Page 80. where C) refers to estimation cell (defined by industry and, for selected industries, region)

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1 Nonresponse Adjustment in the Current Statistis Survey 1 Kennon R. Copeland U.S. Bureau of Labor Statistis 2 Massahusetts Avenue, N.E. Washington, DC (Copeland.Kennon@bls.gov) I. Introdution The Bureau of Labor Statistis (BLS) Current Statistis (CES) survey ollets employment, hours, and earnings data monthly from a sample of over 300,000 U.S. establishments. To provide timely information, initial estimates are generated three to four weeks after the survey referene period. Final estimates, inorporating late reports reeived after prodution of the preliminary estimates, are released two months later. Benhmark estimates, inorporating administrative population data from the BLS ES-202 program for Marh of the prior year, are released annually with the data for May. Nonresponse potentially introdues bias into survey estimates, if respondents differ from nonrespondents relative to the variables of interest, and also redues the effetive sample size of a survey, thereby inreasing varianes for survey estimates. Estimation methods are developed so as to aount for nonresponse and lessen its impat on bias and variane. These methods, however, assume nonresponse is ignorable within defined estimation ells and, hene, do not distinguish among various patterns of nonresponse. Nonresponse is used here to enompass both nonreporting and late reporting. Late reporting is temporal nonresponse, as the data beome available at a subsequent point in time. This paper ontinues researh presented in Copeland (2003). Setion II presents a brief overview of the CES survey design, Setion III defines and profiles CES survey reporting patterns, Setion IV examines effets of late reporting and nonresponse on CES survey estimates, and Setion V disusses alternative nonresponse and late reporting adjustment models. II. CES Survey Design The BLS reently ompleted a major redesign of the CES survey (Werking, 1997; Bureau of Labor Statistis, 2003), moving the survey from its historial quota sample design to a probability sampling basis. The new sample design is a stratified, simple random sample of establishments from the BLS s Longitudinal Data Base, with strata defined by state, industry, and employment size. Sampling rates for eah stratum are determined through optimum alloation to minimize variane of total employment level. Data must be reported within a two to three week period for inlusion in the initial published estimates (referred to as first losing estimates) for the month. As additional responses are reeived after this first losing of the olletion period, the estimates for a given month are revised twie (referred to as seond and third losing estimates) to inorporate data from late reporters. The first losing estimate of month-to-month hange is derived by subtrating the prior month s seond losing estimate from the urrent month s first losing estimate. Estimates are generated through use of a weighted link-relative estimator, whih uses a weighted sample trend within an estimation ell, based upon ommon reporters between the prior and urrent months, to move forward the prior month s estimate for that ell. The urrent estimator for total employment (Bureau of Labor Statistis, 2001) takes the following form for month t and losing k = 1,2,3 Yˆ t k = C = 1 i i s t ( ) w iyti s ( ) C t, t 1 k Yˆ ( t ) k + = t ( t ) ky ˆ 1 ( 1), 1 wiy i = 1, k [ ( k + 1) ] where ( = 1,..., C) refers to estimation ell (defined by industry and, for seleted industries, region) s t ( t 1) k, represents the set of sample establishments in estimation ell that, as of losing k, reported data for both months t and t 1 w i is the sampling weight for sample establishment i Y ti is the total employment reported for month t by sample establishment i 1 Any opinions expressed in this paper are those of the author and do not onstitute poliy of the Bureau of Labor Statistis Page 80

