1. “The New Normal”: Structural vs.Cyclical U.S.Unemployment
Econometrics II
May 2, 2014
Joshua T. Rome

2. One topicat the forefrontof U.S.economicdevelopmentoverthe pastseveral yearssince the
financial crisishasbeenunemployment. The catalystof thisdiscourse isnomystery.Unemployment
impactsmanyAmericansandthe relationshipwithGDPisempiricallyverifiable (thesocalled“Okun’s
law”). The mainquestionregardingthe persistentlyhigh levelsof unemployment iswhetherthishas
beena structural or prolongedcyclical effect. Thispaperseekstounderstandthe recentchangesinthe
unemploymentrate inthe contextof the previoussixtyyearsof unemploymentdatathatisavailable.
The firstportionof the analysiswill be composedof lookingatthe patternof the unemploymentrate as
a standalone time series. Followingasolidunderstanding of the historictrend;the unemploymentrate
will be comparedwithtotal jobopeningsforfurthercluestothe nature of the recentunemployment
levels.
Analyzing the data
The firststepin derivingarelationshipbetweenthissetof variablesistosimplyobserve the dataover
time;andto analyze if there are any
trends,seasonalityorotherdiscernible
patterns. We beginbylookingat time
graphs of our mainvariablesbeginning
withunemployment. Aswithmany
macroeconomictime series
unemploymentisstronglytrended,
showingcyclical peaksandtroughs,
althoughvaryingindurationaswell asmagnitude. Itisclear thatlevel of unemploymenttodaystrongly
dependsonthe level of unemploymentyesterday. If modeledasafirstorder autoregressivemodel:
𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑡 = 𝐵0 + 𝐵1 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑡−1 + 𝜀 𝑡

3. The model appearsto be verysignificant,withthe overall level of significance of the F-Statistic
at zero withanR-squaredof almost94%. Unfortunatelythesespurious resultsare anartifact of the high
levelsof autocorrelation. Because ourmodel includesarighthandside dependentvariable any
autocorrelationcausesestimatesof the regressiontobe inconsistentandinvalid;unfortunatelyaswell
the Durbin-Watsonteststatisticwillnotbe validandcannotbe used. Thuswe will use Durbin’s‘h’test
whichisdesignedforexactlythissituation. We firstcompute the DurbinWatsonteststatistic:
DW=.9878363 and from thisstatisticwe can backout our estimate for rho. 𝑃̂ = 1 −
𝐷𝑊
2
andwe
compute thisvalue tobe .50608185. ℎ =
𝑃̂√
𝑛∗
(1−𝑛∗)𝑆𝐸.𝐵̂
ℎ = .51√
256
(255).000240
= 32.715 >
2.56 thus we rejectthe null hypothesisthat
there isno autocorrelationforthismodel
specification. If apartial Correlogramis used,
whichis basedon the partial autocorrelation
functionintroducedbyBox-Jenkins,we canclearlysee thatthe firsttwolags of the model lie outside of
the 95% confidence interval andthusare notrandom. The coefficientonthe original model alsomight

4. seemtosuggesta unitroot as it isveryclose to one (.96); andthe dickeyfullertestfora unitroot would
be appropriate totest forthis. The resultforthe dickeyfullertestwiththree laggedtermsandatrendis
significantwithap-value of .0385; thuswe rejectthe null hypothesisof arandom-walk.
The processof correctlyspecifyingthe model reliedonsimilarbutunrelatedintuition of how
businesscycleswork. Inthe 1950’s manyeconomistsdescribedthe businesscycle intermsof alag on
investmentdecisiondependingonthe growthof the economy. The resultingspecificationforthis
phenomenonwasa“secondorderdifference equation”where the dependentvariable wasafunctionof
the difference of the laggedfirstdifference of thatvariable. Ingeneral the systemcanresultin
dampeningoranti-dampeningeffectsorstable peaksandtroughs;andof course applicable toother
fields. Basedonthisintuitionthe model forunemploymentisestimated usingaportion of the sample
(observations 1through50) witha laggedtermand a laggedfirstdifference term.
𝑈𝑁𝑅𝐴𝑇𝐸𝑡 = 𝐵0 + 𝐵1 𝑈𝑁𝑅𝐴𝑇𝐸𝑡−1 + 𝐵2( 𝑈𝑁𝑅𝐴𝑇𝐸𝑡−1 − 𝑈𝑁𝑅𝐴𝑇𝐸𝑡−2)+ 𝜀 𝑡
Thismodel isverysignificantwithlow RMSEwhichisgoodfor prediction. Generatingaprediction
variable we cantestthe model we cantestthe model forthe remainingportionof the sample from

