A Forecast of Non-Farm Employment in the United States 4th Quarter 2013 3rd Quarter 2015 By Marius Mihai & Chaoyun Liu University of New Orleans December 2013 Acknowledgments ThisreportwaspreparedbyMariusM.MihaiandChaoyunLiu,GraduateResearchAssistantsatthe University of New Orleans (UNO), as a final project for the Time Series Analysis class. Thanks and recognition is given to Dr. Tumulesh Solanky, for his valuable lessons which allowed us to complete this analysis. Introduction Total non-farm payroll employment in the United States (US) is one of the most important leading economic indicatorsreportedbytheBureauofLaborStatistics(BLS)onamonthlybasis.Monitoringthistimeseriesis imperativewhenassessingthestrengthofthenationaleconomy.Forecastingsuchaseriesisalsocrucial, becauseitprovidesagoodoverviewofhowthejobmarketwillperforminfuturetimeperiods.This informationisveryimportantnotonlytothegeneralpublic,butalsotoalldecisionmakersinabusiness environment. Forsimplicity,throughoutthereportwewilluseUSnon-farmpayrollemploymentandUSemployment interchangeably. The data selected was seasonally adjusted and it goes back to 1980. The analysis and forecast will be done on a quarterly basis. A total of 135 data points were collected. A.Preliminary Analysis 1.Time Series Plot Total non-farm employment in the United States had a positive growth from 1980 to 2013. The time series plot is presented on therightanditshowsaclearpositive trendwithfoursignificantdownturns whichrepresentmajorrecessionsinthe UnitedStates.Thefirstmajordropin economicactivityvisibleinourplotwas theearly1980srecessionthatstemmed fromthe1979energycrisis.Thiscrisis originatedfromtheIranianRevolution, and that led to sharp increases in oil prices aroundtheworld.Anotherdropinthe numberofUSjobsoccurredintheearly 1990swhichalsocoincidedwithaperiod of economic turmoil nationwide. The third andfourthdeclinesin thenumber ofjobs atanationallevelwerealsotheresultof therecessionintheearly2000sandthe Great Recession of 2009. 2.Autocorrelation Plot and Autocorrelation Check for White Noise Inordertobeabletomodelthedata, variousassumptionshavetobeverifiedto see if our figures indeed follow a time series pattern.Theautocorrelation(ACF)plot(on the right)isa decaying function, butitdoes notdecreasefastenoughinordertomake theseriesstationary.Therefore,thedatain itsoriginalformisnon-stationary.The resultsoftheACFcheckforwhitenoiseare presentedinthetablerightbelow.Thep-valuesaresmall,thustherearenon-zero autocorrelationspresentinthedata.The timeseriesstructureassumptionisverified, sotheUSnon-farmemploymentcanbe modeled as a time series. Autocorrelation Check for White Noise To LagChi-SquareDFPr>Chi-Square 6739.636 |t|Lag MU205.89901136.149911.510.13320 AR1,10.930870.0472319.71Chi-Square 610.2230.0168 1211.6090.2367 1814.17150.5127 Number (In Millions)8000090000100000110000120000130000140000Date01JAN1980 01JAN1985 01JAN1990 01JAN1995 01JAN2000 01JAN2005 01JAN2010 01JAN2015Quarterly US NonFarm Employment 1980-2013PLOT US_employment Forecast for US_employment26.AR non-zero parameters at 1, 3, 7, 11 Thismodelisanautoregressivemodelwiththe presentvaluebasedonthepreviousvalue,the previousthirdvalue,thepreviousseventhvalue, andthepreviouseleventhvalue.Theforecast madebythismodelfitsthedataverywell.The conditional least squares estimation shows that the p-valuesofthefirstandsecondparameterare significant. The AIC and SBC of this model are 1,695 and1,709,andthestandard deviation oftheerror is 277. Conditional Least Square Estimation ParameterEstimateStd. Errort ValuePr > |t|Lag MU220.25644124.891191.760.08050 AR1,11.010070.0620716.27Chi-Square 66.6020.0369 128.6080.3773 1811.24140.6669 