Spurious Seasonal Patterns and Excess Smoothness in the BLS Local Area Unemployment Statistics

Transcription

1 Spurous Seasonal Patterns and Excess Smoothness n the BLS Local Area Unemployment Statstcs Keth R. Phllps and Janguo Wang Federal Reserve Bank of Dallas Research Department Workng Paper 1305 September 2013

2 Spurous Seasonal Patterns and Excess Smoothness n the BLS Local Area Unemployment Statstcs Keth R. Phllps 1 Janguo Wang Abstract State level unemployment statstcs are some of the most mportant and wdely used data sources for local analysts and publc offcals to gauge the health of ther state s economy. We fnd statstcally sgnfcant seasonal patterns n the state level seasonally adjusted Local Area Unemployment Statstcs (LAUS) released by the U.S. Bureau of Labor Statstcs (BLS). We fnd that the pro-rata factors used n the benchmarkng process can nvoke spurous seasonal patterns n ths data. We also fnd that the Henderson 13 flter used by the BLS to smooth the seasonally adjusted data may reduce monthly volatlty too much n the sense that the aggregated state data s much smoother than the ndependently estmated natonal data. To reduce these problems, we suggest that the BLS use seasonally adjusted data when benchmarkng regons to natonal totals. Keywords: Local Area Unemployment Statstcs; Data Revsons; Seasonal Adjustment JEL Codes: C13, C8 1 Correspondng author: Tel.: : E-mal keth.r.phllps@dal.frb.org. The vews expressed are those of the authors and do not necessarly reflect those of the Federal Reserve Bank of Dallas, or the Board of Governors of the Federal Reserve System. Any remanng errors are our own. 1

3 1. Introducton The Bureau of Labor Statstcs (BLS) Local Area Unemployment Statstcs (LAUS) s a jont Federal-State program whch produces monthly estmates of total employed and unemployed for approxmately 7,300 areas. At the state level, LAUS reports both the seasonally non-adjusted (NSA) and seasonally adjusted (SA) data. The LAUS estmates provde valuable local labor market nformaton for workers, analysts and polcy makers. In an effort to mprove the qualty of data produced n prevous LAUS models, BLS ntated a major redesgn n One sgnfcant change s the ntroducton of a real-tme benchmark where ndvdual state estmates are controlled each month to the Current Populaton Survey (CPS) natonal estmate. In practce, the BLS monthly benchmark conssts of two steps. Frst, the US s dvded nto nne census dvsons. Employment and unemployment (and thus labor force as the sum of the two) n these regons are controlled to the natonal total based on ther shares. Second, state employment and unemployment estmates are created wth models usng nput varables such as data from the CPS, establshment survey employment and clams for unemployment nsurance. Each state s estmate s then controlled to the regonal total. The monthly benchmark nsures that state values sum to the regon and regons sum to the naton. The 2005 LAUS redesgn mplemented the monthly benchmark for the NSA state estmates. However, after the redesgn, monthly movements n the state SA seres became qute volatle. Because of the ncreased volatlty, n January 2010 the BLS started applyng a 13-month Henderson Trend flter to the seasonally adjusted estmates for the states (and D.C.), whch s ncorporated nto the offcal estmates. They also began benchmarkng the state SA data to the naton every month. In the benchmark adjustment for the SA data, the same pro-rata factors computed from the NSA data are used drectly to adjust the SA data 2. Before that, the states SA data were controlled only annually to the census dvson and the naton for the annual average NSA values. 3 One would expect the state level seasonally adjusted (SA) estmates to be free of any sgnfcant seasonal patterns. However, we fnd strong evdence ndcatng there are seasonal movements n many of them. We apply three dfferent seasonalty tests to the monthly changes of state SA data usng the Census Bureau X- ARIMA model 4. The stable seasonalty test assumes the seasonal factors are stable. The movng seasonalty test allows the seasonal factors to change over tme. The last one combnes the frst 2 See answer to queston 14 from Bureau of Labor Statstcs (2010). 3 BLS uses the Denton method for the annual benchmark. For more detals, readers are referred to BLS webste. 4 We use statstcal package SAS for the tests. 2