2 Y ˆ represents the prior month, t 1, link-relative estimate for estimation ell based upon data reported as of ( t 1) ( k + 1) losing k +1 (with a maximum value of three) for month t 1 (whih orresponds to losing k for month t ) The link-relative,, is thus a growth rate estimate for the period t 1 to t. Differenes in estimates between losings t, ( t 1) will be due solely to the inlusion of late responses, while differenes between estimated and benhmark values will be due to the ombined effets of sampling, nonresponse, late reporting (if omparing first or seond losing estimates), and measurement error. An implit assumption of the estimator is that, within an estimation ell, establishments not reporting data (nonsampled, nonreporting, late reporting) for both months t and t 1 are assumed to have the same growth rate as for those establishments reporting data, i.e., the sampling, response, and reporting timeliness mehanisms are ignorable (Rubin, 1976). III. Reporting Patterns Survey nonresponse is frequently lassified on the basis of reason for nonresponse. Panel surveys add another dimension to the response mehanism, that being response status by survey period. Surveys that publish revised estimates offer yet another dimension to the response mehanism, that being timeliness of reporting. Little and David (1983) distinguished three types of panel survey nonresponse attrition (sample unit stops reporting), late entry (sample unit does not report initially), and reentry (sample unit has a gap in reporting). While this ategorization desribes general patterns of nonresponse, the types are not mutually exlusive. A sample unit that stops reporting (attrition) ould have had gaps in reporting for time periods prior to attrition (reentry) and may not have reported initially (late entry). Little and Su (1989) identified two patterns of panel survey nonresponse monotone (the only type of nonresponse is attrition) and haphazard (nonresponse is either late entry or reentry or both). Although a fully monotone pattern of nonresponse is unlikely, the atual pattern may be approximately monotone (e.g., dropouts in linial trials). Haphazard nonresponse enompasses a wide variety of nonresponse patterns (i.e., Little and David s late entry and reentry panel nonresponse types, as well as any ombination of the three nonresponse types). These two taxonomies ould be refined to reflet more ompletely the nature of reporting patterns. The Little and David taxonomy does not address mixtures of patterns, while the haphazard pattern of Little and Su does not provide distintions among haphazard patterns. Clarifying these distintions ould prove useful, as distributional properties ould differ among patterns. In addition, omplete nonresponse (sample unit never reports) should be added to the list of nonresponse types and omplete response (sample unit always reports) should be added so all sample units are enompassed by the lassifiation. As a result, it may be more appropriate to talk in terms of panel survey reporting patterns rather than nonresponse patterns. There are five basi types of reporting patterns. Basi Reporting Patterns Complete Response unit reports every time period Complete Nonresponse unit does not report for any time period Attrition unit stops reporting after a given time period Late Entry unit begins reporting after the first time period Episodi Nonresponse unit experienes a mixture of reporting and nonreporting An expanded and refined set of reporting patterns for panel surveys an be defined by mixtures of the basi reporting patterns. This taxonomy for reporting patterns, along with illustrations, is provided in Attahment 1. Note that lassifiation of a sample unit in terms of a reporting pattern is temporary, unless the survey has ended and there will be no further time periods for whih data will be olleted. Reporting patterns defined by only one basi pattern may be thought of as first order reporting patterns, while other reporting patterns (based upon a ombination of basi patterns) may be thought of as interation reporting patterns. These reporting patterns are of interest in that distributional properties may differ among the patterns, thereby affeting the assumptions of the underlying estimation model. Table 1 presents the CES survey reporting pattern distribution for four industries for the period Jan 01 - Jun 02, exluding Complete Nonresponse. Complete Response aounts for 47% - 57% of the sample. Other first order reporting patterns (Strit Attrition, Strit Late Entry, Strit Episodi Nonresponse) aount for 34% - 41% of the sample. Attrition (lassified based on observing reporting patterns through De 02) ourred for 12% to 16% of the sample, while some type of episodi nonresponse ourred for 24% - 30% of the sample. (Note: Late entry ould not be distinguished from initiation of new Page 81