2414.90200.7821 Number (In Millions)8000090000100000110000120000130000140000Date01JAN1980 01JAN1985 01JAN1990 01JAN1995 01JAN2000 01JAN2005 01JAN2010 01JAN2015Quarterly US NonFarm Employment 1980-2013PLOT US_employment Forecast for US_employment2 C.Model Selection AIC,SBCandSt.Deviationwereplotted and compared in order to make the best model selection. Asitcanbeseen,AICsandSBCswere not very different - that made it hard to makeadecisionbasedsolelyonthose twocriteria.Thus,moreweightwas giventothestandarddeviationvalue. AR1,7wasselectedovertheother modelsbecauseithadtheminimum deviation from the actual values.AR1,7wasappliedtoalldatapoints and the following results were obtained: Fromtheparameterselection,it appears that only the lag 1 parameter wassignificant.Theparameteratlag 7,althoughitwasnotsignificant,its p-valuewasnotextraordinarilyhigh- thereforeitsrejectionwasnota strong one. The autocorrelation check forresidualswasalsogood.P-values werehighandtheydidnotindicate anytimeseriespatterninthe residuals. Conditional Least Square Estimation ParameterEstimateStd. Errort ValuePr > |t|Lag MU213.22130.591.630.10490 AR1,10.890.0420.87Chi-Square 611.7960.0669 1215.25120.2280 1817.30180.5025 332665181274 281 27702004006008001,0001,2001,4001,6001,800AR 1,2,11 AR 1,4 AR 1,7 AR 1, 2, 7 AR 1, 5, 7 AR 1, 3, 7,11AIC, SBC, St. Deviation ComparisonAICSBCSt. Dev. Above, there is the forecast plot for the next 8 quarters along with its 95% confidence limits.According to our model,USnon-farmemploymentwillcontinuetoincreaseoverthenexttwoyears.Inaddition,the95% confidence limits were assumed to represent various scenarios in the US economy. Thus, the upper 95% limit represents the number of non-farm jobs amid a potential boom in the national economy, while the lower 95% limit shows the number of jobs in case another recession happens.Otherwise, with everything else assumed tobeequal,inthenext twoyearsUSnon-farm employmentshouldfollowtheoptimal forecastrepresented by the red line in our plot above. The table below presents the actual forecast, upper 95, and lower 95 values generated by our model. Date Forecast(million) Optimal conditions Lower 95(million) Economic Recession Upper 95(million) Economic Boom 2013 Q4136.6136.0137.1 2014 Q1136.9135.7138.1 2014 Q2137.3135.4139.2 2014 Q3137.6134.9140.3 2014 Q4137.9134.3141.4 2015 Q1138.1133.8142.4 2015 Q2138.3133.1143.5 2015 Q3138.5132.5144.5 Number (In Millions)8000090000100000110000120000130000140000150000Date01JAN1980 01JAN1985 01JAN1990 01JAN1995 01JAN2000 01JAN2005 01JAN2010 01JAN2015 01JAN2020Quarterly Forecast US NonFarm Employment 2013 Q4-2015 Q3PLOTUS_employment Forecast for US_employmentUpper 95% Confidence Limit Lower 95% Confidence LimitD.Conclusions and LimitationsMostrecentdataindicatesthatasofthethirdquarterof2013,thetotalUSnon-farmemploymenttotaled about136.2millionjobs.Basedontheresultsofourmodel,theUSeconomyisprojectedtoreachabout 138.5 million non-farm jobs by the end of the third quarter 2015. That is an increase of about 2.3 million jobs, or 1.7% under optimal growth conditions, and assuming no other extraordinary events will distort the national economy. Limitation: The BLS (Bureau of Labor Statistics) revises this data relatively often.Our forecasted values would change should the BLS update the US non-farm employment figures. Thus, our analysis is solely based on the figuresreleasedforthemonthofNovember2013,andshouldberevisediftheBLSprovidesupdatestoour current numbers. E.Data Sources OurprimarydatasourcewastheBureauofLaborStatistics.Below,weprovidedthelinkandtheSeriesId where this data can be downloaded from.http://data.bls.gov/cgi-bin/srgate Series ID: CES0000000001