Small Area Co-Modeling of Point Estimates and Their Variances for Domains in the Current Employment Statistics Survey

Transcription

1 Small Area Co-Modelng of Pont Estmates and Ther Varances for Domans n the Current Employment Statstcs Survey Jule Gershunskaya, Terrance D. Savtsky U.S. Bureau of Labor Statstcs FCSM, March 2018 Dsclamer: Any opnons expressed n ths paper are those of the authors and do not consttute polcy of the Bureau of Labor Statstcs 1 U.S. BUREAU OF LABOR STATISTICS bls.gov

2 2 U.S. BUREAU OF LABOR STATISTICS bls.gov Introducton CES publshes monthly estmates of employment at detaled levels by ndustry and geography In small samples, estmates can be unstable: SAE methods are used currently n use: Fay-Herrot (FH) model at supersector ndustral level for select States. Goal: extend the use of FH to detaled sub-ndustres and MSAs Concerns: - possble exstence of clusterng of employment growth by sub-ndustres and geographc areas - nstablty of estmated samplng varances, especally n small samples: (co-modelng consdered by Mat et al. 2014, Sugasawa et al. 2017)

3 M1: Fay Herrot (FH) For a gven month, for domans = 1,..., N: q -- over-the-month change n employment level n doman q y -- drect sample-based estmate of v -- varance of sample-based estmate y (assumed known) x -- covarate (hstorcal change, from admnstratve data source: Quarterly Census of Employment and Wages (QCEW) ) 3 U.S. BUREAU OF LABOR STATISTICS bls.gov

4 M1: Fay Herrot (FH) For a gven month, for domans = 1,..., N: What may go wrong? In samplng model: - v s assumed known (yet estmate or a proxy s used) - normalty may not hold: possble outlers In lnkng model: - lnearty assumpton m+ bx may be volated - normalty may not hold: e.g. exstence of clusters 4 U.S. BUREAU OF LABOR STATISTICS bls.gov

5 M2: Fay Herrot wth clusters n lnkng model (CFH) Assume a mxture of normal dstrbutons for the lnkng model: Prors: æa a ö pk ~ Drchlet,..., ç èk K ø, 1 k N m m ~ ( 0, l - ), ~ N ( 0, ) 1 b l - 2 ; al,, l, t - ~ G( 1,1) b m b 5 U.S. BUREAU OF LABOR STATISTICS bls.gov

6 M3: Co modelng: pont estmates and varances (FHS) 2 (, ) q s -- target parameters for doman (, ) y v -- drect sample-based estmates for doman 6 U.S. BUREAU OF LABOR STATISTICS bls.gov

7 M4: Co modelng and clusterng (CFHS) 2 (, ) q s -- target parameters for doman (, ) y v -- drect sample-based estmates for doman 7 U.S. BUREAU OF LABOR STATISTICS bls.gov

8 M5: Co modelng and co clusterng (CFHSc) 2 (, ) q s -- target parameters for doman (, ) y v -- drect sample-based estmates for doman 8 U.S. BUREAU OF LABOR STATISTICS bls.gov

9 the cheat sheet Level FH CFH FHS CFHS CFHSc Pont Estmate Samplng Varance Samplng model Lnkng model Samplng model Lnkng model normal normal normal normal normal normal normal mxture normal normal mxture normal mxture gamma gamma gamma gamma gamma gamma mxture 9 U.S. BUREAU OF LABOR STATISTICS bls.gov

10 Models comparson based on CES data Domans: Statewde/detaled ndustry Drect estmator of over-the-month relatve change: Ft models for each of 12 months, obtan ftted values: Derve level estmate as: Due to dfferent seasonalty patterns between QCEW (admnstratve source) and CES, the most mportant comparson s after 12 months of estmaton: MAD N 1 N Y,12 Y,12 10 U.S. BUREAU OF LABOR STATISTICS bls.gov 1

11 Real Data Results (after 12 months), Sep 2008-Sep 2009 estmaton cycle Ind N Drect FH BRR CFH BRR FH V CFH V FHS CFHS CFHSc Overall U.S. BUREAU OF LABOR STATISTICS bls.gov 1 N 1,12,12 MAD N Y Y

12 Real Data Results (after 12 months), Sep 2009-Sep 2010 estmaton cycle Ind N Drect FH BRR CFH BRR FH V CFH V FHS CFHS CFHSc Overall U.S. BUREAU OF LABOR STATISTICS bls.gov 1 N 1,12,12 MAD N Y Y

13 Real Data Results (after 12 months), Sep 2010-Sep 2011 estmaton cycle Ind N Drect FH BRR CFH BRR FH V CFH V FHS CFHS CFHSc Overall U.S. BUREAU OF LABOR STATISTICS bls.gov 1 N 1,12,12 MAD N Y Y

14 Estmated vs true varances of drect estmator (nd 6562, month #1) (sze of ponts s proportonal to y - q v ) BRR FHS CFHS CFHSc ( ) 2 T 2 z E és... ù γ ë û = w1 y - q + w 2v + w 3be, w depends on an. weght 2 14 U.S. BUREAU OF LABOR STATISTICS bls.gov

15 Model based screenng It s a good practce to perform careful model checks However, thorough model evaluaton may be unrealstc n a tghtly scheduled CES producton envronment The usual strategy: canddate models 1,..., W are thoroughly tested on a number of hstorcal seres over several years; after that one of them, model, s accepted for producton w What f w works well n general but fals for some domans n some months? 15 U.S. BUREAU OF LABOR STATISTICS bls.gov

16 Model based screenng Use Bayesan posteror predctve dstrbuton p( y y, w) Compute p = Pr { y generated by } Declare dscoveres : domans wth small w p Analysts have to revew the lst and determne f extreme y s due to (1) defcency of the sample (e.g., nfluental sample unts, small sample, low response, etc) (2) falure of the model lnearty assumpton (analysts may have addtonal out-of-sample nformaton to support ther judgement) 16 U.S. BUREAU OF LABOR STATISTICS bls.gov

17 17 U.S. BUREAU OF LABOR STATISTICS bls.gov

18 Summary We appled jont modelng of the pont estmates and varances to CES data. Jont modelng resulted n lower MAD than models wth plugged n fxed and known varances Ftted values for samplng varance are a useful by-product of the jont modelng We extended the models of Mat et al. (2014) and Sugasawa et al. (2017) by allowng the data to estmate a clusterng structure on estmated means and varances. Co-clusterng model provdes better estmates of samplng varances when there s a lot of varablty n varances Devsed an automated, fast computng testng procedure based on the Bayesan FDR to nomnate a small subset of domans for analyst revew on a tmely bass. Ths procedure could become a useful tool to mark unusual estmates before they are publshed 18 U.S. BUREAU OF LABOR STATISTICS bls.gov

19 Contact Informaton Jule Gershunskaya Mathematcal Statstcan SMS/OEUS U.S. BUREAU OF LABOR STATISTICS bls.gov