth/death model will involve the

examination of variables that can be incorporated on a concurrent or lagged basis. These variables may provide more

recent information than what is currently present in the model.

Notes

1

 The Bureau’s unemployment insurance ( UI) universe count is a quarterly tabulation, from administrative records, of the number of employees

covered by unemployment insurance laws. UI universe counts, available

on a lagged basis, contain individual employer records for more than 8

million establishments and cover a little more than 97 percent of total

nonfarm employment; they thus provide a benchmark for the sample-based

estimates. For the small segment of the population not covered by UI, BLS

develops employment benchmarks from several alternative sources. More

information on benchmarking of the CES estimates can be found on the

Internet at http://www.bls.gov/web/cesbmart.htm.

2A probability-based sample is selected through a random process, and

the probabilities of selection are known for each unit in the population. A

quota-based sample is derived through a sampling process that is repeated,

until a minimum responding sample, or quota, is obtained for each characteristic of interest. Details on the implementation of the CES redesign

are available in an article by Sharon Strifas, “Revisions to the Current

Employment Statistics National Estimates Effective May 2003,” Employment and Earnings, June 2003, pp. 3–19.

3

 The Business Employment Dynamics data are a set of statistics generated from the Quarterly Census of Employment and Wages, or ES–202,

program. These quarterly data series consist of gross job gains and gross

job losses statistics from 1992 forward. These data help to provide a picture of the dynamic state of the labor market. More information on the

Business Employment Dynamics data can be found on the Internet at http:/

/www.bls.gov/bdm/home.htm.

4

 Exceptions occur when all worksites are reported in either an aggregate single report or to the Electronic Data Interchange Center; then the

location going out-of-business is reported.

5

ARIMAmodeling uses lags and shifts in the historical data to uncover

patterns, such as moving averages and seasonality.

6

 More detailed technical model descriptions have been published in

the Statistical Proceedings of the American Statistical Association and are

available on the Internet at http://www.bls.gov/ore/abstract/st/

st020090.htm.

Forecasted net of business births

and deaths

Actual net of business births

and deaths

Forecasted

Chart 2. Total private forecasted versus actual net of business births and deaths, not seasonally

adjusted, April 2002–March 2004

Employment

(in thousands)

Employment

(in thousands)

April July October January April July October January

-600

-500

-400

-300

-200

-100

0

100

200

300

-600

-500

-400

-300

-200

-100

0

100

200

300

2002 2003 2004