3 sample units (whih was arried out on a flow basis); thus, some establishments lassified as late entry may atually belong to the next higher level. In addition, some establishments lassified as attrition may have beome out of business.) Table 1 Reporting Pattern Distributions Seleted Industries, Jan '01 - Jun '02 Manufaturing NAICS 31xx-33xx Wholesale Trade NAICS 42xx-43xx Mining NAICS 1133, 21xx Constrution NAICS 23xx Complete Response 57.0% 49.8% 51.2% 47.4% Strit Attrition 9.3% 11.8% 10.6% 9.4% Strit Late Entry 7.0% 10.5% 10.2% 9.9% Strit Late Entry Attrition 2.1% 3.5% 3.2% 3.5% Attrition with Episodi Nonresponse Late Entry with Episodi Nonresponse Late Entry Attrition with Episodi Nonresponse 4.1% 4.6% 4.2% 5.4% 2.0% 2.8% 2.0% 2.5% 0.6% 0.6% 0.6% 0.4% Strit Episodi Nonresponse 17.8% 16.5% 17.9% 21.5% For omplete nonresponse and attrition, reason for nonresponse (e.g., refusal, nonontat) ould be of interest as it may provide an indiation of the establishment s situation (nonontats may indiate out of business). Reason for episodi nonresponse (e.g., on vaation, data unavailable) may also be of interest for understanding and addressing nonresponse. For a survey suh as the CES survey, in whih estimates are revised several times, late reporting adds another dimension to reporting patterns, as illustrated in Attahment 2. Late reporting units are treated differently than on-time reporters, thus affeting the eligible sample for the first losing link-relative estimator. The key aspet of timeliness of reporting relative to the urrent form of the link-relative estimator is the fat that late reporting establishments that reported (whether on-time or late) the prior month are not utilized in the link-relative estimation for the urrent month. This serves as a omplement to the key aspet of nonreporting relative to the urrent form of the link-relative estimator being the fat that on-time reporters for the urrent month are not utilized in the link-relative estimation if they did not report in the prior month. For the CES survey, timeliness of reporting is an issue for most sample establishments, although not on a ontinual basis. Table 2 presents top-level distribution of frequeny of first-losing reporting for establishments in the Complete Response reporting pattern, for the eighteen-month period Jan 01 Jun 02. The proportion of establishments in the Complete Response reporting pattern that reported on-time every month ranged from 23% to 29% at the industry level, while the proportion of establishments that reported late every month ranged from 1% to 12%. Further lassifiation of timeliness of reporting patterns ould take into aount shorter time frames (perhaps most reent six months), relationship with length of reporting period (e.g., only late when reporting period less than 11 days), and harateristis of the sample establishments (e.g., length of pay period). Table 2 Timeliness of Reporting Pattern Distributions Seleted Industries, Jan '01 - Jun '02 Sample Reporting all Eighteen Months Manufaturing NAICS 31xx-33xx Wholesale Trade NAICS 42xx-43xx Mining NAICS 1133, 21xx Constrution NAICS 23xx Every Month by First 27.7% 22.7% 22.8% 29.1% Months by First 55.4% 53.6% 51.3% 60.3% 6-11 Months by First 10.6% 8.3% 16.2% 8.1% 1-5 Months by First 4.0% 3.1% 7.6% 2.0% No Month by First 2.2% 12.3% 2.1% 0.6% Page 82

4 Copeland (2003) provides additional tabulations of CES survey reporting patterns. The distributional information on reporting patterns and timeliness of reporting indiates: 1) when viewed aross long time periods, inomplete data or late reported data ours for a large proportion of sample establishments; 2) prior CES survey reported employment information is available for many nonreporting/late reporting sample establishments. IV. Impat of Late Reporting and Nonresponse The impat of nonresponse in the CES survey may be examined diretly for late reporting, and indiretly for both late reporting and nonresponse. Comparisons of first and third losing estimates provide a diret indiation of the impat of late reporting, as the only differene between the two estimates is the inlusion of late reporters into the sample. The