Small Business Indicators of Macro-Economic Performance: an Update by NFIB

Small Business Indicators of Macro-economic Performance: An Update

July 2012

Michael J. Chow The NFIB Research Foundation is a small business-oriented research and information organi- zation affiliated with the National Federation of Independent Business, the nation’s largest small and independent business advocacy organiza- tion. Located in Washington, DC, the Foundation’s primary purpose is to explore the policy-related problems small-business owners encounter. Its peri- odic reports include Small Business Economic Trends, Small Business Problems and Priorities, and now the National Small Business Poll. The Foundation also publishes ad hoc reports on issues of concern to small-business owners. Executive Summary

• Since small business produces somewhat less than one-half of private GDP and employs somewhat more than one-half of the private workforce, measures of small business economic performance should correlate closely with government-produced indicators of macroeconomic performance. The flatter structure of small firms relative to large firms also arguably means that decision-makers in small firms receive information faster than decision-makers in large firms and therefore change course more quickly, providing timelier insight into the future course of national economic activity.

• NFIB has collected data quarterly on the economic performance of small businesses and their owners’ economic expectations since 1973, nearly 40 years. These quarterly data are the basis for the analysis presented here. Collection of identical data on a monthly basis began in 1986, though the monthly numbers are not employed in this analysis. The data are published each month in Small Business Economic Trends.

• The data collected from mail surveys of NFIB member samples include small business measures of sales performance, earnings, prices, labor market conditions including job openings, hiring plans and compensation, credit conditions including credit availability and interest rates, inventory satisfaction and plans, planned capital outlays, expansion plans, and overall expectations.

• The analysis presents an extensive series of equations and graphs showing the capacity of small business data to forecast (predict) the course of national economic performance. They relate the former to the latter, in most cases from 1973 to 2008. Some relationships prove much stronger (better predictors) than others.

• The analysis also presents a series of “out-of-sample” forecasts from 2009 through 2011 covering part of the Great Recession and its immediate aftermath. The results are effectively free (not updated quarterly) forecasts of economic activity for one of the most tumultuous periods in American economic history.

• The headline NFIB Optimism Index, an equally-weighted index of ten NFIB survey measures, does a reasonable job of predicting changes in quarterly real GDP and final sales to private domestic purchasers. Out-of-sample forecasts of real GDP growth for 2009:Q1 through 2011:Q4 are consistent with the view that the small business sector lagged performance of the large business sector and the broader economy since the Great Recession began.

• The NFIB labor market measures do an admirable job predicting changes in both private sector employment and the unemployment rate.

• The consistently best small business forecasts are of price changes. The NFIB price measures do an excellent job predicting changes in the Consumer Price Index (CPI) and the Personal Consumption Expenditures (PCE) index. However, they have difficulty predicting movements in “core” measures of CPI or PCE.

• Large, capital-intensive businesses make the lion’s share of inventory purchases and capital investments in the United States. Still, NFIB measures explain a reasonably large share of the changes in private business inventories, a notoriously volatile number, and measures of fixed private investment. • The relative interest rate paid by small business owners and small business credit “tightness” are strongly correlated with the federal funds rate and the yields on common government debt securities.

• The NFIB Optimism Index outperforms both the Conference Board’s Consumer Confidence Index and the University of Michigan’s Index of Consumer Sentiment as a predictor of changes in real GDP. Table of Contents

Introduction ...... 1

Real GDP Growth ...... 4

Employment, Unemployment, and Labor Markets ...... 12 Employment ...... 13 Unemployment ...... 14 Labor Compensation ...... 16

Inflation ...... 18

Business Inventories ...... 25

Capital Expenditures ...... 29

Capital Markets ...... 33

Other Indicators ...... 38

Concluding Observations ...... 41

Appendix A. Small Busines Economic Survey ...... 42

Appendix B. Notes Regarding Model Specification and Selection ...... 46

Appendix C. Notes Regarding Time Series Analysis ...... 47

Appendix D. Augmented Dickey-Fuller Test Results ...... 49

Appendix E. Granger Causality Test Results and Forecast Analysis ...... 51 “Today bringsthemostimportantbusinesssurvey—ifnotimpor- The NationalFederationofIndependentBusi- This mailingwasfollowedbyasecondabout I 4 3 2 1 first monthofeachquarter,andabout660 was selected,andasurveyformmailed yield averages about 1,850 responses in the tant economicrelease—ofthemonth.TheNFIBsurveyofsmallerbusi- NFIB’s smallbusinessownermembersona ing survey,anditsfailuretorecoverproperly,evenastheISMrebounded questionnaire hasbeenmailedtoasampleof questionnaire isincludedinAppendixA. covers nearly 40 years. A copy of the current that time,avirtuallyidenticalthree-page than quarterly.Responsesarecollectedfor ten dayslater.SinceJanuary1986,thesame to themonthefirstdayofeveryquarter. ness (NFIB)beganconductingeconomic random sampleoftheNFIBmembershiplist regular basis,therebypreservingthecompara- about 25days,andduplicatesarepurged.The procedure hasbeenfollowedmonthlyrather nesses spottedtherecessioncomingayearaheadofISMmanufactur- surveys ofitsmembershipin1973. bility ofthedataseriesovertimewhichnow sluggish overthepastcoupleofyears.” strongly, explainswhytheoverallperformanceofeconomyhasbeenso

ntroduction 110-343, 13May 2010. Panel, submitted under Section125(b)(1)ofTitle1 oftheEmergencyEconomicStabilization Actof2008,Pub.L.No. report oftheCouncilEconomic Advisers,UnitedStatesGovernmentPrintingOffice,Washington: 2011. See, forexample: small-business-economic-trends. Electronic versions of In theearly1980s,responsibilityforsurveywastechnicallytransferred fromNFIBtotheResearchFoundation. Economic Activity,”DatabasesfortheStudyofEntrepreneurship,(ed.) JeromeA.Katz,JAI,NewYork,2000. liam C.Dunkelberg,“SmallBusinessEconomicTrends:AQuarterCentury LongitudinalDataBaseofSmallBusiness A descriptionoftheoriginandcontentNFIB’seconomicsurvey can befoundin:WilliamJ.Dennis,Jr.,andWil- From Octoberof1973through1985,a “The SmallBusinessCreditCrunch andtheImpactofTARP,”MayOversightReport,Congressional Oversight Small BusinessTrends,PolicyandSupervisoryStudies,Federal ReserveBankofAtlanta,May2011. The 2011EconomicReportofthe President,transmittedtotheCongressFebruary 2011togetherwiththeannual – IanShepherdson,ChiefU.S.Economist Small BusinessEconomicTrends are available at www.nfib.com/research-foundation/surveys/ 1,2 Since , HighFrequencyEconomics Response rateshaverangedovertimefrom18 others. on thefindingsfromsurvey,SmallBusi- the TroubledAssetReliefProgram,among to economictrendsinthebroadereconomy. the firstandsubsequentmonthsinquarter. reflecting thedifferenceinsamplesizesused responses ineachofthefollowingtwomonths, and theCongressionalOversightPanelfor emerging trendsintheeconomy.Thelistof data toobtainabetterunderstandingof data setisitspredictivepowerwithrespect acteristic oftheearlyyearsandlatter percent to 33 percent, the formermore char- ment agencies use these small business survey more recenttimes.Amonthlyreportbased government entities that follow the NFIB data include theCouncilofEconomicAdvisers in bothelectronicandprintedforms. ness Economic Trends, isavailablefromNFIB Many privateforecastersaswellgovern- 4 OfinteresttofollowersoftheNFIB , February14,2012 3

1 | Small Business Indicators of Macro-economic Performance: An Update 2 | Small Business Indicators of Macro-economic Performance: An Update The lastcomprehensive,publishedanalysis 8 7 6 5 firms aredomesticallyfocused.Thesediffer- well theestimatedmodelspresentedperform with morerecentsegmentsofdataseriesbeing which includetheunsettlingGreatReces- was releasedin2003. Federal Reserve policy, tax-based fiscal policy, Federal Reservepolicy,tax-basedfiscal composition of “large” and “small” firms does composition of“large”and“small”firmsdoes fraction of the total economy, it is logical to fraction ofthetotaleconomy,itislogicalto for timeseriesanalysis.Ingeneral,regressions for small and large businesses. The sectoral for smallandlargebusinesses.Thesectoral the earliestdatepossiblethrough2008:Q4 tion and many services. Large firms are heavily tion andmanyservices.Largefirmsareheavily nated by industries like manufacturing, and the nated byindustrieslikemanufacturing,andthe nels throughwhichtheypropagatemaydiffer reinforced by the notion that the same basic reinforced bythenotionthatsamebasic look to indicators of their collective economic look toindicatorsoftheircollectiveeconomic left outtoallowforout-of-sampleforecasting rating updated(andlonger)timeseries,ones depth andaftermathoftheGreatRecession. economic activitylikerealGDPgrowth,unem- analysis. Theregressionsdemonstratehow are runusingNFIBdataseriesstartingfrom econometric techniquesintendedspecifically economy’s performance. differ, with the largefirm sectorbeingdomi- affect businesses of every size, although the affect businesses of every size, althoughthe economic forcesimpactallfirms,largeorsmall. assessing the predictive ability of these data ployment, inflation,andinvestmentduringthe upon the 2003 analysis not only by incorpo- particular effectsofpoliciesandthechan- health as reliable indicators of the broader health asreliableindicatorsofthebroader sion anditsaftermath,butalsobyemploying small firmsectorbeingdominatedbyconstruc- shifts in consumer spending, for example, all shifts inconsumerspending,forexample,all in predictinghighlyvisiblemeasuresofmacro- involved in international trade, while small involved ininternationaltrade,whilesmall

and labormarketisavailablethroughtheSBA’sFAQ,athttp://web.sba.gov/faqs/faqindex.cfm?areaID=24. net newjobsoverthepast17years.Moreinformationonsmall business sector’simportancetotheU.S.economy vate grossdomesticproduct,employsoverhalfofallprivatesectoremployees andgenerated65percentofthenation’s According to the U.S. Small Business Administration (SBA), the “small business sector” produces half of nonfarm pri- Activity, NFIBResearchFoundation,2003. See Dunkelberg,WilliamC.,JonathanA.Scott,andJ.Dennis, Jr.,SmallBusinessIndicatorsofMacroeconomic “large businesssector.” health ofsmallfirmsrelativelymore responsivetochangesinthebroadereconomicclimatethanindicators reflectingthe changes ineconomicconditionsmore quicklythantheircounterpartsinlargefirms,makingindicators of theeconomic An argumentcanbemadethatsince smallfirmsare“flatter”organizationsthanlargefirms,ownersof smallfirmssense #SBA2A-0084-01, mimeo,1983. pendent Business Sample ofSmallFirmsintheU.S.,” OfficeofAdvocacy,U.S.Small BusinessAdministration,contract William C.DunkelbergandJonathan A.Scott,“ReportontheRepresentativenessofNationalFederation ofInde- Because small firms make up such a large Because smallfirmsmakeupsuchalarge 5 Thismonographbuilds 6 This argument is This argument is But asthismonographwillshow,small-busi- NFIB membershipandthebroadersmallbusi- NFIB surveyvariables’usefulnessasindicators NFIB membershipandtheoverallsmallbusi- NFIB dataisprimarilyanempiricalone—do collectively diverge. Such divergences weaken collectively diverge.Suchdivergencesweaken of theoverallsmallbusinesssectorarescarce, of aggregatemacroeconomicactivitytothe for economic analysis even when the fortunes of for economicanalysisevenwhenthefortunesof accord withdatageneratedfromlargefirms. the predictive power of small-business-based the predictivepowerofsmall-business-based these twoconcernsareforpracticalpurposes time seriesdataontheeconomicperformance tain states. However, the membership’s tion forpredictingandunderstandingvariation the NFIBmeasuresprovideusefulinforma- the smallbusinesspopulationbutisnota ness populationand(b)indicatorsofeconomic ness populationmatterinananalysisofthe representativeness of the overall small business representative sampleofit. economic fortunes of large and small firms economic fortunesoflargeandsmallfirms ences helpexplainwhyfromtimetotime,the are relatively better at predicting aggregate extent that(a)therearematerialdifferences economic activity.Differencesbetweenthe performance forthesmallbusinesspopulation population, although desirable, is not a neces- macroeconomic activity.Sincecomprehensive members tendtobeolderandover-repre- sary conditionfortheNFIBsurveyvariablesto sented intheMidwestern,Plains,andMoun- between theeconomicperformanceof be usefulforecastinginstrumentsofaggregate large and small firms diverge, let alone when in large andsmallfirmsdiverge,letalonewhenin indicators toward macroeconomic variables. indicators towardmacroeconomicvariables. irrelevant. Thetestoftheusefulness ness-based survey indicators remain very useful ness-based surveyindicatorsremainveryuseful The NFIBmembershipreasonablyreflects 8 Forexample, 7 1973 comparedto26percentin2011. 10 9 firms madeup40percentofthesamplein Somewhat over40percentinbothtime ysis. Insomecases,ordinaryleastsquares NFIB samplehave,inatleastoneregard, NFIB examinedtheimpactofexcludingall of employeesperfirm)isvirtuallyidenticalto changed materiallyovertime.Today’sbusi- order autoregressivemodel(orAR(1)model) construction firmsmadeup10percentofthe construction firmsfromthesampleandagain, cant changeintheindicators.Morerecently, that recordedintheearlydaysofsurvey. focus ofthismonograph.Inthepast,NFIB term forecasting. terms. Incertaincaseswheretheapplicationof the owner(s);aboutsevenpercenthad40or three plusyearspriortothepublicationofthis through thefourthquarterof2008,some the resultswerenotindustrydependent. ness sizedistribution(measuredbynumber results, Box-Jenkinsmethodologyisappliedto develop a model that may be useful for short- an AR(1)modeldoesnotprovidemeaningful due to serial correlation are detected, a first- ability ofNFIBindicatorstowardselected data werenotincludedintheregressionswas prominent macroeconomicvariablesofinterest periods employ five or fewer workers including has experimentedwithweightingthedatato more employees.Incontrast,industrydistri- monograph. Again,thereasonmorerecent match Censusdistributionswithnosignifi- ship. Inmanyinstanceswherecomplications sample comparedto19percentin2011.Retail sions wereperformedfordataextendingonly bution has changed dramatically, particularly is usedtocorrectfordisturbancesintheerror is themethodusedtoquantifyrelation- is quantifiedusingtimeseriesregressionanal- in the construction and retail sectors. In 1973, in importantmacroeconomicmeasures,the