5. 1962-2014. The resultsof this out-of-sampleforecastare verytightlyfitaroundthe actual datawitha
meanresidual of .1621 as the difference betweenthe actual unemployment.
There are twomainsourcesof uncertaintyregardingprediction;inthismodel aswell asany
other. If the true valuesof all of the modelscoefficients wereknown;the rootmeansquarederror
wouldbe the standarddeviationof the forecastwhichwe couldassume the errortermisnormally
distributedaboutthe mean. Itisnot possible toknow the true value of the coefficients,becausefor
each sample thatisdrawn;new coefficientswillbe estimated. Tocompute the variance of the estimate
Var(є) we compute Var(𝑦 − 𝑦̂) whichequalsVar(𝑦̂)+Var(y) –2Cov(𝑦̂, 𝑦).
Mathematically;the implicationsof thismodel are numerous. Firstlythe modelimpliesalong-
run unemploymentrate of 5% basedon the data. Thiscan easilybe shownby solvingforthe steady
state where 𝑥 𝑡 = 𝑥 𝑡−1 = 𝑥 𝑡−2
Thus: 𝑥∗ = .75 + .85𝑥∗ + .55( 𝑥∗ − 𝑥∗)
Resultingin: .15𝑥∗ = .75
𝐷𝑖𝑣𝑖𝑑𝑒 𝑏𝑦 .15
⇒ 𝑥∗ = 5
Thismodel wasestimated
fromthe sample from
1950-1962, all other
estimatesare out-of -
sample forecasts;from
whichwe observe thatthe
model fitsthe datavery
closely.

6. Economicallythismaynotbe the mostgranularapproach to estimatinganequilibrium
unemploymentlevel;butthe figure doesappeartobe reasonable. IndeedSt.LouisFederal reserve data
estimatesNROUthe natural rate of unemploymentwithameanvalue of 5.55% anda value exactly
equal to5% fromthe years2000-2009. A more accurate predictionof the longrun“natural”level of
unemploymentshouldtake intoaccountdemographicsof the population. Anadditional implicationof
thismodel specificationisthat the coefficientof the laggedfirstdifference at.55 is that the specification
isunstable;butwithdampeningeffect. Inotherwordsany shocksto the systemwill resultinsmaller
and smallerdifference fromthe steadystate level;the systemisdynamicallystable.
For the nonmathematical non-statisticalreaderwhatwe learnfromthismodel isthe
dependencyof the currentlevel of unemploymentonpreviouslevelsof unemployment. Predictionwith
thismodel issomethingakintopredictingthe weather tomorrow bylookingoutthe window today;
brightand sunnyandseventywe cansay withsome certaintythatit ishighlyunlikelytosnow.With
unemploymentatagivenlevel we canmake similarobservations. Thismodel alsomakesanother
implicitpredictionof alongrun rate of unemploymentof five percent,althoughthe accuracyof this
predictioncanbe greatlyimprovedwithothereconomicdatasuchas populationdemographics.
Nowthat we understandthe nature of the unemploymentdataovertime we shiftouranalysis
towardsthe recenttrend. The unemploymentrate hadnot reachedheightsof levelsabove 8% since the
1980’s, and yearslateraftera recoveryinequitypricesthe unemploymentrate isstill atitshighestlevel
0
2
4
6
8
10
12
0 10 20 30 40 50 60
Thisdiagramillustratesthe dynamic
stabilityof the model specifiedfrom
the regression. The firstfew
observationsare takenfromthe
actual data;the restare the
predictionsbasedonthe model.
Randomshocksare exogenously
introducedat32-38 and40 to
illustrate the dynamicstability.