relative differene between first and third losing estimates for month t, ˆ ˆ Yt 1 Yt 3 RelDiff t( 1,3) = 100% ˆ Y t 3 and the differene between first and third losing estimates of the month-to-month hange from month t 1 to month t, [ 2 ] [ Yˆ t 3 Yˆ 3 ] = t, 1 t, Difft( 1,3) = ˆ t 1 Yˆ Y 3 provide measures of the extent to whih growth rates for late reporters differed from those for early reporters. Large differenes provide an indiation of nonignorability of late reporting. Figure 1 presents relative differenes between first and third losing non-seasonally adjusted estimates of monthly employment for the period May 01 Feb 02 and May 02 Feb 03 for the four industries for whih probability sampling had been implemented as of May Marh and April were exluded from this graph due to the nature of CES survey proessing, with annual benhmark data inorporated with the publiation of first losing estimates for May (and thus seond losing for April and third losing for Marh), and thus negating the ability to measure solely late reporting impat for these months. Although the larger industries have experiened fairly small revisions (absolute relative differenes less than 0.25%), the revisions for Mining have been muh greater, with the absolute relative differene as high as 1.1% in Feb % Figure 1 First Revision, Relative to Third Estimate Seleted Industries: May '01 - Feb '02, May '02 - Feb '03 0.9% Relative Estimate 0.6% 0.3% 0.0% -0.3% -0.6% -0.9% -1.2% Manufaturing Wholesale Trade Mining Constrution May-01 Jun-01 Jul-01 Aug-01 Sep-01 Ot-01 Nov-01 De-01 Jan-02 Feb-02 Mar-02 Apr-02 May-02 Jun-02 Jul-02 Aug-02 Sep-02 Ot-02 Nov-02 De-02 Jan-03 Feb-03 Month Revisions in the monthly employment estimates and in the estimates of month-to-month hange in employment an also be ompared with the month-to-month hange in employment, whih is a primary measure for assessing the employment data. Revisions that are large relative to the estimated hange ould serve to derease the utility of the preliminary reports. Table 3 ompares the magnitudes of the revisions in monthly and month-to-month hange in employment to the first losing estimate of month-to-month hange in employment for the period May 02 Feb 03. Page 83

5 Table 3 First Revisions Relative to First Month-to-Month Change Seleted Industries: May '02 - Feb '03 (Numbers in thousands) Manufaturing Wholesale Trade Mining Constrution (1st ) Change from Prior Month (1st ) Change (1st ) Change from Prior Month (1st ) Change (1st ) Change from Prior Month (1st ) Change (1st ) Change from Prior Month (1st ) May-02 16, , , Change Jun-02 16, , , Jul-02 16, , , Aug-02 16, , , Sep-02 16, , , Ot-02 16, , , Nov-02 16, , , De-02 16, , , Jan-03 16, , , Feb-03 16, , , Although revisions for several months are larger than the first losing estimate of month-to-month employment hange, the hanges in these situations are small. For months with larger employment hanges, revisions are not of the magnitude of the hange, but ould nonetheless be viewed as substantial (five of eighteen first losing hanges of at least 50,000 saw a revision in the first losing estimated employment level that was 10%+ of the magnitude of the first losing estimated hange, while four saw a 10%+ revision in the magnitude of the hange). Viewed from this perspetive, late reporting ould be onsidered to have an impat on the auray of the first losing estimates. A diret indiation of the appropriateness of the assumption of ignorability for late reporting an be made by omparing growth rates for late reporters with those for preliminary reporters. Table 4 provides omparisons of urrent month-to-month growth rates for urrent month first losing reporters and late reporters, for those sample establishments for whih data were available for the prior month. Table 4 Month-to-Month Growth Rates by Current Month Timeliness Status Seleted Industries, Jan '02 - De '02 Establishments with 50+ Manufaturing Wholesale Trade Mining Constrution Month 1st 2nd/3rd 1st 2nd/3rd 1st 2nd/3rd 1st 2nd/3rd Jan '02-0.9% -1.5% -0.9% -0.1% -1.6% -0.6% -4.4% -4.8% Feb ' % -0.7% -0.8% -0.7% -0.8% -1.0% -0.2% -0.9% Mar ' % -0.5% -0.4% -0.3% -0.4% 0.0% 1.0% 1.7% Apr ' % -0.3% 0.2% 0.2% 1.2% 2.8% 2.5% 1.5% May ' % -0.4% 0.0% -0.3% 1.4% 1.0% 1.8% 0.5% Jun '02 0.5% 0.3% 0.1% 0.8% 0.8% -0.5% 2.1% 1.0% Jul '02-0.5% -0.4% -0.1% -0.1% -0.1% -0.3% 0.9% 1.4% Aug '02 0.1% -0.3% -0.3% -0.3% -0.1% 2.5% 0.5% 1.5% Sep '02-0.7% -0.5% 0.2% -0.6% -0.9% -0.8% -1.0% -0.1% Ot '02-0.7% 0.1% -0.1% -0.3% -0.2% 0.0% -0.7% -0.4% Nov '02-0.4% -0.6% -0.4% -0.2% -1.3% -0.6% -2.1% -2.3% De '02-0.2% -0.3% 0.1% -0.5% 0.6% 0.0% -2.6% -2.1% Prior month-to-month growth rates for first losing and late reporters differ by more than one perentage point four times for Mining, three times for Constrution, and no times for Manufaturing and Wholesale Trade. In one instane (for Mining) the differenes are greater than two perentage points. Deriving a rough impat on the overall estimate (aounting for the relative sizes of the first losing and late reporting samples) showed the impat would generally be less than two-tenths of a perentage point, although in some ases the impat ould be greater than seven-tenths of a perentage point. Page 84

6 Assessing the impat of nonresponse is more diffiult, as reported survey data are not available. Although annual benhmark revisions provide an indiation of overall error in the third losing estimates the net result of sampling, nonresponse, and measurement errors nonresponse error annot be isolated from the benhmark results alone. One approah for assessing nonresponse effets would be to use ES-202 data at the establishment level as a proxy for CES survey data, and ompare estimates derived inluding and exluding nonrespondents. An indiret measure of the potential for a nonresponse impat on third losing estimates an also be obtained by omparing prior employment trends between reporters and nonreporters. The urrent estimator assumes nonresponse is ignorable within an estimation ell, and thus makes the implit assumption of equality of month-to-month growth rates for respondents and nonrespondents within an estimation ell. Comparing immediately prior growth rates for urrent period reporters and nonreporters for whih prior data are available provides an indiret indiation of the appropriateness of the equivalene assumption. Table 5 provides omparisons of prior month-to-month growth rates for urrent month reporters and nonreporters, for those sample establishments for whih data were available for the prior two months. Table 5 Prior Month-to-Month Growth Rates by Current Month Reporting Status Seleted Industries, Jan '02 - De '02 Establishments with 50+ Manufaturing Wholesale Trade Mining Constrution Month Nonreporters Reporters Nonreporters Reporters Nonreporters Reporters Nonreporters Reporters Jan '02-0.9% -0.4% -1.1% -0.1% -2.3% -1.0% -2.2% -2.9% Feb ' % -1.1% -1.5% -0.5% -1.0% -1.1% -5.1% -4.4% Mar ' % -0.5% 0.1% -0.8% -3.3% -0.7% 1.6% -0.4% Apr ' % -0.5% -0.2% -0.5% -0.3% -0.5% 1.2% 1.0% May ' % -0.2% 0.2% 0.2% 12.2% 0.8% 3.4% 2.2% Jun '02-0.2% -0.1% 0.4% -0.2% 0.8% 1.2% 0.3% 1.6% Jul '02 0.4% 0.5% 0.6% 0.4% 0.8% 0.4% 2.2% 1.8% Aug '02-0.5% -0.5% 0.3% -0.1% 0.6% -0.2% 2.2% 0.9% Sep '02-1.0% -0.1% -2.4% -0.3% -0.6% 0.9% -0.5% 0.8% Ot '02-0.9% -0.6% -1.5% 0.0% -1.4% -0.8% 0.0% -0.9% Nov '02 0.2% -0.5% -1.3% 0.0% -0.6% -0.1% -0.3% -0.6% De '02-1.1% -0.4% -1.1% -0.2% -2.3% -1.0% -1.6% -2.2% Results show prior month-to-month growth rates for reporters and nonreporters differ by more than one perentage point five times eah for Mining and Constrution, three times for Wholesale Trade, an no times for Manufaturing. In three instanes (twie for Mining and one for Manufaturing) the differenes are greater than two perentage points. Deriving a rough impat on the overall estimate (aounting for the relative sizes of the reporting and nonreporting samples) showed the impat would generally be less than one-tenth of a perentage point, although in some ases the impat ould be greater than eight-tenths of a perentage point. Taken together, these results suggest the implit assumption of equivalene between reporters and nonreporters and of first losing and late reporters may not hold, and that the lak of equivalene may impat both first and third losing estimates. V. Alternative Models The working model that applies to the CES survey estimator of total employment is a proportional regression model, in whih the urrent month s value is assumed proportional to the prior month s value (West, et al, 1989), with the proportionality fator, ρ, assumed to vary by estimation ell, ( = 1, K, C) (whih are ollapsed sample design ells), and month Y = ρ ty + k 2 ( 0, σ Y ) k ~ iid N k ( t 1) This proportional regression model has appeal for use in establishment surveys, where inferene is often made about the rate of hange for the population. In that sense, it an be thought of as a longitudinal analogue to the mean imputation model. However, the weakness of this model lies in its assumption of ignorable nonresponse (for both nonreporters and late reporters) within an estimation ell, and its failure to utilize reported data for establishments other than those reporting for both months t 1 and t. Page 85