regression equation. The term“future” herereferstotimeperiodswhich extendbeyondtheendof time seriesusedtoestimatethe series analysis. For moreinformationonautoregressive modelsandBox-Jenkinsmethodology,pleaserefertotheappendix ontime The demographicdistributionsofthe In thefollowingsections,predictive It mustbereemphasizedthatregres- 9 “time” or“period”t (quarters, forcurrentpurposes)fromthe (or “realized”)datapoints. Out-of-sample forecastingreferstotheuseof GDP growth,intheempiricalrelationshipon Instead, their chronological counterpart, lags, ysis arecollectedinthefirstmonthofeach NFIB publishesonevalueforeachquarterly February, andMarch.IfNFIBdataleadbyone value. Therearenorevisions.Themacroeco- variable lagsthereferenceperiodbyn quarter: January,April,July,andOctober. casts that can be compared with the “actual” quarter, thentheJanuarysurveyanticipates quarterly valueofGDPgrowthforJanuary, quarterly valuesprovidedbythegovernment case ofthisanalysis,onequarter).Similarly,a of “-1”meansthatthesubscriptedvariable of uptofivemonths. of atleastonetotwomonthsintoaregres- the variablex the estimatedregressionequationsaregener- the secondquarter (representing April, May, timing sometimesbuildsinanimplicit“lead” reference period. regressions estimatedusinghistoricaldatato nomic indicatorsusedinthisanalysisarethe ated fordates2009:Q1through2011:Q4, able. In this monograph, forecasts for several of using the regressions herein could be observed. lags thereference period, usuallyreferredtoas predict “future” are denotedthroughoutthetextbynegative and June)GDPgrowthvalue,animplicitlead a concurrentbasis,thenitactuallypredictsthe providing 12datapointsofout-of-samplefore- periods. Forexample,thetermx predicts thedependentvariableofinterest,say so thatout-of-sampleforecastingaccuracy subscript of“-n”meansthatthesubscripted subscripts onthelaggingvariables.Asubscript sion model. Forexample, if theJanuary survey statistical agenciesthatpublishthem.This The NFIBsurveydatausedinthisanal- Leads arenotformallydenotedinthetext. laggedbytwotimeperiods 10 valuesofthedependentvari- , byonetimeperiod(inthe -2 refersto time

3 | Small Business Indicators of Macro-economic Performance: An Update 4 | Small Business Indicators of Macro-economic Performance: An Update R This sectionexploresthepredictiveabilityofkeymeasuresinNFIB 16 15 14 13 12 11 GDP exist.Themostcommonlyuseddefi- Gross domesticproductisthebroadest Economic growthisanimportantconcern of incomesearnedintheeconomyduringa of valueaddedintheeconomyduringagiven for anexpandingpopulationsinceitisonly the standardofliving.Analystsgenerally through growththatfullemploymentcanbe time. PositiveGDPgrowthisassociatedwith the mostcloselyfollowed.Threedefinitionsof nition isthevalueoffinalgoodsandservices data settowardgrossdomesticproduct(GDP).Inparticular,theNFIB achieved withoutsimultaneouslydecreasing and investmentbyhouseholdsfirms. and servicesareproducedforconsumption an expandingeconomyinwhichmoregoods period to the next, as this measure provides pally interestedinthechangeGDPfromone period. ThethirddefinitionofGDPisthesum period. Asecond,relateddefinitionisthesum produced in the economy during a given measure of economic activity and also, perhaps, given period. insight intohowtheeconomyisgrowingover changes in real GDP growth. shown toholdsubstantialpredictivepowertowardchangesinfinalsales. shown toholdconsiderableexplanatorypowertowardquarter-to-quarter survey’s headlineOptimismIndexandseveralofitscomponentsare

general businessconditionswillbe betterthantheyarenow,aboutthesame,orworse?” The surveyquestionforEBCDdatareads:“Abouttheeconomyin general,doyouthinkthatsixmonthsfromnow to expandsubstantially?” The surveyquestionforGTEXdatareads:“Doyouthinkthenextthree monthswillbeagoodtimeforsmallbusiness number ofpeople workingforyou?” The surveyquestion forXLFCHdatareads:“Inthe nextthreemonths,doyouexpect toincreaseordecreasethetotal of goodsand/orservicesthatyouwill sellduringthenextthreemonths?” The surveyquestionforESALdata reads:“Overall,whatdoyouexpecttohappentherealvolume(number ofunits) the lastcalendarquarterhigher,lower, oraboutthesameastheywereforquarterbefore?” The surveyquestionforNEARNdata reads:“Wereyournetearningsor‘income’(aftertaxes)from businessduring tion ofthisfunctionalformisprovidedinAppendixContimeseries analysis. common to time series analysis like serial correlation and a lack of weak dependency. A discussion regarding the selec- change. Transforming time series variables in this manner for regression analysis has the benefit of reducing problems Throughout thisanalysis,regressionvariablesarefrequentlyrepresented intermsoftheirquarter-to-quarterpercentage eal Economists andotheranalystsareprinci- P G GDP rowth 11 Variables from the NFIB data setare also • • • • • can haveamaterialimpactonnominalGDP the NFIBdataset.Thosevariablesare: the NFIBsurveyisIndexofSmallBusi- ness Optimism(INDEX),constructedasan equally-weighted averageof10variablesfrom prefer realGDPtonominalGDP, as inflation growth, butitisthegrowthinrealoutputthat is themajorconcern. Good TimeforBusiness Outlook fortheEconomy: Better orWorse(EBCD) Expansion (GTEX) Net EarningsTrends:Higher Employment (XLFCH) Plans toIncrease/Decrease Higher orLower(ESAL) Expected RealSalesVolume: or Lower(NEARN) The mostwidelyreportedindicatorfrom 12 14

16 15 13

• • • • • (for example,thepercentplanningcapital 22 21 20 19 18 17 working forthefirm.Forthesesevenques- vorable responses (“worse,” “decrease”) from offering an affirmative answer isincluded or “decrease”thetotalnumberofpeople of thequestionsusedtoconstructINDEX three questions,onlythepercentofowners to provideanetpercent.Fortheother the favorableresponses(“better,”“increase”) tions, a“balance”variable(ordiffusionindex) tory satisfaction,whicharepotentiallygood looking measuresofownerexpectationsand expects theeconomytobe“better”or“worse” are symmetric,suchaswhethertheowner as thetrendinearningsgrowthandinven- predictors offutureeconomicactivity.Most plans forsales,employment,inventory,credit, spending orreportingthatthecurrentperiod is formedbysubtractingthepercentofunfa- in thenextsixmonthsorplansto“increase” investment, andbusinessconditions,aswell

Job OpeningsNotAbletoFill(NJOBOP) Too HighorLow(INVSAT) Conditions: EasierorHarder(XCRED) Current InventorySatisfaction: Expected ChangeinCreditMarket Planned InventoryChange:Increase Planned CapitalExpenditures(CXPLAN) or Decrease(INVPLN) right, orinadequate?” The surveyquestionforINVSATdatareads:“Atthepresenttime, doyoufeelyourinventoriesaretoolarge,about The surveyquestionforNJOBOPdatareads:“Doyouhaveanyjobopenings thatyouarenotabletofillrightnow?” the analysisofout-of-sample forecastingaccuracy. for theassociated NFIBdataseriesandendingwith 2008:Q4.Datafrom2009:Q1onward wereomittedtoallowfor Allregressionspresentedinthisanalysis wereestimatedusingquarterlydatabeginningwiththeearliest recordedentry three tosixmonths,doyouexpect tomakeanycapitalexpendituresforplantand/orphysicalequipment?” from 1974:4withthisquestionincluded. ThesurveyquestionforCXPLANdatareads:“Lookingahead tothenext The surveys began in October, 1973. This question was added a year later and consequently, the INDEX is available during thenextthreemonths?” The surveyquestionforXCREDdatareads:“Doyouexpecttofind it easierorhardertoobtainyourrequiredfinancing to addyourinventories,keepthemaboutthesame,ordecreasethem?” The surveyquestionforINVPLNdatareads:“Lookingaheadtothenext threetosixmonths,doyouexpect,onbalance, The INDEXincludesmostlyforward- 19

17 21

1986 (1986=100),themiddleof1980s 1.1). The modeltendstodoabetterjobpredicting The INDEXisbasedtoitsaveragevaluein The INDEXiscomputedasthesumof10 (%∆RGDP). Asimpleregressionof%RGDP GDP growth.Thecoefficientisalsostatisti- INDEX canbeexpectedtoholdsubstantial NFIB timeseries. values) shouldbecorrelatedwithmorerobust compared tothelate1970searly1980sera. of timewhentheGDPserieswasconsiderably cally significantatthe0.05level(p=0.000). of thequarter-to-quarterchanges(Equation on INDEXshowsthatdoesafairjobof of the correct sign, since stronger performance or expectedcreditconditions.All10variables to-quarter percentagechangeinrealGDP the INDEX’sexplanatorypowerisquarter- real output.TheGDPmeasureusedtoassess less volatile(untilthe2007/8financialcrisis) little ornone,suchascapitalspendingplans explanatory powerforchangesinaggregate expansion andthebeginningofmonthly are seasonallyadjustedandequallyweighted. prevent the INDEX from becoming negative. predicting %∆RGDP,explaining38.3percent patterns, suchashiringplans.Othershave movements inGDPfollowing1982,aperiod ment forone-halfoftheprivateeconomy, seasonally adjustedcomponentsplus100to sion). Somevariableshavestrongseasonal in thesmallbusinesssector(higherINDEX is agoodtimeforsmallbusinessexpan- As a broad measure of economic senti- 22 Theslopecoefficient value(0.495) is

5 | Small Business Indicators of Macro-economic Performance: An Update 6 | Small Business Indicators of Macro-economic Performance: An Update 24 23 overall output.OfficialmeasuresofGDPfor tilities ofchangesinGDPgenerateddirectly to thesame economic andpolicy forces as not currentlyproduced,socomparingthevola- real GDPfrom2009:Q1to2011:Q4wasesti- large firms,onemightexpectameasureof a considerableamountofthemovementsin model, an out-of-sample forecast of changes in model, anout-of-sampleforecastofchangesin small businessandlargesectorsare small firmeconomicperformancetoexplain by thesetworespectivesectorsisnotpossible.

QUARTER-TO-QUARTER CHANGE IN REAL GDP (PERCENT) according tothis metric. the SIC values of two or more models, the model with the lowervalue is considered the model of “superior” quality The Schwarzinformationcriterion (SIC)isanalternatemeasureofmodelquality.AswiththeAIC,when comparing information onmodelselectioncriteria isavailableinAppendixB. analyst shouldconcernhimselfwith, nottheabsolutevalueofcriterioninrelationtosomecriticalvalue. Additional “judge” model quality, it is therelative standing amodel’s criterion holds compared to other models’ criteria that the like traditional“test”statistics thet-statisticorF-statistic.Whenusingmodelselection criterialiketheAICto For readersunfamiliarwithmodelselectioncriteria,itisimportant to notethattheiruseinregressionanalysisisun- more models,themodelwithlowervalueisconsideredof“superior”qualityaccordingtothis metric. The Akaikeinformationcriterion(AIC)isameasureofmodelquality. WhencomparingtheAICvaluesoftwoor -10 10 15 20 -5 To test the forecasting prowess of the above To testtheforecastingprowessofabove

RGDP = -46.208 + 0.495 INDEX 0.495 + -46.208 = %∆RGDP Since thesmallbusinesssectorisexposed R 0 5 F 1975 2 orecast =0.383, Adj. R C 1980 hange 2 = 0.378, F = 83.900,= AIC 0.378,F =

in (0.054) R 1985 eal Actual GDPU 1990 sing C hart Fitted 23 = 4.784,SIC = NFIBO occurred. Thisoutcomeisundesirableifequa- forecasting instrument for real GDP, but the forecasting instrumentforrealGDP,butthe tion 1.1 is to be considered as a standalone tion 1.1 is to be considered as astandalone the positive economic growth which actually results are consistent with the experience of the results areconsistentwiththeexperienceof levels ofcorporateprofitsreportedwhileperfor- evolution from 2009:Q1 through 2011:Q4 evolution from2009:Q1through2011:Q4 demonstrates thatapredictionofrealGDP economy post-Great Recession, that is, the large economy post-GreatRecession,thatis,thelarge mated using equation 1.1 (Chart 2). The chart mated usingequation1.1(Chart2).Thechart mance inthesmallbusinesssectorhaslagged. generated by equation 1.1 underestimates generated byequation1.1underestimates business sector has performed well with record business sectorhasperformedwellwithrecord 1 1995 ptimism Residual 24 = 4.827, DW = 1.805 = 4.827,DW = 2000 I ndex (E 2005 quation (1.1) 1.1) -10 10 15