4 two tests, along wth a non-parametrc Kruskal-Walls test for stable seasonalty, to test the presence of dentfable seasonalty. Table 1 summarzes our fndngs. Table 1. Seasonalty Test for Seasonally Adjusted State Labor Force Data Varable 5 Number of States that Number of States that Number of States Stable Seasonalty s Movng Seasonalty s Showng Presence of found Present at 0.1 found Present at 1 Identfable Percent Level 6 Percent Level Seasonalty Based on combned test Cvlan Labor Force Number of Employed Number of Unemployed Unemployment Rate Notes: The sample perod covers from January 1990 to May The data ncludes Washngton, DC, whch s treated as an ndvdual state n ths paper. All three tests unanmously support the strong presence of seasonalty n the SA cvlan labor force and number of employed, although the evdence s weaker for the number of unemployed and the unemployment rate. For nstance, we fnd dentfable seasonalty n 39 out of the 51 state SA employment seres. We also tred dfferent sample perods and fnd the above results are qute robust. 2. Tracng the Source of Seasonalty What s the man source of seasonalty found n the state level SA labor force estmates? One obvous possblty s the resdual seasonalty nherted from the correspondng NSA data. However, there s another mportant possble source; the pro-rata factors computed from the NSA data that are used n benchmarkng the SA data. To show the second possblty, consder the followng hypothetcal scenaro where a census dvson only conssts of two states, A and B. Assume the labor force n A and B are statonary over tme and ther movement can fully be descrbed by ther seasonal changes. Assume the (stable) seasonal 5 All tests are appled to the monthly changes of the nterested varables. We have also tested the presence of seasonalty n the SA labor force estmates usng the level data. Our man concluson remans largely the same. 6 Notce that the sgnfcant levels of the seasonalty tests are much smaller than the conventonal values used n many other tests. For more nformaton on the seasonalty tests, see, for example, Lothan and Morry (1978). 3

5 components of two NSA labor force data seres for the two states are X andy respectvely. For a gven year, X andy can be represented as X a D 1 { and Y b D 1, where D are seasonal dummes for the months wthn the year; { a } and b } are the seasonal factors. Based on the two seasonal components, the proporton of state A n ths hypothetcal dvson, or the pro-rata factor for state A becomes prf X X Y 1 ( A) (1) 1 ( a b ) D a D It s not hard to see that the prf (A) can be smplfed to prf a ( A) D (2) 1 a b Equaton (2) shows that, n general the pro-rata factor for state A wll dsplay seasonal patterns, wth seasonal factors beng{ a /( a b )} 1,.... Only under the specal crcumstance that state A and state B have dentcal seasonal factors wll prf (A) be a constant. To see ths, assume state A and state B have dentcal seasonal pattern, then for any month n the year the two seasonal factors are proportonal to each other b a where 1 7. In ths case a /( a b ) becomes 1/(1 ), a constant that does not vary from month to month. It should be noted that the seasonal pattern for prf (A) s n general dfferent from the orgnal seasonal pattern for the NSA data X. To further llustrate possble seasonalty caused by pro-rata factors computed from NSA data, we take the LAUS NSA employment data for the states of Alaska (AL) and Texas, whose seasonal patterns are very dfferent due to obvous reasons such as clmate and geographcal locaton. Assumng Alaska and Texas were the only two states n the same census dvson, we construct the pseudo pro-rata factor for Alaska through dvdng the NSA employment seres of Alaska by the sum of the two states NSA employment seres. Fgure 1 shows the constructed pro-rata factors along wth the orgnal NSA employment seres of Alaska. The pseudo pro-rata factors clearly dsplay a seasonal pattern. In addton, the peaks and troughs of the two seres dffer substantally. 7 equals -1 n the polar case where the two states have exactly the opposte seasonal patterns. 4

6 Feb-90 Nov-90 Aug-91 May-92 Feb-93 Nov-93 Aug-94 May-95 Feb-96 Nov-96 Aug-97 May-98 Feb-99 Nov-99 Aug-00 May-01 Feb-02 Nov-02 Aug-03 May-04 Feb-05 Nov-05 Aug-06 May-07 Feb-08 Nov-08 Aug-09 May-10 Feb-11 Nov-11 Aug- May-13 Fgure 1. Seasonal Pattern n AL Employment BLS NSA Employment vs. the Constructed Pseudo Pro-rata Factor Pseudo Pro-rata Factor for AL Employment Annualzed Growth n AL Employment (NSA) The example here shows that adjustng SA data usng the pro-rata factors based on the NSA data may ntroduce undesrable seasonalty. Ths secondary seasonal pattern nvoked n the benchmarked data may dffer dramatcally from the orgnal seasonal pattern n the NSA data. 3. Some Emprcal Evdence As dscussed n the prevous secton, theoretcally there are varous possble causes of seasonalty n the SA state labor force data, thus t s worthwhle to carry out an emprcal exercse to see whch one s more mportant. For ths purpose, we frst estmate the stable seasonal factors usng the annualzed monthly growth rates of the followng 1) The SA labor force data n those states where the combned test showng 5