7 Review of data from late reporters and nonreporters provided in this paper suggests the ignorability assumption may not always be met. Thus, some refinement to the model may provide opportunities for improvement. Prior researh into ourrene of nonresponse and late reporting (Copeland, 2003) indiates roughly 5% of urrent month first losing reporters are not used in the CES estimator due to lak of data for the prior month, and roughly 15% - 25% of prior month first and seond losing reporters are not used in the CES estimator due to lak of first losing data for the urrent month. Thus, approahes inorporating this urrent information may provide opportunities for improvement. One useful path for further researh would appear to be refinement of estimation ell definitions, in an attempt to define a more appropriate ignorable nonresponse model, using a response propensity approah as desribed in David, et al (1983). Fators for onsideration beyond industry, based upon researh to date, would inlude size of establishment and geography. These fators are utilized in the sample design, but not (with a few exeptions) in the definition of estimation ells. If the estimation ell refinements were to involve suh auxiliary data from the frame, the urrent model ould be ontinued. A seond path would be to explore other ignorable nonresponse models. Auxiliary information known for sample establishments, suh as length of pay period and prior employment hanges may be orrelated with reporting status and/or growth, and therefore be useful in a refined model. However, these auxiliary variables annot be inorporated into the urrent model, as they are not known for the population. One approah would result in imputing for missing values due to late reporters and nonrespondents under a model defined for the sample establishments, with the ompleted sample data file being used to reate link-relative estimates at the ell level as in the urrent approah. The differene would be that all sample establishments, not just those reporting urrent and prior months data, would be used in the estimator. This approah would thus allow use of auxiliary data known only for the sample. A simple model for deriving imputed values would be the urrent proportionality model, with the proportionality fator, ρ, assumed to vary by imputation ell g ( = 1, K, G), defined by a ombination of design and sample auxiliary variables Y tgi = ρ tgy gi + ktgi 2 ( 0, σ Y ) k tgi ~ iid N k gi The proportionality fators ould be estimated from the reporting sample, then used to impute values (using either a deterministi or a stohasti approah) for late reporters and nonreporters. The ompleted data set (reported data for preliminary reporters, imputed values for late reporters and nonrespondents) ould then be used in the urrent link-relative estimator to derive employment estimates. A third path would be to address potential nonignorability of nonresponse. The impat assessment of CES nonreporting and late reporting suggests refinement of the model to allow proportionality fators to vary by reporting pattern within estimation ell. If the assumption of ignorable nonresponse is not used, the question beomes how to estimate the month-to-month employment growth rates (proportionality fators) for nonreporters and late reporters. In addition, if differing proportionality fators are assumed for nonreporters and late reporters, it is neessary to predit whether a nonrespondent at first losing will report late or will be a nonreporter. Little (1993) proposed the use of pattern-mixture models for handling inomplete multivariate data, suh as that arising from a panel survey. Under this approah, models are defined for reporters and nonreporters, with identifying restritions established to allow for estimation of parameters that are non-estimable under