-5

0 5

S RESIDUAL 27 26 25 28 ESAL (the expected change in real sales ESAL (theexpectedchangeinrealsales volume), andSAL quarter) resultsinbothahigherR tional explanatory variables to the regression tional explanatoryvariablestotheregression to theregressionequationwillatworstleaveR not-unexpected result since adding a predictor not-unexpected resultsinceaddingapredictor equation. Regressing%∆ equation 1.1 are achieved by including addi- sales volume during the previous calendar sales volumeduringthepreviouscalendar

because theinclusionofadditionalindependentvariablesintoregression equationwillalwaysleadtoanewR independent variables. However, some analysts believe it to be a less useful measure in the multiple regression context instead oforinadditiontothetraditionalR In asimpleregressionmodelwithonedependentvariableand explanatoryvariable,thestatisticR or aboutthesameasitwasforquarterbefore?” The survey question for SAL data reads: “During the last calendar quarter, was your dollar sales volume higher, lower, F-statistics, toname twocommonstatistics,shouldalso beconsideredwhenjudgingspecifications. which tojudgethe applicabilityaparticularmodelholds towardasetofdata.Othermeasures likeR-squaredvaluesand We usetheterm“maybe”hereto underlinethefactthatmodelselectioncriteriaaresimplyoneset ofmetricsby The adjustedR emphasized thatalowR is “explained”bytheindependentvariable.LowR the coefficientofdetermination,isinterpretedasfraction samplevariationinthedependentvariablethat is thenumberofobservationsandk isthenumberofindependentvariables) andR that is greater than or equal to the original. For this reason, some analysts prefer to refer to the regression context,R “data mine.”Thepenaltycanbeobserved intheequationsforadjustedR introducing additionalindependent variables to amodel.This penaltycanbethoughtofasadisincentiveforanalyststo additional independentvariables(an increaseink)withoutreducingSSRwilldecrease adjustedR Improvements to the regression results in Improvementstotheregressionresultsin QUARTER-TO-QUARTER CHANGE IN REAL GDP (PERCENT) -10 10 15 20 O -5 0 5 ut 1975 - of 2 measureismoreattractivethanthestandardR -S 25 ample 2 continuestobeanestimateofhowmuchvariationinthedependent variable is“explained”bythe (the actual change in dollar (the actualchangeindollar 2 valuebyitselfdoesnotindicatethataparticularsetofregressionresults ispoor.Inamultiple 1980 F RGDP on INDEX, RGDP onINDEX, orecast 1985 2 (0.431) (a (0.431)(a

of 2 measure(seefootnote10). C hange 2 Actual C valuesarenotuncommoninthesocialsciences,anditshouldbe 1990 2 hart

1.2]. Although the p-value for the coefficient of SAL Although thep-valueforcoefficientofSAL in (a measure of goods and services produced (a measureofgoodsandservicesproduced which should be better correlated with GDP which shouldbebettercorrelatedwithGDP the same)andadjustedR lower AIC and SIC values indicate that the lower AICandSICvaluesindicatethatthe related componentsoftheOptimismIndex, ) than other index components. and mostlysold)thanotherindexcomponents. model expressedin1.2maybe is relatively high (p = 0.260), the comparatively is relativelyhigh(p=0.260),thecomparatively 2 2 R measureprimarilybecauseofthepenaltyitimposeson 1995 26, 27 eal Predicted Thisspecificationemphasizesthesales- GDPU 2 (1–[SSR/(nk1)]/[SST/(1)],where n 2000 2 (1–(SSR/n)/(SST/)).Introducing sing E quation 2005 2 (0.419) [Equation (0.419)[Equation 2 adjusted R . 28 an improved animproved 1.1 2010 2 , knownas 2 measure 2 value

7 | Small Business Indicators of Macro-economic Performance: An Update 8 | Small Business Indicators of Macro-economic Performance: An Update 1.3). Nonetheless,thespecificationremains 29 SIC values also serve to temper any outstanding SIC valuesalsoservetotemperany outstanding ESAL results in lower AIC and SIC values, but concerns regarding multicollinearity among the concerns regardingmulticollinearityamongthe of SALintheregressionequation.TheAICand also lowerR and regressing%∆RGDPonlyonINDEX explanatory variables. specification over 1.1, arguing for the inclusion specification over1.1,arguingfortheinclusion

QUARTER-TO-QUARTER CHANGE IN REAL GDP (PERCENT) much theintroduction ofESALaffectsthevariance ofINDEX’scoefficient. variable automatically introduces multicollinearity. How detrimental this multicollinearity proves depends upon how rejected inasignificancetest.The introductionofESALintoanequationalreadycontainingINDEXas anindependent of multicollinearitycanleadtolarge variancesforOLScoefficients,makingthemlessefficientand morelikelytobe Multicollinearity referstohigh,but notperfect,correlationbetweentwoormoreindependentvariables. Thepresence -10 10 15 20

RGDP = -17.708 + 0.177 INDEX + 0.137 ESAL 0.137 + INDEX 0.177 + -17.708 = %∆RGDP ESAL 0.109 + SAL 0.038 + INDEX 0.208 + -20.350 = %∆RGDP Removing SALfromtheaboveequation R R -5 0 5 2 2 1975 =0.426, Adj. R 0.431,= Adj.R 2 andadjustedR F orecast 1980 and 2 2 29 = 0.418, F = 49.800, AIC = 4.726, SIC = 4.790, DW = 2.027 = 4.790,DW = 4.726,SIC 49.800,= = AIC 0.418,F = 2.041 = 4.817,DW = 4.731,SIC 33.696,= = AIC 0.419,F = As with equation 1.1, Aswithequation1.1, E C (0.113) (0.116) xpected hange 2 values(Equation 1985 Actual

in R R eal (0.043) eal 1990 S (0.034) GDPU ales C hart Fitted M SAL and ESAL are also positive, satisfying the SAL andESALarealsopositive,satisfyingthe considered asthesuperiorforecastingtoolfor future changesinrealGDPislefttotheread- the coefficient for INDEX is positive although the coefficientforINDEXispositivealthough economic intuition that with higher sales comes economic intuitionthatwithhighersalescomes er’s discretion. as towhetherequation1.2or1.3shouldbe more growth. smaller in magnitude. The coefficients for both smaller inmagnitude.Thecoefficientsforboth superior tothatofequation1.1.Thejudgment 3 easure (0.050) sing 1995 NFIBO (E Residual quation 2000 ptimism 1.3) I 2005 ndex (1.3) (1.2)

-8 -4

0 4 8

S RESIDUAL 30 change for each of these measures was used in change foreachofthesemeasureswasusedin the regressions.Simpleregressionsof%∆ that arestatisticallysignificant. real GDP, the quarter-to-quarter percentage real GDP,thequarter-to-quarterpercentage necessarily sold. The difference between final domestic purchasers (FSALPRIV). As with domestic purchasers(FSALPRIV).Aswith dependent variable:(1)finalsalesofdomestic distinct fromgrossdomesticproductsinceGDP product (FSAL) and (2) final sales to private product (FSAL)and(2)finalsalestoprivate measures of final domestic sales on INDEX and measures offinaldomesticsalesonINDEXand mance isfinaldomesticsales.Finalsalesare sales and GDP constitutes changes in sellers’ sales andGDPconstituteschangesinsellers’ services its sales components produce OLS coefficients its salescomponentsproduceOLScoefficients inventories during a given period. Regressions of is ameasureoftheamountfinalgoodsand

since agents’expectations shouldmanifestthemselves inrealeconomicactivityafuture timeperiod(notinstantaneously). greater thanoneand indicatesthenumberoflagged periods, typicallyonequarter“-1”.Here,ESALis laggedoneperiod Throughout thistext,laggedvariables willbedenotedwithasubscriptoftheform“-x”wherex A relatedmeasureofeconomicperfor- Two measures of final sales were used as the Two measuresoffinalsaleswereusedasthe

FSAL = 0.430 + 0.108 ESAL 0.108 + 0.430 = %∆FSAL SAL 0.121 + 2.287 = %∆FSAL FSAL = -32.720 + 0.359 INDEX 0.359 + -32.720 = %∆FSAL R R R 2 2 2 = 0.150,= Adj.R 0.119,= Adj.R =0.267, Adj. R during a given time period, not produced duringagiventimeperiod,not 2 2 2 = 0.144, F = 24.360, AIC = 4.829, SIC = 4.871, DW = 1.904 = 4.871,DW = 4.829,SIC 24.360,= = AIC 0.144,F = 1.915 = 4.901,DW = 4.859,SIC 18.214,= = AIC 0.112,F = 1.986 = 4.717,DW = 4.674,SIC 49.279,= = AIC 0.262,F = (0.028) (0.022) (0.051) -1

FSAL FSAL An increaseinsmallbusinesseconomicperfor- The results for these three regressions are given The resultsforthesethreeregressionsaregiven (INDEX) ofthevariationsin%∆ final domestic sales, depending upon changes final domesticsales,dependinguponchanges on INDEX,SAL,andESAL cally correct, lagged expectations of higher real cally correct,laggedexpectationsof higher real tically significant coefficient estimates at the tically significantcoefficientestimatesatthe the expectationsofbusinessownersaretypi- 0.05 level and of the correct (positive) sign. as higherfinalsalesinthecurrentperiod. mance or sales should translate into increased mance orsalesshouldtranslateintoincreased sales from the previous period should show up sales fromthepreviousperiodshouldshowup selection criteriaindicatethatINDEXisthe best explanatory variable for a simple regression. best explanatory variable for a simple regression. between 11percent(ESAL in the sales of large businesses. Additionally, if in thesalesoflargebusinesses.Additionally,if in equations1.4through1.6. Individually, these SBET indictors explain Individually, theseSBETindictorsexplain is a variable equal to or isavariableequaltoor -1 ) and 27 percent ) and27percent -1 (1.6) (1.5) (1.4) producestatis- FSAL. Model FSAL. Model 30

9 | Small Business Indicators of Macro-economic Performance: An Update 10 | Small Business Indicators of Macro-economic Performance: An Update 31 PRIV onINDEXandSALproduceimproved order autoregressivemodelwasestimated on those same two indicators, but only with results comparedtoregressionsof%∆FSAL adjustments madetocorrectforfirst-order problem (Equations1.7and1.8). purchasers. Simpleregressionsof%∆FSAL- predictors offinalsalestoprivatedomestic serial correlationintheerrorterms.Afirst- be mentionedthatneitherestimatingatradi- in both cases tocorrect the serial correlation

models arealsoreferred toasARmodels.Anautoregressive modeloforderp Autoregressive models are a method of modeling serial correlation in the error terms in time series analysis. Autoregressive u QUARTER-TO-QUARTER CHANGE IN FINAL SALES t-1 The NFIBmeasuresappeartobebetter

FSALPRIV = 2.689 + 0.115 SAL 0.115 + 2.689 = %∆FSALPRIV FSALPRIV = -54.865 + 0.585 INDEX 0.585 + -54.865 = %∆FSALPRIV R R u u -10 F +p 10 15 20 t t -5 2 2 orecast =0.353u u 0.186 = 0 5 =0.489, Adj. R =0.255, Adj. R 1975 2 *u t-2 +.p C t-1 t-1 hange +ε +ε 1980 2 2 p t t *u = 0.244, F = 22.779, AIC = 5.118, SIC = 5.183, DW = 2.031 = 5.183,DW = 5.118,SIC 22.779,= = AIC 0.244,F = 1.949 = 4.806,DW = 4.742,SIC 63.562,= = AIC 0.481,F =

t-p in +ε (0.049) F (0.063) t inal . Afirst-orderautoregressive modelisthereforealso referredtoasanAR(1)model. 1985 Actual S 31 Itshould ales U 1990 C sing hart Fitted NFIBO INDEX explains48.9percentofthevariation PRIV comparedto11.9percentfor%∆FSAL. for %∆FSAL,whereasSALexplains25.5 tional simple regression model nor a first-order 0.05 levelandofthecorrect(positive)sign. autoregressive model produced statistically atory variable. percent ofthechangeinvariation%FSAL- sions are also statistically significant at the significant resultswhenESAL in %∆FSALPRIVcomparedto26.7 percent 4 1995 The slopecoefficientsfortheseregres- ptimism Residual , denotedasAR(p 2000 I ndex (E 2005 ), hastheform:u quation -1 (1.8) (1.7) wastheexplan- 1.4) -10 10 15

t -5

=p 0 5

S 1 RESIDUAL * F QUARTER-TO-QUARTER CHANGE IN FINAL SALES (PERCENT) orecast

-20 -10 10 20 0 1975

C hange 1980

F inal P 1985 rivate Actual S ales 1990 C hart

U Fitted sing 5

1995 NFIB Residual O ptimism 2000

I ndex 2005 (E quation 12 -8 -4

0 4 8

1.7)