7. inat leastone decade. Inorderto understandthistrendwe mustturnto the Beveridgecurve that
relatesthe numberof nonfarmpayroll openingstothe unemploymentrate.
In the figure we see the monthly dataof the two time seriesplottedagainsteachother fromthe
yearsDec 2000- Mar 2014 formingthe so-calledBeveridgeCurve. Itappearsobviousthatthere isa
structural differencebetweentwodifferenttime periods;visuallyone couldidentifytwolinesthatbest
fitthe data. Basedon intuitionthere isadownwardsloping
line whichwe specifyas (RestrictedModel):
𝐽𝑜𝑏 𝑉𝑎𝑐𝑎𝑛𝑐𝑦 𝑅𝑎𝑡𝑒𝑡 = 𝛽0 + 𝛽1 𝑈𝑁𝑅𝐴𝑇𝐸𝑡 + 𝜀 𝑡
Our coefficientof betaone isbelievedtobe negative; which
the regressionconfirms. Inallowingthe slopeandcoefficient
to be differentforthe twodifferentperiodswe definea
categorical dummyvariable 𝑑𝑖 thatistrue for all periodsafterAugust2009. The specificationof the
secondperiodmodel is:
𝐽𝑜𝑏 𝑉𝑎𝑐𝑎𝑛𝑐𝑦 𝑅𝑎𝑡𝑒𝑡 = ∝0+∝1 𝑈𝑁𝑅𝐴𝑇𝐸𝑡 + 𝜀 𝑡
In orderto create a more parsimoniousdefinitionof ourmodel inone equationwe mustdefinethe
differencesbetweenthe twoseparate modelcoefficients: Let 𝛿1 =∝0− 𝛽0 𝛿2 =∝1− 𝛽1
The unrestricted model: 𝐽𝑜𝑏 𝑉𝑎𝑐𝑎𝑛𝑐𝑦 𝑅𝑎𝑡𝑒𝑡 = 𝛽0 + 𝛽1 𝑈𝑁𝑅𝐴𝑇𝐸𝑡 + 𝛿1 𝑑 𝑖 + 𝛿2 𝑑𝑖 𝑈𝑁𝑅𝐴𝑇𝐸𝑡 + 𝜀 𝑡
Afterexecutingthe regressionof boththe restrictedandunrestrictedregressionswe are able to
performa chowtestof structural difference. The null hypothesisisthatthe unrestrictedmodelis ∝0=
𝛽0 𝑎𝑛𝑑 ∝1= 𝛽1while the alternative hypothesisisthatthe twoare in fact different.
ChowTest
( 𝑆𝑆𝐸𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑−𝑆𝑆𝐸 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑)∗
1
𝑞
𝑅𝑒𝑠𝑡𝑟𝑖 𝑐 𝑡𝑖 𝑜 𝑛𝑠
𝑆𝑆𝐸 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑∗
1
𝑛−𝑘
=
3.098836765
0.025153714
= 123.19 > 4.605
The sum of squarederrorforthe unrestrictedmodelis 3.89882567, with155 denominatordegreesof
freedom. The Restrictedsumof squarederroris 10.0964992 and the numberof restrictionsistwo

8. correspondingtothe numeratordegreesof freedom. Giventhese degreesof freedomthe chow testwe
can rejectthe null hypothesisthatthere isnostructural break at the 1% significance level.
The cause generallyattributedtothe shiftinthe Beveridgecurve isincreasedfrictionsin
matchingbetweenemployeesandemployers. Followingthe greatrecessionunemploymentbenefits
were greatlyextendedtobeyondone year;impeding searchersfromincreasingtheireffort,thus
decreasingmatchingefficiency. Structurallythe principallyaffectedindustryof the crisisfollowingthe
housingboomhadbeenthe constructionindustry. Thisindustryhasrelatively lessfrictioninmatching
compared to otherhigherskill industries thathave lesshirespervacancy suchas engineering. Inan
article fromthe IMF EconomicReviewHobijnandSahinattribute muchof this shiftbetweenthese two
factors1.
Hobijn’sandSahin’sstudywasa longitudinal analysisof thirteencountriesoverfifteenyears.
Interestingfindingsof theirresearch are thataside fromthe U.S. onlythree othercountriesexperienced
a rightwardshiftinthe Beveridge curve: Portugal,Spain,andthe UnitedKingdom. (The othercountries
analyzedinthe sample were Australia,Austria,Belgium, France,Germany,Japan,Netherlands,Norway
and Switzerland.) Whatthese three countrieshadincommonwasa disproportionate decline in
construction, acorollaryof the steepdeclinesinhousingprices. Inaddition,the researchwasputintoa
historical perspectivewithBeveridgeshiftsof the 70’s and 80’s that had reversedtheirrightwardshift
followingrecessions. The conclusionsof theiranalysis are thatthe rate of adjustmentof U.S.labor
relative toothercountriesisveryhigh,andgiventhat unemploymentinsurance increasesare not
permanent;the questioniswhenthiscyclical effectwill subside.
Shiftingfocustothe latestiterationof the Beveridge Curve;althougharightwardshifthas
occurredwhichis consistentwith“structural unemployment”,the curve appearstobe on a path back to
itspreviousstructural levelslendingsupporttothe “prolongedcycle”argument. The observations are
connectedintime anddecreasinginunemploymentwhilstincreasinginNonfarmjobopenings. This