the base models. For the CES survey, a simple pattern-mixture approah would be to extend the proportional regression model to allow different growth rates by reporting pattern in the urrent and prior months. Before spefying the model, it is helpful to define two reporting status indiator variables,, for late reporting () and nonreporting (NR). The pair, NR = 0,0, 1,0, 0,1 defines the NR ( { }, ) ( ) ( ) ( ) ( ) th month t reporting status for the i establishment in estimation ell. 1if r = 0 if r 1 3 = 0 and r = 0 or r 3 1 = 1( for month t) = 1(not for month t) NR 1if r = 0 if r 3 3 = 0 (NR for month t) = 1(not NR for month t) where r represents the month t reporting status, as of losing k ( = 1,2,3 ), for establishment i in estimation ell k Page 86

8 A simple extension of the CES model an then be written as Y + k = ρ Y( t 1) ln NR NR NR NR ( ρ ) = ln( ρ ) + 0t + 0t + 1( t 1) ( t 1) + 1( t 1) + e 2 ( 0, ) iid ~ N k k σ 2 ( 0, ) iid ~ N e e σ Note that the approah to assigning reporting status indiator variables also establishes underlying proportionality fators at the estimation ell level, ρ, based upon onsistent preliminary reporters (PR) (i.e., based upon zero values for and NR status in both months). This is analogous to the urrent approah of estimating the proportionality fator for an estimation ell based solely upon PR establishments whih were either PR or in the prior month; however, the extended model reognizes the proportionality fator ould vary for and NR establishments. The oeffients for the reporting status indiators, NR NR 0 t, 0t, 1( t 1), 1( t 1), are not estimable at first losing. Therefore, further assumptions are required for estimation a set of identifying restritions linking the nonestimable parameters to some set of estimable parameters. A simple set of identifying restritions is that the expeted value of the oeffients is invariant over time. + τ 0 t = 0 + τ NR NR 0 t = 0 t NR t = τ 1( t 1) 1 + = τ NR NR NR 1( t 1) 1 + where the τ ' s are assumed normal with mean 0 and onstant variane This model also requires predition of urrent month s reporting status for establishments, given reporting status is only known for first losing reporters. A simple logit preditive model for urrent month s reporting status, based on prior months reporting status may be appropriate. π log π where π π R R( t 1), R( t 2) NR R( t 1), R( t 2) = α + β R( t 1) + β R( t 2) ( = r = 0, R R ) R t, R = P t 1, ( 1) ( 2) 1 ( t 1) ( t 2) = π NR 1 R ( t 1), R( t 2) R( t i), R( t 2 ) 0 if r = 1if r 2 if r = 1(PR) = 0, r 3 = 0 (NR) = 1() This approah an be used, as in the extended ignorable nonresponse approah desribed previously, to impute values for late reporters and nonrespondents and use the ompleted sample data in the weighted link-relative estimator. A more extensive hange would involve imputing values for nonsampled establishments as well, with the resultant omplete population file used to tabulate estimates. Estimation for this model an be arried out through Bayesian analysis utilizing Markov Chains Monte Carlo (MCMC) methods. Evaluation of the performane of the model an be arried out in several ways omparison with third losing Page 87

9 estimates, and omparison with CES benhmark estimates. Based upon the results of a performane analysis of the alternative model, refinements may be proposed and evaluated. An additional hallenge will be model validation; however, this is no different than that faed with the urrent working model. VI. Summary The urrent CES survey estimator of total employment assumes ignorable nonresponse within an estimation ell. Findings suggest that assumption may not always hold and, as a result, employment estimates may be adversely impated. Although the impat may be relatively small, it may be sizeable in terms of employment hange. Further work is needed to evaluate estimation ell definitions and to inorporate information on standard errors of the estimates into the impat assessment. Alternative models, inorporating auxiliary information from sample establishments under an ignorable nonresponse mehanism may provide an opportunity to aount for variability not addressed by the urrent model. Further work is needed to explore the nature of the variability in employment data and to establish and evaluate the performane of appropriate working models addressing this variability. A