S RESIDUAL

11 | Small Business Indicators of Macro-economic Performance: An Update 12 | Small Business Indicators of Macro-economic Performance: An Update A E This sectionexploresthepredictiveabilityofkeymeasuresinNFIB (NJOBOP). Smallbusinessesemployhalf 33 32 firms (EMPCH) Because smallfirmsplayacriticalroleinthe job inpredictingbothchangesprivateemploymentandtheunemploy- with changesintotalprivateemployment. who reportatleastonehard-to-filljobopening in laborcompensationatsmallfirmsarealsoanalyzedfortheirpredictive of theprivatesectorworkforceandfirst cator of tightness in the small business labor cator of tightness in the small business labor conditions amongsmallbusinesses.Twosurvey job creation process, report expandingtotalemploymentattheir level and signals that owners are having more level and signals that owners are having more level ofemploymentatthefirmanditsactual data set toward private sector employment as measured by the establish- difficulty getting employees. Such instances difficulty gettingemployees.Suchinstances and otherlabormarketindicators.TheNFIB market. A high level of unfilled job openings market. A high level of unfilled job openings measures are used to explain recent variations measures ofaggregate employment growth measures shouldhaveastrongrelationshipto generally indicate a “tight” labor market, but generally indicatea“tight”labormarket,but small businessemployment,shouldcorrelate survey measure(EMPCH),changesintotal survey includesquestionsintendedtomeasure both currentandanticipatedemployment indicates disequilibrium between the desired indicates disequilibriumbetweenthedesired in employment:thenetpercentofownerswho ment payrollsurveyandtheunemploymentrate.NFIBmeasuresofchanges ment rate,butdonotaswellpredictingchangesinlaborcompensation. sure oflaborcompensationavailable.TheNFIBmeasuresdoanexcellent ability towardtheemploymentcostindex,mostcomprehensivemea-

http://web.sba.gov/faqs/faqindex.cfm?areaID=24. business sector’simportance to theU.S.economyandlabor marketisavailable through theSBA’sFAQ,availableat employees andgenerated65percent ofthenation’snetnewjobsoverpast17years.Moreinformation onthesmall According totheU.S.SmallBusiness Administration (SBA),thesmallbusinesssectoremployshalfofallprivate pendent variable in regressions. the magnitude of change is. Data corresponding to the firm increase,decrease,orstayabout thesame?”Respondentswhoreportachangeinemploymentare askedhowlarge The surveyquestionforEMPCHdata reads:“Duringthelastthreemonths,didtotalnumberofemployees inyour mployment nd The secondmeasure(NJOBOP)isanindi-

L 33 abor andthepercentofowners 32 the NFIB employment

M , U arkets nemployment net changein small business employment was used as the inde- This disequilibrium between desired and actual This disequilibriumbetweendesiredandactual (collecting applications, interviewing candidates, (collecting applications,interviewingcandidates, (XLFCH). Thecontributionofsmallfirmsto fill job openings should therefore, in general, be fill jobopeningsshouldtherefore,ingeneral,be with underwater mortgages who cannot relocate. with underwatermortgageswhocannotrelocate. of ownersplanningtoexpandtotalemploy- job creationsuggeststhatalargernetpercent to changes in the labor market, such as, workers to changesinthelabormarket,suchas,workers to changetotalemploymentattheirfirms the netpercentofownerswhoreportplans levels of employment takes time to resolve levels ofemploymenttakestimetoresolve and adeclineintheunemploymentrate. etc.). Thepercentofownersreportinghard-to- an inabilityoflaborsupplytoquicklyrespond areas, such as, the natural gas shale boom, and pate future changes in small business employ- positively correlatedwithemploymentgrowth ment throughathirdstatisticwhichmeasures may alsobecausedbyfactorsotherthana general shortage in labor, including regional general shortageinlabor,includingregional ment growthinfutureperiods. ment inthemonthsfollowingsurvey since the hiring process is not instantaneous since thehiringprocessisnotinstantaneous should correspondwithmorerobustemploy- imbalances caused by rapid growth in some imbalances caused by rapidgrowth in some The NFIBsurveyalsoattemptstoantici- , A. Employment A closely followed measure of employment A closelyfollowedmeasureofemployment XLFCH ( Since the small business sector constitutes Since thesmallbusinesssectorconstitutes quarter changes in private sector employment quarter changesinprivatesectoremployment new jobs,changesinsmallbusinessemploy- roughly halfofU.S.privatesectoremployment as measured by the establishment payroll survey as measuredbytheestablishmentpayrollsurvey employment closely.Regressionsofquarter-to- and accounts fortwo-thirds of the nation’s net employment intheestablishmentsurvey. employment and increases in the net percent approximately 70percentofmovementsin private employment(Equations2.1and2.2). ment should track changes in overall private ment shouldtrackchangesinoverallprivate growth is the quarterly change in private sector growth isthequarterlychangeinprivatesector ∆

QUARTER-TO-QUARTER CHANGE IN PRIVATE EMPLOYMENT (THOUSANDS) PRIVEMPL) on EMPCH, NJOBOP, and -1,000 1,000 1,500 PRIVEMPL = 284.886 + 177.623 EMPCH + 8.975 XLFCH 8.975 + EMPCH 177.623 + 284.886 = ∆PRIVEMPL

Positive changesinsmallbusiness R u -500 500 t 2 =0.805u =0.700, Adj. R 0 E 76 -1 mployment show that these variables can explain showthatthesevariablescanexplain F orecast 78 t-1 80 +ε C C 2 82 t = 0.693, F = 97.431, AIC = 13.902, SIC = 13.991, DW = 1.842 = 13.991,DW = 13.902,SIC 97.431,= = AIC 0.693,F = hange hange 84 (146.957)

in 86 and Actual P rivate E 88 xpected 90 E C 34 mployment hart 92

Fitted E (8.073)

mployment An increaseinNJOBOPduringaperiodof (lagged oneperiod)arebothassociatedwith NJOBOP inequation2.2supportsthisview. change inemploymentwasaone-timeevent cies. Insuchanoccasion,onemightexpect conjunction withotherlabormarketmeasures. openings, NJOBOP,isameasureoflabor of ownerswhoplantoexpandemployment the increaseinNJOBOPtobeprecededby number ofownersreportinghard-to-filljob decline. Thepositivecoefficientsignfor and notacontinuousprocessofgrowthor an increasein∆ able laborisinsufficienttofillnewjobvacan- demand atatimewhenthepoolofavail- economic growthsignalsanincreaseinlabor market tightnessthatisbestinterpretedin increases inprivatesectoremployment.The 6 94 96 U sing Residual 98 -1 C

hange NFIBM 00 PRIVEMPL, especiallyifthe 02 (E quation easure 04 06

of (2.1) 2.1) 08

-1,000 1,000 -500 500

S RESIDUAL

13 | Small Business Indicators of Macro-economic Performance: An Update 14 | Small Business Indicators of Macro-economic Performance: An Update A secondindicatorofinteresttoanalysts ∆u onEMPCH,XLFCH,and NJOBOPusing B. Unemployment 2.4, and2.5,respectively. The modelsbelow (Chart 7). This is a noteworthy outcome given Labor Statistics. Individually, the three NFIB quarter-to-quarter movements. Regressionsof the AR(1)modelaregiven inequations2.3, the magnitudeoflabormarketdislocations the overalllevelofprivateemploymentwell tion 2.2predictsout-of-samplemovementsin roughly 43percentand53 oftherate’s reasonably goodjobpredictingchangesinthe labor marketmeasuresdescribedabovedoa and policymakersisthenationalunemploy- unemployment rate(∆u),explainingbetween predict changes inthelevelofunemploy - ment ratereportedmonthlybytheBureauof ment ratewell. in theaftermathof2007/8financialcrisis, PRIVEMPL = 46.796 + 214.444 EMPCH + 16.170 NJOBOP 16.170 + EMPCH 214.444 + 46.796 = ∆PRIVEMPL The regressionmodelexpressedinequa-

R QUARTER-TO-QUARTER CHANGE IN PRIVATE EMPLOYMENT (THOUSANDS) u t 2 =0.777u -2,500 -2,000 -1,500 -1,000 =0.704, Adj. R 1,000 1,500 -500 500 0 1975 t-1 +ε 2 O t = 0.696, F = 98.872, AIC = 13.892, SIC = 13.981, DW = 1.894 = 13.981,DW = 13.892,SIC 98.872,= = AIC 0.696,F = ut 1980 E - of mployment (141.981) -S ample 1985 F L orecast Actual evels C hart 1990 (9.576) U -0.062) despitethefactthatithaslowest

January valueforXLFCHpredicts changesin This result may be due to the fact that quar- sing firing employeesmay chooseto dosowithin R of on XLFCHinthecurrentperiodaresupe- forecasts inthedirectionalchangeofprivate tudes ofthosechanges. the unemploymentrate for January, February, the firstmonthofeachquarter, suchthatthe terly NFIBsurveyvaluesare associatedwith rior tothoseofaregression∆uonthe regression of∆uonEMPCHisthebestspec- although themodel“undershoots”local and March.Employers whoanticipatehiring or minimum oftheactualdataseries.Atleast same explanatoryvariablelaggedonequarter. sector employment,ifnottheactualmagni- ification ofthethree(AIC=-0.128,SIC in recentyears,thismodelprovidesaccurate 7 2 C values. The results of a regression of According tomodelselectioncriteria,a Predicted E hange 1995 quation

in P 2000 2.1 rivate

2005 (2.2) 2010 ∆u ∆u thanXLFCH a (relatively)shorttimeframe(withinthree plans by owners to hire. The interpretation of plans byownerstohire.Theinterpretationof months), makingXLFCHabetterpredictorof business employment are associated with a fall business employmentareassociatedwithafall in the unemployment rate, as are increases in in theunemploymentrate,asareincreases

QUARTER-TO-QUARTER CHANGE IN UNEMPLOYMENT RATE (PERCENT) u = 0.016 - 0.362 EMPCH 0.362 - 0.016 = ∆u u = 0.601 - 0.029 NJOBOP 0.029 - 0.601 = ∆u XLFCH 0.038 - 0.388 = ∆u Theory suggests that increases in small Theory suggeststhatincreasesinsmall

R R R u u u -1.0 -0.5 0.0 0.5 1.0 1.5 t t t 2 2 2 =0.693u =0.600u =0.558u =0.450, Adj. R 0.531,= Adj.R =0.437, Adj. R 76 F C 78 (0.148) (0.006) orecast hange t-1 t-1 t-1 -1 (0.008) 80 . +ε +ε +ε

2 2 2 in t t t = 0.442, F = 55.675, AIC = 0.126, SIC = 0.189, DW = 1.935 = 0.189,DW = 0.126,SIC 55.675,= = AIC 0.442,F = 2.065 = 0.031,DW = -0.033,SIC 76.920,= = AIC 0.524,F = 2.107 = -0.062,DW = -0.128,SIC 48.927,= = AIC 0.428,F = C 82 S hange mall 84 B

86 in usiness Actual N 88 ational E 90 C mployment hart U 92 Fitted nemployment job openings indicates tighter labor markets, job openingsindicatestighterlabormarkets, the coefficient in equation 2.5 is that an increase the coefficientinequation2.5isthatanincrease reflected inthisinstancebyafalltheunem- and positive association found between NJOBOP positive associationfoundbetweenNJOBOP ployment rate.Thisresultisconsistentwiththe in the number of owners reporting hard-to-fill in thenumberofownersreportinghard-to-fill 8 94 ∆ PRIVEMPL inequation2.2. M 96 easure Residual 98 R 00 ate (E quation U 02 sing 04 NFIB 2.3) (2.3) (2.5) (2.4) 06 08

-1.0 -0.5

0.0 0.5 1.0

S RESIDUAL

15 | Small Business Indicators of Macro-economic Performance: An Update 16 | Small Business Indicators of Macro-economic Performance: An Update The majorcostincurredbysmallbusinessis 36 35 C. LaborCompensation which serveasusefulpredictorsof∆u.Unem- NFIB measureslaggedaperiodmightactas cover laborcosts will fail. Since April 1982, the NFIBsurveyhasaskedaseriesofquestions the net percent of owners planning to increase the netpercentofownersplanning toincrease the priorthree-monthperiod.PLANWAGE the to overallemploymentandjobcreation.What reporting that they raised labor compensation in reporting thattheyraisedlaborcompensationin addition toindicatorsoflabordemand. about past andplanned labor cost changes in drives the price level because firms thatcannot usually labor.Overall,thepathoflaborcosts unremarkable, giventhesector’simportance predictors of theunemployment rate is by itself ployment isconsideredtobealaggingindicator by economists,andonemightpresupposethat in thesmallbusinesssectorserveasuseful is noteworthythatittheNFIBmeasuresin

benefits butNOT SocialSecurity,U.C.taxes,etc.) during thenextthreemonths?” The surveyquestion forPLANWAGEdatareads:“Do youplantochangeaverageemployee compensation(wagesand sation (wagesandbenefitsbutNOT SocialSecurity,U.C.taxes,etc.)?” The surveyquestionforPASTWAGE datareads:“Overthepastthreemonths,didyouchangeaverageemployee compen- O current periodandnotinpreviousperiods That indicatorsoflabormarketconditions