9. componentof the recenttrendiscyclical. But itis importanttonote that the trend isnot a straightline,
nor convex asthe Beveridge Curve isgenerallyportrayed. Thisnonlinearstructure resemblinga
downwardopeningparabolacanbe modeledby
regressingnonfarmjobopenings onafirstorder
‘UNRATE’ term witha squared ‘UNRATE’ term. The
coefficientof the squaredtermisexpectedtobe
negative because the curve isdownwardopening,and
giventhe tightbandof variationthe model is
expectedtobe verystatisticallysignificantwithahighr-squared.
Specification: 𝐽𝑜𝑏 𝑉𝑎𝑐𝑎𝑛𝑐𝑦 𝑅𝑎𝑡𝑒𝑡 = 𝛽0 + 𝛽1 𝑈𝑁𝑅𝐴𝑇𝐸𝑡 + 𝛽1 𝑈𝑁𝑅𝐴𝑇𝐸1
2
+ 𝜀 𝑡
The regressionof the newmodel satisfiedall of the apriori assumptionsbut withone unique concern,a
verystatisticallyinsignificantconstantterm. Afterconsiderationof the context;the unemploymentrate
isrelativelyfarfromzeroconsideringthe spacingof the observationsandquantityof observations. In
thiscontextthe lowsignificanceof the constanttermisunimportantandmerelyreflectsalarge distance
fromthe y axisfromthe observations. Economically the empiricallyderivedcurve lendsevidence tothe
prolongedbusinesscycle theoryregardingthe unemployment. Inthe contextof the previousBeveridge

10. curve ex ante the greatrecession,the model predictsthatwe are on a path that leadstothe old
structure of the Beveridge Curve. The currenttrendthuscan be decomposedintotwocomponents;a
currentcyclical trendof reducedunemploymentandincreasedjobopenings,andaleftwardshifttothe
olderlevelsof matchingefficiency. As
extensionsof unemploymentinsurance
are eliminatedandthe housingmarket
recovers,higherturnoverpositionswill
constitute alargercompositionof the
overall USjob marketandlabor market
efficiencywillslowlyreturn. Although
the economyhasrecovered
significantlysince the greatrecession,the recoveryhasbeenslow goingandiscontinuingtothisday.
Despite specious evidenceof apermanentstructural change,a“new normal”,the relativelyhigh
levelsof unemploymentinactualityare nothingmore thana painfullyslow businesscycle. The analysis
done by Hobijnand Sahindiffersinthattheirfocusisa cross-countryanalysis asopposedtoa specific
trendanalysis, butcomplementsthisresearchwithrichhistoricdataand cross-countrycomparisons.
Althoughdemographicfactorsplaya large role inshiftingstructuresof employment;the coincidenceof
such a change duringthisbusinesscycle isnotseentobe the dominatingfactor. In the comingyearsthe
data suggesta returnto the “old normal”as labormarketinefficienciestaperfromthe market. In
practice,onlytime will tellwhetherthe recessionchange hasbeenpermanent, neverthelesscurrent
researchindicatesasanguine outlook.

11. Works Cited
1. Hobijn,B.,& Şahin,A. (2013). Beveridge Curve ShiftsacrossCountriessince the Great
Recession.IMFEconomicReview,61(4),566-600. doi:10.1057/imfer.2013.18
2. Diamond,P.(2013). Cyclical Unemployment,Structural Unemployment.IMFEconomicReview,
61(3), 410-455.
3. Data Source:FRED, Federal Reserve EconomicData,Federal Reserve Bankof St.Louis:Civilian
UnemploymentRate [UNRATE];U.S.Departmentof Labor:Bureau of Labor Statistics;
http://research.stlouisfed.org/fred2/series/UNRATE;accessed May1st
, 2014.
4. Data Source:FRED, Federal Reserve EconomicData,Federal Reserve Bankof St.Louis:Natural
UnemploymentRate [NROU] ;U.S. Congressional BudgetOffice;
http://research.stlouisfed.org/fred2/series/NROU;
5. Data Source:FRED, Federal Reserve EconomicData,Federal Reserve Bankof St.Louis:Job
Openings:Total Nonfarm[JTSJOR];U.S.Departmentof Labor:Bureauof Labor Statistics;
http://research.stlouisfed.org/fred2/series/JTSJOR;accessedMay1st, 2014.