broad reporting pattern lassifiation that aounts for both reporting status and timeliness of reporting may provide a struture for developing a pattern-mixture model to estimate growth rates without the assumption of ignorable nonresponse. Alternative models would seek to leverage prior information about nonreporters where available, thereby improving upon the urrent working model that only inorporates information about onstant reporters. Further work is needed to explore appliation of the pattern-mixture model with CES survey data, establish a reasonable working model, identify appropriate identifying restritions (espeally where no prior information is available), and determine impat on estimator auray. Referenes Bureau of Labor Statistis. (2001), Chapter 7, Estimation, Current Statistis Manual: U.S. Bureau of Labor Statistis, Washington, D.C. Bureau of Labor Statistis. (2003), BLS Establishment Estimates Revised to Inorporate Marh 2002 Benhmarks, and Earnings: U.S. Bureau of Labor Statistis, Washington, D.C. Copeland, K.R. (2003), Reporting Patterns in the Current Statistis Survey, Proeedings of the Setion on Survey Researh Methods, Amerian Statistial Assoation, (forthoming). David, M.H., Little, R., Samuhel, M., Triest, R. (1983), Imputation Models Based On the Propensity to Respond, Proeedings of the Setion on Business and Eonomi Statistis, Amerian Statistial Assoation, Little, R.J.A. (1993), Pattern-Mixture Models for Multivariate Inomplete Data, Journal of the Amerian Statistial Assoation, 88, Little, R.J.A. and David, M.H. (1983), Weighting Adjustments for Non-response in Panel Surveys, Working paper: U.S. Bureau of the Census, Washington, D.C. Little, R.J.A. and Su, H.-L. (1989), Item Nonresponse in Panel Surveys, in Kasprzyk, D., Dunan, G., Kalton, G., and Singh, M.P. (eds.), Panel Surveys (pp ), New York: John Wiley and Sons, In. Rubin, D.B. (1976), Inferene and Missing Data, Biometrika, 63, Werking, G.S. (1997), Overview of the CES Redesign, Proeedings of the Setion on Survey Researh Methods, Amerian Statistial Assoation, pp West, S., Butani, S., Witt, M., and Adkins, C. (1989), Alternative Imputation Methods for Data, Proeedings of the Setion on Survey Researh Methods, Amerian Statistial Assoation, Page 88

10 Response Pattern Illustrations Shaded area represents data reported for month Month Attahment 1 Response Pattern Classifiation Total Response Total Nonresponse Strit Attrition Strit Late Entry Strit Late Entry Attrition Response Pattern Desription 1 2 t1 t2 T-1 T Unit reports every time period Unit does not report for any time period Unit reports for every time period until some point in time, after whih it no longer reports Unit does not report until some point in time subsequent to the first time period, after whih it ontinues to report for every time period Unit does not report until some point in time subsequent to the first time period, after whih it ontinues to report for every time period until some point in time, after whih it no longer reports Attrition with Episodi Nonresponse Unit reports for the first time period, then experienes a mixture of reporting and nonreporting until some point in time, after whih it no longer reports Late Entry with Episodi Nonresponse Unit does not report until some point in time subsequent to the first time period, after whih it experienes a mixture of reporting and nonreporting for sueeding time periods Late Entry Attrition with Episodi Nonresponse Unit does not report until some point in time subsequent to the first time period, after whih it experienes a mixture of reporting and nonreporting until some point in time, after whih it no longer reports Strit Episodi Nonresponse Unit reports for the first time period, and experienes a mixture of reporting and nonreporting for all subsequent time periods Page 89

11 Timeliness Pattern Illustrations Shaded area represents data reported on-time for month Dotted area represents late reported data for month Month Response Pattern Timeliness Classifiation T-1 T Use Classifiation Current, Prior Month Reporter On-Time both months On-time urrent month only On-time prior month only Late both months Preliminary Preliminary Final Final Attahment 2 Current, Prior Month Nonreporter N/a No Prior Month Only Reporter Current Month Only Reporter On-time Late On-time Late No No No No Page 90