PASTWAGE QUARTER-TO-QUARTER CHANGE IN UNPEMPLOYMENT RATE (PERCENT) ut -1.0 -0.5 - 0.0 0.5 1.0 1.5 2.0 of -S 1975 ample 35 is the net percent of owners isthenetpercentofowners F orecast 1980

of 1985 C hange 36 Actual 1990 C

is is in hart U nemployment WAGE and PLANWAGE are direct measures of WAGE andPLANWAGEaredirectmeasuresof XLFCH (Table 1). More vacancies and plans to XLFCH (Table1).Morevacanciesandplansto 2.2’s reliabilityasaforecastingtoolfordirec- which supportwageincreases. NFIB wage measures are strongly correlated not NFIB wagemeasuresarestronglycorrelatednot only with each other, but also with NJOBOP and only witheachother,butalsoNJOBOPand changes inthesupplyanddemandforit.Thetwo of the price of labor and, as such, should vary with the priceoflaborand,assuch,shouldvarywith tional movementsinchangesthelevelof the directionalmovementsofactualchanges this isnotnecessarilythecase. the bestexplanatoryvariablesforregressions labor compensation during the next three-month labor compensationduringthenextthree-month actual andanticipatedchangesinlaborcompen- equation 2.4doesanadmirablejobpredicting period. Bothareseasonallyadjusted.PAST- private sectoremployment. sation (wages and benefits). Wages represent sation (wagesandbenefits).Wagesrepresent increase hiring indicate tightening labor markets, increase hiringindicatetighteninglabormarkets, in theunemploymentrate,similartoequation 9 ∆u. But,theaboveempiricalresultsshow 1995 In atestofout-of-sampleforecasting, Predicted 2000 R ate U sing 2005 E quation 2010 2.4 Cost Index (ECI) is the most comprehensive ECI indexincorporatesinformationonwages, Revisiting thisanalysisonce theECIhas values were higher and thecoefficients ofthe observations forthisanalysis.EveniftheR that theresultsareinfluencedbysmall the BureauofLaborStatisticsusingsurveys representing justwageandsalaryorbenefits relatively short in duration. The Employment right signsinequations2.6,2.7,and2.8,the labor compensation,PLANWAGEwithalag are alsoavailable.ECIdataavailablequar- and themostpopularofthesetimeseriesis and PASTWAGEinthecurrentperiod.Macro against readingtoomuch intotheresults. positive relationship to macromeasuresof measure oflaborcostsavailable,compiledby measures oflaborcompensationarescarce series beginsin2001:Q1,providingjust32 sample sizeoftheECItimeseries.The salaries, and benefits, but separate indices small samplesizewouldencouragecaution both privateandpublic sectors. Theheadline These disappointmentsaside,itispossible The NFIBwagevariablesshouldhavea

ECI = 0.205 + 0.035 PLANWAGE0.035 + 0.205 = %∆ECI PASTWAGE0.015 + 0.379 = %∆ECI ECI = 0.256 - 0.009 PASTWAGE + 0.044 PLANWAGE-1PASTWAGE0.044 0.009 + - 0.256 = %∆ECI R R R

C 2 2 2 =0.207, Adj. R =0.083, Adj. R 0.217,= Adj.R

XLFCH NJOBOP PLANWAGE PASTWAGE orrelation (0.014) M 2 2 2 (0.009) (0.013) = 0.179, F = 7.557, AIC = -0.648, SIC = -0.555, DW = 1.877 = -0.555,DW = -0.648,SIC 7.557,= = AIC 0.179,F = 2.031 = -0.410,DW = -0.502,SIC 2.627,= = AIC 0.051,F = 1.844 = -0.458,DW = -0.596,SIC 3.887,= = AIC 0.161,F = atrix

of NJOBOP 0.709297 1.000000 0.871097 0.874038 NFIBL -1

(0.020) abor T 2 able M 0.738056 0.874673 1.000000 XLFCH WAGE inequation2.6isnotstatisticallysignif- 2.7, and2.8).TheOLScoefficientforPAST- %∆ECI onPASTWAGEandPLANWAGE

worker compensationarenot anticipatedwell worthwhile endeavor. tant macrolabormarketvariables.Changes tion measuresindicatethatPASTWAGE terly from2001:Q1,and2005servesasthe respectively, ofmovementsintheECI. explain just8.3percentand20.7percent, are highlycorrelatedwithtwoofthreeimpor- and PLANWAGE predicting changesintheECI(Equations2.6, ployment ratearebothverywellanticipated percentage changeofthewageandsalary specification. Meanwhile,simpleregressionsof by NFIBmeasures. by theNFIBsurveymeasures.Changesin become amorematuretimeseriesmaybe icant (p in privatesectoremploymentandtheunem- index (%∆ECI)onNFIB labor compensa- index’s referenceyear(2005=100). 1 arket

Overall, theNFIBlabormarketindicators Regressions ofthequarter-to-quarter

and = 0.543),makingequation2.6apoor C PASTWAGE PLANWAGE ompensation 0.860684 1.000000

-1 do a relatively poor job M (2.7) (2.8) (2.6) 1.000000 easure -1

17 | Small Business Indicators of Macro-economic Performance: An Update 18 | Small Business Indicators of Macro-economic Performance: An Update I This sectiondiscussesthepredictiveabilityofmeasuresinNFIBdata Using afirst-orderautoregressivemodel,theNFIBmeasuresdoanexcel- 39 38 37 NFIB survey questions address this economic NFIB surveyquestionsaddressthiseconomic changes, since price changes implemented by changes, sincepricechangesimplementedby the past threemonths(PASTP) reported changes in average selling prices over reported changesinaveragesellingpricesover lowering prices (the net percent, seasonally lowering prices(thenetpercent,seasonally adjusted). PASTP should hold explanatory adjusted). PASTPshouldholdexplanatory phenomenon in the small business sector: phenomenon inthesmallbusinesssector: power toward current consumer price index power towardcurrentconsumerpriceindex percent ofownerswhoreportraisingaverage plans for raising selling prices in the next three plans forraisingsellingpricesinthenextthree months (PLANP). be employedtoobtainamodelthatpredictswellchangesin“core”CPI. selling prices less the percent who report selling priceslessthepercentwhoreport penditure index,andGDPdeflatorareregressedagainstNFIBmeasures price index(CPI),“core”consumerindex,personalconsumptionex- business owners in the three months prior to business ownersinthethreemonthspriorto lent jobpredictingchangesintheregularCPI,personalconsumption is the major concern of economic policy. Two is themajorconcernofeconomicpolicy.Two of pastandplannedchangesinsellingpricesbysmallbusinessowners. expenditure index,andtheGDPdeflator.Box-Jenkinsmethodologycan set toward changesin various formsofinflation.The regular consumer

nflation The surveyquestionforPASTPdata reads:“Howareyouraveragesellingpricesnowcomparedtothree monthsago?” these several cases, practice is inconsistent with theory, as regressions containing PLANP Theory suggeststhatinequation3.1 andsomeothersthatfollow,PLANPshouldbelaggedbyatleast onequarter.In of yourgoodsand/orservices?” The surveyquestionforPLANPdata reads:“Inthenextthreemonths,doyouplantochangeaverage sellingprices estimated coefficients provedtobestatisticallyinsignificant, thenPLANPwassubstituted forPLANP ated poorresults. Asageneralrulethroughoutthissection, regressionscontainingPLANP Along with “full employment,” inflation Along with“fullemployment,”inflation

CPI = -2.027 + 0.051 PASTP + 0.230 PLANP 0.230 + PASTP 0.051 + -2.027 = %∆CPI R u t 2 =0.458u =0.690, Adj. R t-1 +ε 38 The variable PASTP is the ThevariablePASTPisthe 2 t = 0.683, F = 100.175, AIC = 4.124, SIC = 4.208, DW = 1.784 = 4.208,DW = 4.124,SIC 100.175,= = AIC 0.683,F = (0.026) 37 and reported and reported (0.051) first-order autoregressive model. Price increases first-order autoregressivemodel.Priceincreases PASTP explain 69.0 percent of the annualized PASTP explain69.0percentoftheannualized Plans from the prior quarter should show up as Plans fromthepriorquartershouldshowupas changes inpricesduringthecurrentperiod. current period.Inasimilarfashion,PLANP,the the survey will impact price measures in the the surveywillimpactpricemeasuresin average selling prices, should lead CPI changes. average sellingprices,shouldleadCPIchanges. percentage change in the headline CPI using a percentage changeinthe headline CPIusinga predict well changes in the consumer price predict wellchangesintheconsumerprice percent ofownersplanningtoincreaseaverage selling prices less the percent planning to reduce selling priceslessthepercentplanningtoreduce by owners, both actual and planned, anticipate by owners, both actual and planned, anticipate increases intheconsumerpriceindex. index (Equation3.1).Together,PLANP The two NFIB measures of price changes The two NFIB measures of price changes -1 -1 werefirstattempted. Ifthe in place ofPLANP gener- (3.1) -1 . 39 and and with thelabormarketmodels,thismodelalso tends toaccuratelypredictpost-GreatReces- to-quarter changeintheconsumerpriceindex using themodelexpressedinequation3.1.As predicted versusactualvaluesofthequarter-

QUARTER-TO-QUARTER CHANGE IN CPI (PERCENT) QUARTER-TO-QUARTER CHANGE IN CPI (PERCENT) -10 -10 Chart 11showstheout-of-sample 10 15 20 10 15 20 -5 -5 0 5 0 5 1975 1975 O ut - of 1980 1980 F -S orecast ample NFIB P F 1985 C 1985 orecast hange Actual rice

M 1990 Actual in of 1990 C C C easure C hart hart onsumer hange Fitted 10 11 changes inthepersonalconsumptionexpendi- ture indexandtheGDPdeflator,aswillbe to bethecasewithout-of-sampleforecastsof this timewithaslightlag.Thiswillalsoprove shown later. sion directionalmovementsinthepriceindices, 1995 (E

in Predicted 1995 quation P CPIU rice Residual 2000 I ndex sing 3.1) 2000 E U quation 2005 sing

2005 3.1 2010 -12

-8 -4

0 4 8

S RESIDUAL

19 | Small Business Indicators of Macro-economic Performance: An Update 20 | Small Business Indicators of Macro-economic Performance: An Update Jenkins modelingapproachsuggeststheinclu- 40 OLS and AR(1) models do not prove to be OLS andAR(1)modelsdonotprovetobe volatile energy and food prices. The standard volatile energyandfoodprices.Thestandard average price level. In other words, informa- the disturbanceterm.ApplicationofBox- that is,theincidenceof extremely highor tion in the tails of distribution of price changes, tude ofpastandplannedpricechangesincate- extremely lowreportsofactual andplanned distribution ofreportedpricechangesshould estimating change in Core CPI, which excludes estimating change in Core CPI, which excludes price changes,movementsinthetailsof have animportantimpactonchangesinthe good fits for the data due to serial correlation in good fitsforthedataduetoserialcorrelationin gorical classifications. selling priceschanges,should addmeaningful

5.0% -7.9%;(7) 8.0% -9.9%;(8)10.0%ormore. The categoriesreported are:(1)lessthan1.0%;(2) 1.0% -1.9%;(3)2.0%2.9%;(4)3.0% -3.9%;(5)4.0%4.9%;(6) The NFIBsurveyasksfortheactualmagni- The NFIB measures are less successful The NFIBmeasures are lesssuccessful

CPICORE = 1.101 + 0.074 PASTP + 0.059 PLANP 0.059 + PASTP 0.074 + 1.101 = %∆CPICORE R u t 2 =0.444u

QUARTER-TO-QUARTER CHANGE IN CORE CPI (PERCENT) =0.823, Adj. R 15.0 10.0 12.5 0.0 2.5 5.0 7.5 1975 t-1 + 0.415 u 0.415 + F orecast 40 2 1980 = 0.817, F = 152.957, AIC = 3.214, SIC = 3.321, DW = 2.105 = 3.321,DW = 3.214,SIC 152.957,= = AIC 0.817,F = Duringperiodsofrapid U sing (0.021) t-3 C +ε NFIBP 1985 hange t Actual

rice in “C 1990 (0.032) C M hart ore easure Fitted ” C 12 CPICORE values (Chart 12) that the model CPICORE values(Chart12)thatthemodel 3.2) produces ahighR volatility, asoccurredfrom1978to1983. correlation problems. Such a model (Equation correlation problems.Suchamodel(Equation obvious from a graph of actual and predicted obvious from a graph of actual and predicted the pastthreemonths,andPLANP>5is rapid pricechanges). average offivepercentormoreinthenextthree average pricehikesoffivepercentormorein and PLANP>5withAR(1) andAR(3)terms predictive content(atleast,duringperiodsof percent of firms planning to raise prices by an has great difficulty capturing high levels of price has greatdifficultycapturinghighlevelsofprice months (notseasonallyadjusted).Aregres- sion of AR(1) and AR(3) terms to mitigate serial sion ofAR(1)andAR(3)termstomitigateserial sion of%∆CPICOREonPASTP,PASTP>5, included producesresults similartothose 1995 onsumer PASTP>5 isthepercentoffirmsreporting (E quation Residual P 2000 rice 3.2) I ndex 2 value (0.823), but it is value (0.823), butit is 2005

(3.2)

-6 -4 -2

0 2 4 6

S RESIDUAL (Equation 3.5).ThePCEindexisconstructed (%∆PCE) thanintheconsumerpriceindex Consumption Expenditurespriceindex whereas PCEallowsthebasketofgoodsto other datasources.Akeydifferencebetween of firmswhoreportraisingpricesinthe for equation3.2(Equation3.3).Increasesin the CPIandPCEisthatrepre- regression of%∆CPICOREonthepercent using theCPI,ProducerPriceIndex,and percent of firms who report loweringprices previous threemonths(PHIGHER)andthe sents a“fixed”(relatively)basketofgoods both PASTP>5andPLANP>5contributeto increases in the general price level. As before, ipating orpredictingchangesinthePersonal