7 presence of dentfable seasonalty; 2) The NSA labor force data n the same states as n 1); 3) The US natonal NSA labor force data; 4) NSA labor force data for the nne census dvsons. We then run the followng regresson, whch s ntended to decompose the varaton of seasonalty detected n the state level SA labor force data. SF _ state _ SAjt 1 SF _ state _ NSAjt 2SF _ US _ NSAjt 3 SF _ Dvson _ NSA jt jt Here j refers to the state of nterest and t 1,2,..., denotes the twelve months. The dependent varable s the seasonal factors estmated from the state level SA data. The three ndependent varables are the seasonal factors estmated from the state level NSA data, the seasonal factors estmated from the natonal NSA data and the seasonal factors estmated from the assocated census dvson NSA data. Table 2 reports the results. The seasonal pattern n the US natonal data are found to be the most mportant sngle factor explanng the seasonal movements n the state level SA cvlan labor force and employment. Statstcally the coeffcent estmates on the natonal seasonal factors are hghly sgnfcant. Take January as an example, f on average the seasonal factor drves up the annualzed growth rate n US cvlan labor force by 4.9% when compared to other months, there wll be a 0.2% upward seasonal adjustment for January (4.9%*0.041) n the annualzed growth rate for state level cvlan labor force. For the number of unemployed, the seasonal pattern n the regonal NSA data s found to be correlated wth the seasonalty n the SA state unemployment, albet margnally sgnfcant. The negatve sgn of the coeffcent estmates s consstent wth fact that the NSA benchmark total enters the denomnator when computng the shares. The small magntude of the coeffcent estmates s also expected f the seasonalty n the state level SA data manly comes from the pro-rata factors. In contrast, the seasonal pattern n the state level SA data s found to be very dfferent from that n the state level NSA data. Only n the number of employed seres we fnd the two are margnally correlated; and the coeffcent estmate s less than one thrd of the coeffcent estmate on the natonal NSA employment. Thus, emprcally the seasonalty from the pro-rata factors seems to be the domnant source of seasonalty found n the SA state labor force data. 6

8 Table 2. Decomposng the Seasonalty n the SA State Labor Force Data 8 Seasonal Factors Estmated from State SA Data Cvlan Force Labor Employment Unemployment Adj. R-sq = Adj. R-sq = Adj. R-sq = Seasonal Factors Estmated from assocated Census Dvson NSA data ( ) ( ) * ( ) Seasonal Factors Estmated from US natonal NSA data *** ( ) *** ( ) ( ) Seasonal Factors Estmated from state NSA data Notes: Standard errors n parentheses (0.005) * ( ) ( ) *** Sgnfcant at 1 percent level ** Sgnfcant at 5 percent level * Sgnfcant at 10 percent level 4. Use of the Henderson Flter Because of the volatlty caused by the monthly benchmark the BLS apples a Henderson trend flter to the SA data before they release the offcal estmates. Whle ths causes the state data to look very smooth the flter may msrepresent actual volatlty n the seres. To better llustrate ths problem, we calculate a dfferent verson of US natonal unemployment rate than the one publshed by BLS. More specfcally, we dvde the sum of all state SA unemployment by the sum of all state SA cvlan labor force. Fgure 2 compares the monthly changes n the derved SA unemployment rate wth those of the offcal BLS SA unemployment rate. Not surprsngly, the derved SA US unemployment s much 8 We have also tred ncorporatng the state fxed effect. It turns out the results are bascally the same as the ones reported n Table 2. 7

9 smoother because of the Henderson trend flter. When we study the month-to-month changes, n 99 out of the total 281 months (or about 35 % of the tme), the offcal BLS SA estmate moves n the opposte drecton as the derved SA estmate. Ths dscrepancy between the two estmates mples that the SA state level labor markets often show an nconsstent or even conflctng vew than the natonal labor market does. Ths s surprsng snce the benchmark process was supposed to make the states and regons more consstent wth the naton. 5. Concludng Remarks We fnd statstcally sgnfcant seasonalty n the many of the seasonally adjusted state LAUS seres. We also fnd that the seasonalty s possbly drven by pro-rata factors used n the benchmarkng process. Ths mples these seasonal changes are spurous and do not represent true regonal dynamcs. If, as the present paper suggests, the seasonalty n the SA state level LAUS data truly comes from the pro-rata factors, one straghtforward remedy would be to compute the pro-rata factors based on SA data nstead of the NSA data. To get the NSA data for each state, the BLS can multply the SA adjusted data by the state seasonal factors. Dong benchmark adjustment n ths manner may reduce the volatlty n the state SA estmates and may reduce the need for the Henderson trend flter whch seems to be creatng too much smoothness n the state estmates. 8

10 Fgure 2. US Unemployment Rate Offcal BLS V.S. Derved SA estmate 10% 8% 6% 4% 2% 0% -2% -4% -6% -8% -10% Derved SA US UR Offcal BLS US UR 9

11 References Bureau of Labor Statstcs, Questons and Answers on the Local Area Unemployment Statstcs (LAUS) Program Redesgn for 2005 at Bureau of Labor Statstcs, LAUS Estmaton Methodology at Bureau of Labor Statstcs, Smoothed-Seasonally-Adjusted Estmates (SSA) Questons and Answers at Lothan, J. and Morry, M., A Test for the Presence of Identfable Seasonalty When Usng the X- 11-ARIMA Program, Stat Can Staff Paper STC2118, Seasonal Adjustment and Tme Seres Analyss Staff, Statstcs Canada, Ottawa. Phllps K and Nordlund J., 20. The Effcency of the Benchmark Revsons to the CES Data Economc Letters 115,