PCE = -1.541 + 0.027 PASTP + 0.202 PLANP 0.202 + PASTP 0.027 + -1.541 = %∆PCE PLOWER 0.116 – PHIGHER 0.105 + 2.129 = %∆CPICORE PLANP>5-1 0.094 + PASTP>5 0.151 + PASTP 0.041 + 0.666 = %∆CPICORE Similar resultsareobtainedthrougha PASTP andPLANPdoabetterjobantic- R R R u u u t t t 2 2 2 =0.678u =0.444u =0.352u =0.785, Adj. R =0.822, Adj. R 0.831,= Adj.R t-1 t-1 t-1 +0.460u +ε u 0.414 + 2 2 2 t = 0.780, F = 164.355, AIC = 3.353, SIC = 3.438, DW = 2.000 = 3.438,DW = 3.353,SIC 164.355,= = AIC 0.780,F = 2.090 = 3.321,DW = 3.215,SIC 152.870,= = AIC 0.817,F = 2.077 = 3.263,DW = 3.134,SIC 127.805,= = AIC 0.824,F = (0.020) (0.026) (0.021) t-3 t-3 +ε +ε t t (0.035) (0.048) (0.060) (PLOWER) [Equation3.4].Inthismodel,a cial crisis. cut pricesdramaticallytoreduceexcessive change quartertoquarter.Incontrast,theCPI the modelhasdifficultyaccuratelypredicting to decreases. to increasesinthegeneralpricelevel,anda larger percentageoffirmsloweringpricesleads larger percentageoffirmsraisingpricesleads levels ofinventorycreatedby lower consumer distributed andsmalluntil2008,whenfirms periods ofhighpricevolatility. measures explain78.5percentofmovements spending followingthebeginningoffinan- basket isupdatedeverytwoyears. in thePCEindex.Theresidualsarewell Using anAR(1)model,theNFIB (0.048) (3.5) (3.3) (3.4)

21 | Small Business Indicators of Macro-economic Performance: An Update 22 | Small Business Indicators of Macro-economic Performance: An Update

QUARTER-TO-QUARTER CHANGE IN PCE INDEX (PERCENT) QUARTER-TO-QUARTER CHANGE IN PCE (PERCENT)

-10 12 16 -8 -4 10 15 -5 0 4 8 0 5 O 1975 1975 ut F - orecast of -S ample 1980 I 1980 ndex C F hange U orecast sing 1985 1985

in NFIBP Actual P

of ersonal C 1990 Actual hange 1990 rice C C hart hart C Fitted M onsumption

in 14 13 1995 easure PCEI Predicted 1995 (E ndex Residual 2000 E quation xpenditures U 2000 sing 2005 3.5) E quation 2005 P rice 2010 3.5

-8 -6 -4 -2

0 2 4

S RESIDUAL 41 GDP deflatormaybepredictedaccurately Core PCEindex,whichomitsenergyand food prices.IntroducingbothanAR(1)and fail toaccurately predict movementsinthe degree ofexplanatorypower(Equation3.6). a MA(1) term gives a model with a high by PASTPorPLANP ARMA(p, q)modelsareaclassofreferred toasautoregressivemovingaveragemodelswhichincludeboth an forecasting butoften lacktheoreticalmeaning. to constructaforecasting modelusingAR,MA,and integrationorderterms.Suchmodels canbeusefulforshort-term gressive integratedmovingaverage) modelingprinciples(alsoreferredtoasBox-Jenkinsmethodology) whichattempt form: u sists oflaggedvaluestheforecast error(nottheresidual),usedtoimprovecurrentforecast.AnMA(q) takesthe autoregressive term(AR)oforder p, aswellamovingaverage(MA)q.Thetermcon termoforder-

GDPDFL = 1.332 + 0.064 PLANP 0.064 + 1.332 = %∆GDPDFL GDPDFL = 1.942 + 0.068 PASTP 0.068 + 1.942 = %∆GDPDFL PLANP 0.049 – PASTP 0.023 + 0.854 = %∆PCECORE Finally, futureshort-termchangesinthe Regular OLSandautoregressivemodels R R R u u u t t t 2 2 2 =0.550u =0.497u =0.970u =0.830, Adj. R =0.845, Adj. R 0.891,= Adj.R t =ε t +θ 1 *ε t-1 t-1 t-1 - 0.581 - +0.306u +0.332u t-1 +θ 2 2 2 = 0.826, F = 214.344, AIC = 2.781, SIC = 2.867, DW = 2.004 = 2.867,DW = 2.781,SIC 214.344,= = AIC 0.826,F = 2.035 = 2.773,DW = 2.688,SIC 239.613,= = AIC 0.841,F = 1.785 = 2.514,DW = 2.408,SIC 273.806,= = AIC 0.888,F = -1 withtheinclusionof 2 *ε θ (0.022) (0.014) t-2 t-1 t-4 t-4 (0.015) +…θ +ε +ε +ε t t t q *ε t-q -1 . ARMA(p,q)modelsarefrequentlyassembled usingARIMA(autore-

(0.049) AR(1) andAR(4)termsinthemodel(Equa- This ARMA(1,1)modelmaybeusefulfor for PLANPrunscountertoconventional tions 3.7and3.8). short-term forecasting of the Core PCE index economic wisdom. despite thefactthatnegativecoefficient 41 (3.8) (3.7) (3.6)

23 | Small Business Indicators of Macro-economic Performance: An Update 24 | Small Business Indicators of Macro-economic Performance: An Update

QUARTER-TO-QUARTER CHANGE IN GDP DELATOR (PERCENT) QUARTER-TO-QUARTER CHANGE IN GDP DEFLATOR (PERCENT)

10 12 14 -2 10 12 O 0 2 4 6 8 1975 0 2 4 6 8 ut 1975 - of -S F ample orecast 1980 1980 F orecast C P rice hange 1985 1985 C

of Actual hange

in C GDP 1990 hange Actual 1990 M C C hart hart easure

in eflator Fitted 1995 GDP 16 15 (E Predicted 1995 quation U sing eflator 2000 Residual NFIBP 3.8) 2000 U 2005 sing lanned E 2005 quation 2010

3.8

-4 -2

0 2 4

S RESIDUAL = 0.6135).Aregressionmodel withINVSAT B NFIB measuresofinventorysatisfactionandchanges(planned 42 will leadtoamismatchbetweentheplanned in overallprivateinventorylevelsasmeasuredbytheNIPAaccounts. consumer (customer)purchasesduringagiven of inventoriesdependsonexpectedsalesin or replacementinventorydesiredbyowners of an AR(1) term into the equation produces of anAR(1)termintotheequationproduces outside therealmofstatistical significance(p from this regression indicate the possible pres- to adjusttheirstockofinventories,and the economy,decisionsbybusinessowners tion decisionsbymakersofgoodsthroughout that, ifpositive,mustbeclosedbyadditional tories, theratioofinventorytosalesthatis the futureperiod,costofholdinginven- the amount ofgoods generated by producers tories. Additionally,mismatchesbetween the coefficientforINVSAT ries arenotoriouslydifficulttopredict.These and thestockonhand.Comparingdesired desirable forthatparticulartypeofbusiness, adjustment model,inwhichthedesiredstock examining inventoryinvestmentisthestock and actuallevelsofinventoryinfutureperiods. during agivenperiodandtheamountofnew adjustments bybusinessownersandconsumer ence of serial correlation. The introduction ence ofserialcorrelation.Theintroduction purchases canleadtolargeswingsininven- period. Mismatchesbetweeninventorystock stock totheonhandproducesagap inventory changesareafunctionofproduc- inventory accumulationand,ifnegative,must improved statistical performance. However, improved statisticalperformance.However, or actual)amongsmallbusinessownersareshowntopredictwellchanges

ness inventoriesis usedinstead. Statistics onbusiness inventoriesforthesmallbusiness sectorarenotcurrentlyproduced, soameasureofoverallbusi- usiness A commonmodelinmacroeconomicsfor A correlogram of the residuals obtained A correlogramoftheresidualsobtained INV = 18.432 + 1.925 + 18.432 = ∆INV

Changes innon-farmbusinessinvento- R 2 = 0.312,= Adj.R 2 (1.459) = 0.302, F = 31.131, AIC = 9.697, SIC = 9.760, DW = 1.145 = 9.760,DW = 9.697,SIC 31.131,= = AIC 0.302,F =

I nventories INVSAT -1 is now well isnowwell -1 +4.676INVPLN (0.873) -1

(INVPLN). years of the time series until 1982, after which years ofthetimeseriesuntil 1982,afterwhich National IncomeandProductAccountsto values, generallybyfailing to matchthevola- faction (INVSAT),thenetpercentofowners future periods should increase in response to the percentofownersplanningtointention- the predicted values deviate from the actual the predictedvaluesdeviate fromtheactual too low,andinventoryplans(INVPLN),the the NFIBsurveymeasuresofinventorysatis- ness amongsmallbusinessesofagapbetween results is merited. The model tracks changes results ismerited.Themodeltrackschanges net percentofownersplanningtointention- reporting thatcurrentholdingsaretoohighor ally addto(orsubtractfrom)inventorystocks desired andactualinventorystocksdrives and actualstocks.Meanwhile,thepervasive- and plannedchangesininventory. and INVPLN ally increaseinventoryholdings. actual quarter-to-quarterchangeinoverallU.S. are loworplantoaddinventory.Thisrelation- percent of owners characterizing theircurrent period measuresofbothinventorysatisfaction stocks as“toohigh”orlow”(INVSAT) specification. Nonetheless,becauseoftheoret- ship istestedinequation4.1,whichrelatesthe situations whereownersfeelcurrentstocks be closedbyreducinginventories.Thenet business inventoriesareregressedonprevious business inventories(∆INV)asreportedinthe is adirectproxyforthegapbetweendesired in business inventories well for the first several in businessinventorieswellforthefirstseveral ical underpinnings,somefurtheranalysisofthe -1 Theory suggests that inventory stocks in

-1 is therefore not the best model isthereforenotthebestmodel (4.1) 42 Changesin

25 | Small Business Indicators of Macro-economic Performance: An Update 26 | Small Business Indicators of Macro-economic Performance: An Update values of INVSAT and INVPLN explain 31.2 values ofINVSATandINVPLNexplain31.2 ciated with positive changes in inventory stocks ciated withpositivechangesininventorystocks owners whothinkinventorystocksare“too correct sign:increasesinthenetpercentof than they are together. Equations 4.2 and 4.3 than theyaretogether.Equations4.2and4.3 to bebetterpredictorsofchangesininventories tility ofactualinventorychangepatterns.This low” orplanonincreasinginventoriesareasso- autoregressive modelof∆ drawback aside,bothcoefficientsareofthe percent of current period movements in U.S. percent ofcurrentperiodmovementsinU.S. show the regression results using the first-order show theregressionresultsusingfirst-order business inventories. period. Together, previous period in thenextperiod.Together,previousperiod QUARTER-TO-QUARTER CHANGE IN IN U.S. BUSINESS IVNETORIES ($BILLIONS) -100 INV = 36.792 + 3.666 INVSAT3.666 + 36.792 = ∆INV INV = 15.774 + 3.819 INVPLN 3.819 + 15.774 = ∆INV

INVSAT and INVPLN individually turn out INVSAT andINVPLNindividuallyturnout 100 150 R R u u -50 50 t t 2 2 =0.492u =0.553u =0.444, Adj. R =0.384, Adj. R 0 1975 t-1 t-1 F +ε +ε I orecast nventory 1980 2 2 (0.775) (1.431) t t = 0.436, F = 54.397, AIC = 9.492, SIC = 9.555, DW = 2.081 = 9.555,DW = 9.492,SIC 54.397,= = AIC 0.436,F = 2.100 = 9.658,DW = 9.595,SIC 42.391,= = AIC 0.375,F = INV onINVSAT C P hange 1985 lanned Actual -1 -1

in C B 1990 usiness hange C hart -1

Fitted M 17 The R OLS method. According to model selection OLS method.Accordingtomodelselection Both equationsalsopossesshigherR INVPLN criteria (AIC and SIC values), both 4.2 and 4.3 criteria (AICandSICvalues),both4.24.3 cients reflecthowincreasesininventorydissat- change patterns.Asbefore,thepositivecoeffi- found when regressing with the traditional found when regressing with the traditional to address issues concerning serial correlation to addressissuesconcerningserialcorrelation autoregressive model is enlisted in this case autoregressive modelisenlistedinthiscase are better fits for the data than equation 4.1. are betterfitsforthedatathanequation4.1. and INVPLN previous period lead to increases in inventory previous periodleadtoincreasesininventory stock inthecurrentperiod. isfaction and plans to add to inventories in the isfaction and plans to add to inventories inthe I nventories easure 1995 2 value for equation 4.3 is highest with value for equation 4.3 is highest with -1 Residual (E explaining 44.4 percent of inventory explaining44.4percentofinventory quation -1 U 2000 , respectively. The first-order , respectively.Thefirst-order sing NFIB 4.3) 2005 (4.3) (4.2) 2 -40 -80 values. values. 40 80

S RESIDUAL 44 43 former involvesaregressionof∆ tory changesintheU.S.economyandsmallbusi- tory changes should track closely with reported tory changesshouldtrackcloselywithreported nesses is, of course, a regression of net number of small business owners who report net numberofsmallbusinessownerswhoreport unreasonable toexpectthataggregateinven- hypothesis is tested in equations 4.4 and 4.5. The hypothesis istestedinequations4.4and4.5.The small businesses make up most of the interface small businessesmakeupmostoftheinterface between sellersandtheendconsumer. increasing theirinventories(INVCH). inventory changes at small businesses, given that inventory changesatsmallbusinesses,giventhat

percent ofallretail firms. make up99.7percent ofallU.S.(employer)retail firms.Retailfirmswithfewer than 20employeesmakeup99.1 According to the Census Bureau’s Statistics of U.S. Businesses database, retail firms with fewer than 500 employees The surveydataforINVCHreads: “Duringthelastthreemonths,didyouincreaseordecreaseyourinventories?” QUARTER-TO-QUARTER CHANGE IN IN U.S. BUSINESS IVNETORIES ($BILLIONS) -100 100 150 A moredirectmodelrelatingaggregateinven- -50 INV = 31.511 + 4.769 INVCH 4.769 + 31.511 = ∆INV INV = 19.825 + 4.160 INVCH + 2.904 INVPLN 2.904 + INVCH 4.160 + 19.825 = ∆INV

R R u u 50 t t 2 2 =0.349u =0.388u 0 = 0.516,= Adj.R =0.493, Adj. R 84 t-1 t-1 F +ε +ε 86 orecast 2 2 t t = 0.502, F = 35.603, AIC = 9.469, SIC = 9.571, DW = 2.037 = 9.571,DW = 9.469,SIC 35.603,= = AIC 0.502,F = 2.040 = 9.574,DW = 9.498,SIC 49.032,= = AIC 0.483,F = (0.847) (0.848) 88 C I nventory 90 hange INV on INVCH INV onINVCH Actual ∆ INV on the INV on the 92 43

It is not Itisnot in M 44 (1.293) B This This 94 easure usiness C hart Fitted 96 18 cators onchangesinsmallbusinessinventories of theindependentvariablesandmodelselec- tion criteria.Fullyhalfofaggregatechangesin than equation4.4basedonexplanatorypower this section. Equation 4.5 is marginally better and inventoryplansbyowners. data thananyoftheprecedingspecificationsin an explanatoryvariable. using the AR(1) model. The latter entails the using theAR(1)model.Thelatterentails same regression,butalsoincludesINVPLN business inventories is explainedby NFIB indi- I (E -1 nventories

98 quation Both regressionsarebettermatchesforthe 00 Residual 4.5) U 02 sing NFIB 04 06 (4.5) 4.4) 08 -120 -80 -40 40 80 0

-1 S RESIDUAL as as

27 | Small Business Indicators of Macro-economic Performance: An Update 28 | Small Business Indicators of Macro-economic Performance: An Update cast using equation 4.3 (Chart 19) shows how cast usingequation4.3(Chart19)showshow of changesininventory.Anout-of-samplefore- nomic variable but “undershoot” local maxima nomic variablebut“undershoot”localmaxima and minima is also found with the NFIB models and minimaisalsofoundwiththeNFIBmodels sample directionalmovementsinamacroeco-

QUARTER-TO-QUARTER CHANGE IN U.S. BUSINESS INVENTORIES ($BILLIONS) O -200 -160 -120 The tendencytoaccuratelypredictout-of-

ut 120 -80 -40 40 80 0 - of 1975 -S ample F 1980 orecast 1985

of C hange Actual 1990 C

in hart B usiness 19 financial crisis, but underestimated the degree financial crisis,butunderestimatedthedegree changes appear to be highly sensitive to swings changes appeartobehighlysensitiveswings of theinventory“firesale.”Thepredicted the NFIB models predict the large decrease in the NFIBmodelspredictlargedecreasein business inventories in the years following the business inventoriesintheyearsfollowing in theINVPLNvariable. 1995 Predicted I nventories 2000 U 2005 sing E quation 2010 4.3 This sectiondiscussesthepredictiveabilityNFIBcapitalexpendituremea- Although individualfirmsrarelymakemassive (in thepriorsixmonths). (in thepriorsixmonths),typicallyreportedby 50 percentto70oftheownersfrom

45 CXPLAN holdsubstantiallygreaterexplan- NFIB indicatorsCXPAST, quarter toquarter.Fourpercentoftheowners capital spendingintheUnitedStates.The can haveasubstantialimpactonaggregate outlays bysixmillionsmallbusinessemployers capital outlays,theaccumulationofsmall of pastcapitalspending,andCXPLAN,the capital expenditurevariablesexplainjust14.1 good predictorsofchangesinfixedcapitalspending. typically report outlays in excess of $500,000 the nextthreetosixmonths,isnotparticu- larly strong(Equation5.1).ThetwoNFIB domestic investment(%∆CAPX)andthe percent ofownersplanningcapitaloutlaysin percent ofchangesinoverallprivateinvest- median outlayforNFIBmembersis$20,000 ment spendingimprovesthefit.CXPASTand ment. Narrowing the definitionofinvest- predictors ofchangesingrossprivatedomesticinvestment,butreasonably measures ofcapitalexpenditure.TheNFIBprovetobepoor sures by small business owners (planned or actual) hold toward aggregate

C to improveorpurchase equipment,buildings,orlands?” The surveyquestion forCXPASTdatareads:“During thelastsixmonthshasyourfirm madeanycapitalexpenditures The relationshipbetweengrossprivate

CXPLAN 1.270 + CXPAST 0.165 - -25.928 = %∆NONRESPRIVFIX CXPLAN 1.431 + CXPAST 0.472 - -14.001 = %∆PRIVFIXED CAPX = -24.945 - 0.557 CXPAST + 1.950 CXPLAN 1.950 + CXPAST 0.557 - -24.945 = %∆CAPX R R u t 2 2 = 0.510 u 0.510 = =0.453, Adj. R 0.141,= Adj.R apital t-1 +ε 2 2 t = 0.438, F = 31.687, AIC = 6.819, SIC = 6.912, DW = 1.916 = 6.912,DW = 6.819,SIC 31.687,= = AIC 0.438,F = 1.761 = 8.354,DW = 8.285,SIC 9.627,= = AIC 0.127,F =

E (0.298) xpenditures 45 theincidence (0.230) (0.194) (0.466) (0.274) SEQUIP) [Equations5.2,5.3,and5.4].All SPRIVFIX) or equipmentonly(%∆NONRE- quarter changes.CXPASTandCXPLANalso closed inapriorperiod). current period(forexample,moreofthegap cient (0.325)suggestsotherwise.Thenegative changes intotalprivatefixedinvestment, regressions, modelselectioncriteriahintthat equation 5.3 provides thebestspecification, explain 35.2percentofmovementsinnonres- explaining 45.3percentofthequarter-to- expenditure dataareavailable. equations areestimatedwithdatabeginning atory powertowardchangesinprivatefixed period, theyarelikelytospendlessduringthe money on capital expenditures in the previous sign onCXPASTsuggeststhatifownersspent between desiredandactualcapitalstockwas but thehighp-valueforCXPAST’scoeffi- idential equipmentpurchases.Ofthefour in 1979:Q1,thefirstquarterthatNFIBpast investment (%∆PRIVFIXEDand%NONRE- (0.258) The NFIBmeasuresdobestinestimating

(5.3) (5.2) (5.1)

29 | Small Business Indicators of Macro-economic Performance: An Update 30 | Small Business Indicators of Macro-economic Performance: An Update

QUARTER-TO-QUARTER CHANGE IN GROSS DOMESTIC PRIVATE INVESTMENT (PERCENT) -60 -40 -20

CXPLAN 1.661 + CXPAST 0.300 - -28.972 = %∆NONRESEQUIP R R u u F 20 40 60 t t 2 2 = 0.198 u 0.198 = =0.360u 0 orecast =0.352, Adj. R =0.400, Adj. R (A ctual 80 C t-1 t-1 82 I +ε +ε hange nvestment 2 2 84 t t = 0.385, F = 25.591, AIC = 6.784, SIC = 6.877, DW = 1.989 = 6.877,DW = 6.784,SIC 25.591,= = AIC 0.385,F = = 0.335, F = 20.841, AIC = 7.127, SIC = 7.221, DW = 1.938 = 7.221,DW = 7.127,SIC 20.841,= = AIC 0.335,F =

in 86 C

apital and 88 Actual (0.129) P E lanned 90 xpenditures 92 C hart I nvestment Fitted 94 20 (0.000) U 96 sing 98 ) M Residual NFIBC easure 00 02 apital (E 04 quation E xpenditure 06 5.1) (5.4) 08 -60 -40 -20 60 20 40 0

S RESIDUAL % to have its source in CXPLAN. Regressions of to haveitssourceinCXPLAN.Regressionsof investment in the previous equations appears investment in the previous equations appears ∆

QUARTER-TO-QUARTER CHANGE IN PRIVATE FIXED INVESTMENT (PERCENT) F PRIVFIXED and%∆ -60 -40 -20 orecast

NONRESPRIVFIX = -20.821 + 0.821 CXPLAN 0.821 + -20.821 = %∆NONRESPRIVFIX PRIVFIXED = -19.379 + 0.736 CXPLAN 0.736 + -19.379 = %∆PRIVFIXED Much of the explanatory power toward fixed Much of the explanatory power toward fixed R R u u 20 40 t t 2 2 0 =0.446u u 0.501 = =0.380, Adj. R =0.368, Adj. R (A ctual 80 C hange 82 t-1 t-1 I +ε +ε nvestment 84 2 2 t t = 0.371, F = 41.699, AIC = 6.893, SIC = 6.956, DW = 2.066 = 6.956,DW = 6.893,SIC 41.699,= = AIC 0.371,F = 1.972 = 7.217,DW = 7.154,SIC 39.548,= = AIC 0.358,F =

in NONRESPRIVFIX on NONRESPRIVFIX on P 86 rivate

(0.209) and 88 Actual F P ixed (0.173) 90 lanned I 92 C nvestment hart I nvestment Fitted 94 21 (Equations 5.5and5.6). CXPLAN using an AR(1) model show that the CXPLAN usinganAR(1)modelshowthatthe NFIB variable individually explains more than 35 NFIB variableindividuallyexplainsmorethan35 percent of changes in either investment measure percent ofchangesineitherinvestmentmeasure 96 U sing 98 ) M Residual NFIBC easure 00 02 (E apital quation 04 E 06 (5.6) (5.5) xpenditure 5.2) 08 -30 -20 -10 10 20 30

S RESIDUAL

31 | Small Business Indicators of Macro-economic Performance: An Update 32 | Small Business Indicators of Macro-economic Performance: An Update

QUARTER-TO-QUARTER CHANGE IN PRIVATE FIXED INVESTMENT (PERCENT) -60 -40 -20

20 40 0 1975 F orecast P lanned 1980 C C hange apital 1985 Actual

in E P xpenditure rivate 1990 C hart F Fitted

ixed 22 M 1995 I easure nvestment Residual (E quation 2000 U sing 5.5) NFIB 2005 -40 -20 20 40

S RESIDUAL This sectionhighlightsthestrongbivariaterelationshipNIFBmeasuresof These transactions,alsoknownasopenmarket Under normalcircumstances,thefederalfunds C financing. Most of the bank lending done with financing. Mostofthebanklendingdonewith financed primarilyusingthesavingsof During the formation phase, small firms are During theformationphase,smallfirmsare Banks serve as the primary source of funds primary sourceoffunds Banks serveasthe will lendtopotentialborrowerswhenthe outcome ofapotentialborrower’sattemptto consists of commercial banks and other deposi- credit marketstypicallytakesonamoreimpor- operations, haveasignificantimpactonthe federal monetarypolicy,whichisimplemented for capitalexpendituresbysmallbusinesses, federal fundsrate(FEDFUNDS),the through bondmarkettransactionsconducted tory institutions,like savings banksandthrifts. tant roleasnewbusinessesmature.Themost turn to other funding sources to finance oper- tion havepassed,ownersandmanagersusually tives. Oncetheinitial phases of business forma- the context of bank lending decisions, banks rates throughouttheeconomybyactingasan rate subsequentlyinfluencesotherinterest acquire creditfromalender.Amongtheseis a sourceforsmallbusinesscapitalexpenditure although creditcardshaveincreasinglybecome ations. Accesstocapitalthroughconventional entrepreneur(s) orthoseofhisfriendsandrela- at whichbankslendtoeachotherovernight. gage loan,oranequipmentloan. ket tightness,includingthefederalfundsrateandinterestratespaid small businesses takes the form of a traditional small businessestakestheformofatraditional by theFederalReserveBankofNewYork. business loansuchasalineofcredit,mort- important source of credit for small businesses important sourceofcreditforsmallbusinesses interest ratefloorforcredittransactions.In on T-billsand10-yeartreasurynotes. small businesscredittightnesshavewithbroadmeasuresofcapitalmar- Numerous factorscaninfluencethe apital

M arkets 1981:Q2, the first quarter data for AVRATE 1981:Q2, thefirstquarterdataforAVRATE The presentinabilityoftheaveragesmallbusi- (AVRATE). Chart 23 shows how movements (AVRATE). Chart23showshowmovements was collected. Table 2 presents the correlation was collected.Table2presentsthecorrelation Movements in AVRATE closely mirror those of Movements inAVRATEcloselymirrorthoseof who borrowed using short term business loans who borrowedusingshorttermbusinessloans FEDFUNDS (ρ FEDFUNDS with an average of 4.6 percentage FEDFUNDS withanaverageof4.6percentage on borrowerswhoseekcapitaltofundsmall the yield on the 10-year treasury note (TNOTE). the yieldon10-yeartreasurynote(TNOTE). the yieldon1-yeartreasurybill(TBILL)and nect astheaverageratepaidontwelve-month rates offeredbybanksforsmallbusinessloans, rate leadtomovementsinotherinterestrates ness loan rate to fall below 6 percent may be and theT-billyield(ρ as thecorrelationbetweenfederalfundsrate ables. ThecorrelationbetweenAVRATEand loan fundswiththeFederalReserveforinter- reported average interest rate paid by owners reported averageinterestratepaidbyowners although since 2008 there seems to be a discon- exceeds theopportunitycostofleaving expected returnoninvestmentfortheloan a reflectionoftheriskpremiumlendersplace points separating the two series starting in points separatingthetwoseriesstartingin percent while the fed fundsrate is near zero. matrix for these four time series. AVRATE is matrix forthesefourtimeseries.AVRATEis money bysmallbusinessownersisstuckat6 major indicators of credit market tightness like major indicatorsofcreditmarkettightnesslike ments inthefedfundsrate,butalsowithother strongly correlatedwithallthreeothervari- bank lending.Movementsinthefederalfunds businesses. in the same direction, including the interest in AVRATEtrackcloselynotonlywithmove- The NFIB survey collects data on the The NFIBsurveycollectsdataonthe = 0.9641) is almost as strong =0.9641)isalmostasstrong 0.9891).

33 | Small Business Indicators of Macro-economic Performance: An Update 34 | Small Business Indicators of Macro-economic Performance: An Update 47 46 of smallbusinesscredittightness.Twoexplicit lending. Given this strong relationship, it and otherinterestrateswhichmoveintandem and FEDFUNDSshowstheinfluencefederal might provetobegoodpredictorsofmeasures monetary policycanhaveonsmallbusiness survey measuresofcredittightnessinthesmall stands toreasonthatthefederalfundsrate business lendingmarketcontainedintheNFIB

months ago?” of yourbusinessactivity,howdoes therateofinterestpayableonyourmostrecentloancomparewith thatpaidthree The surveyquestionforCREDHARD datareads:“Ifyouborrowmoneyregularly(atleastonceevery3 months)aspart CREDHARD. RATEPD data include only those respondents who indicated they were regular borrowers in the surveyquestion for The surveyquestionforRATEPDdata reads:“Aretheseloanseasierorhardertogetthantheywerethree monthsago?” INTEREST RATE (PERCENT) The strongcorrelationbetweenAVRATE

12 16 20

0 4 8 C TNOTE TBILL AVRATE FEDFUNDS 1975 orrelation NFIB A with 1980 M verage C atrix ommon 1985 I

of nterest AVRATE FEDFUNDS NFIBA T BILL AV RATE 0.9378 0.9636 0.9641 1.0000 I nterest 1990 R ate C verage T hart R able

for ates 23 1995 2 for businessloanscomparedtothreemonths three monthsago(CREDHARD) reported ago (RATEPD). ables indicatetightercreditmarketsforsmall a hardertimeobtainingfinancingcomparedto survey arethenetpercentofownersreporting borrowers (at least onceeverythree months) businesses. S 0.9178 0.9891 1.0000 R , 1974:Q4 mall T NOTE FED FUNDS ate

and B relative interestratepaidbyregular usinesse 2000 C to ommon TBILL 47 0.9508 1.0000 2011:Q3

Higherlevelsofbothvari- C 2005 I ompared nterest TNOTE 2010 1.0000

R ates 46 andthe TBILL, andTNOTE,respectively,usingthe (interest ratedecisionsmadebytheFederal first-order autoregressive model.The federal of regressionsRATEPDonFEDFUNDS, funds rate,1-yearT-billyield,and10-year tors ofchangesintheinterestratepaidby treasury noteyieldareallstrongpredic- loans. Thereaderherewillnotethatunlike equations, reflectingtheunderstandingthat able isontheright-handsideofeachthese earlier regressions,thegovernmentdatavari- small business owners on short-term business in manymodels,monetarypolicyshocks

Equations 6.1,6.2,and6.3showtheresults R R R FEDFUNDS 4.456 + -22.947 RATEPD= RATEPD = -20.893 + 3.457 TNOTE+ -20.893 RATEPD= 3.722 TBILL + -18.732 RATEPD= u u u t t t 2 2 2 =0.789u 0.771 = =0.823u =0.592, Adj. R =0.622, Adj. R 0.651,= Adj.R ut-1 t-1 t-1 +ε +ε +ε 2 2 2 t t t = 0.586, F = 99.644, AIC = 7.726, SIC = 7.789, DW = 2.159 = 7.789,DW = 7.726,SIC 99.644,= = AIC 0.586,F = 2.251 = 7.715,DW = 7.652,SIC 112.589,= = AIC 0.616,F = 2.267 = 7.635,DW = 7.572,SIC 127.576,= = AIC 0.646,F = (1.301) (0.886) (0.787) with FEDFUNDSprovidingslightlymore Positive movementsFEDFUNDS,TBILL, R-squares ofallthreeregressionsexceed0.59, Reserve) are assumedtobeexogenous.The owners who report higherrelative interest or TNOTEindicatemonetarypolicytight- the banking system to tighten lending. This three equations). rates inthecurrent period (conveyedthrough ences ofregularly-borrowingsmallbusiness ening whichincentivizeslendersthroughout explanatory powerthanTBILLorTNOTE. process isreflectedintheborrowingexperi- positive regression slope coefficients in these (6.1) (6.3) (6.2)

35 | Small Business Indicators of Macro-economic Performance: An Update 36 | Small Business Indicators of Macro-economic Performance: An Update forecasts of relative interest rates paid, the although allthreetendtounderestimatethe above threeregressionsalldoafairlygoodjob predicting directionalmovementsinRATEPD, RELATIVE INTERST RATE (PERCENT) INTERST RATE (PERCENT) -30 -20 -10 As toolsforgeneratingout-of-sample

-40 -20 10 20 30 40 50 20 40 60 0 0 1975 1975 O ut - of F -S orecast 1980 1980 ample U sing F R orecast 1985 elative F 1985 ederal Actual R

of ate 1990 Actual F R 1990 unds C C P elative hart hart aid Fitted R

by 24 25 estimated usingequation6.1. magnitude ofthevariableitself,therebyunder- shows theout-of-sampleforecastofRATEPD shooting local highs in the series. Chart 25 1995 ate R S Predicted 1995 ate (E mall P quation B aid Residual 2000 usiness U 2000 sing 6.1) O E 2005 wners quation 2005

2010 6.1 -60 -40 -20 20

S RESIDUAL (Equations 6.4,6.5,and6.6).Positiveslope FEDFUNDS, TBILL, and TNOTE, respectively, usingthefirst-orderautoregressive to obtain.RegressionsofCREDHARDon percentage ofownerswhoreportcreditharder model, provideevidenceofthisrelationship standards shouldbereflectedinahigher NET PERCENT OF OWNERS (PERCENT) -10

CREDHARD = 1.822 + 0.639 FEDFUNDS 0.639 + 1.822 = CREDHARD CREDHARD = 2.563 + 0.447 TNOTE+ 2.563 = CREDHARD 0.465 TBILL + 2.924 = CREDHARD Higher interestratesandtighterlending R R R u u u 20 30 10 t t t 2 2 2 =0.609u =0.578u =0.572u 0 = 0.454, Adj. R2 = 0.446, F = 56.877, AIC = 5.045, SIC = 5.108, DW = 2.300 = 5.108,DW = 5.045,SIC 56.877,= = AIC 0.446,F 0.454,= = Adj.R2 =0.464, Adj. R =0.508, Adj. R 1975 F orecast H t-1 t-1 t-1 arder +ε +ε +ε 1980 N 2 2 t t t = 0.456, F = 59.295, AIC = 5.026, SIC = 5.089, DW = 2.278 = 5.089,DW = 5.026,SIC 59.295,= = AIC 0.456,F = 2.251 = 5.004,DW = 4.941,SIC 70.682,= = AIC 0.501,F = et

to P (0.222) (0.142) (0.166) G ercent et 1985 U Actual

sing of S F mall ederal 1990 C hart B Fitted usiness F 26 R-squares for these threeregressions are lower one regressorineachoftheequations. obtain wheninterestratesrise.Althoughthe coefficients inallthreeequationssuggestthat than thoseinequations6.1,6.2,and6.3,they tary tighteningandfindcreditharderto are stillquitestronggiventhepresenceofjust small businessownersaresensitivetomone- unds 1995 O R wners ate Residual (E 2000 W quation ho F ind 6.4) 2005 C (6.4) (6.6) (6.5) redit

-10 -20 10 20

S RESIDUAL

37 | Small Business Indicators of Macro-economic Performance: An Update 38 | Small Business Indicators of Macro-economic Performance: An Update This sectiondiscussestherelativeperformanceofNFIBOptimismIn- Index performsbetterthantwowidely-followedmeasuresofconsumersen- O Purchasing ManagersIndex. (UMCSENT). TheCCIisamonthlyindex Confidence Index(CCI)andtheUniversity Board’s ConsumerConfidenceSurvey,which NFIB OptimismIndex.TheMichiganindexis NFIB survey,reflectthesentimentsandexperi- timent, theConferenceBoard’sConsumerConfidenceIndexandUni- conditions. ThequarterlyCCIseriesusedhere on gauginghouseholdreactiontolabormarket of Michigan’s Index of Consumer Sentiment overall productionintheeconomysuggeststhat overwhelming importanceofconsumptionto for 70 percent of gross domestic product. The for 70 percent of gross domestic product. The these measures of consumer sentiment should these measuresofconsumersentimentshould through theircollectivespendingongoodsand dex asapredictorofchangesinGrossDomesticProduct.TheOptimism act asgoodpredictorsofGDP. ences fromthefirmsideofeconomy.Other produced usingdatafromtheConference versity ofMichigan’sIndexConsumerSentiment.TheOptimism holds. TheConferenceBoard’ssurveyfocuses ment aretheConferenceBoard’sConsumer services produced in the United States, account services producedintheUnitedStates,account surveys capturetheviewsofconsumers,who begins in1975:Q3andisnearlyasoldthe by analysts to track and anticipate changes by analyststotrackandanticipatechanges is basedontheresponsesof5,000house- in economic activity. Many of these, like the in economicactivity.Manyofthese,likethe also performsfavorablycomparedtotheInstituteofSupplyManagement’s Two popularindicesofconsumersenti- Numerous other survey indicators are used Numerous othersurveyindicatorsareused ther

I ndicators 26), reflectingmethodologicaldifferencesin Michigan indexareconsiderablymorevola- ysis beginsin1978:Q1.Allthreeseriesadopt viduals whichfocusesonfinancialandincome of ConsumerSentiment,asurvey500indi- correlation matrix among these three variables the othertwotimeseries,beginningin1946, the indices’constructionsanddisparatetarget tile thantheNFIBOptimismIndex(Chart related, andthetwovariablespossessacorre- real GDPovertime(ρ=0.630). an indexreferencevalueof100. although thetimeseriesdatausedinthisanal- lation coefficientofjust0.470.Acomplete and INDEXUMCSENTfollowthesame and thequarter-to-quarterpercentagechange produced usingdatafromthemonthlySurvey populations. Differencesinvolatilitydonot ments inINDEXandCCIareconsiderablyless situations. The Michigan series is older than sentiment indices,theNFIBOptimismIndex broad patternsovertime(ρ=0.776).Move- indicate anabsenceofcorrelation,however, is themosthighlycorrelatedwithchangesin in real GDP is given in Table 3. Of the three Both theConferenceBoard index andthe tions 7.1,7.2,and7.3).TheAICSIC three indicesindicatethatINDEXisthesupe- rior predictorofchangesinrealGDP(Equa- measures forequation7.1arebothlowerthan QUARTER-TO-QUARTER CHANGE IN REAL GDP (PERCENT)

RGDP = -0.129 + 0.032 CCI 0.032 + -0.129 = %∆RGDP RGDP = -46.208 + 0.495 INDEX 0.495 + -46.208 = %∆RGDP Regressions of %∆RGDPoneachthe -15 -10 R u

10 15 20 25 -5 t 2 =0.274u 0 5 =0.383, Adj. R CCI %∆RGDP INDEX UMCSENT 1975 C orrelation t-1 +ε NFIB O 1980 2 t = 0.378, F = 83.900, AIC = 4.784, SIC = 4.827, DW = 1.805 = 4.827,DW = 4.784,SIC 83.900,= = AIC 0.378,F = S entiment (0.027) (0.054) C ptimism M 1985 ompared atrix INDEX I 0.630 0.776 0.470 1.000 UMCSENT INDEX ndices I

ndex of

1990 to NFIBO C C

T and and hart hanges able O C 1995 27 UMCSENT. 3 to 13.5 percent for CCI and 24.2 percent for tions. Additionally,INDEXexplains38.3 their counterpartsfortheothertwoequa- percent ofmovementsinrealGDP,compared ptimism hange ther 0.293 0.533 1.000 CCI

in PCHGRGDP CCI R S

entiment eal I in 2000 ndex R GDP eal UMCSENT V GDP 0.501 1.000 ersu I

ndices 2005 O ther

%∆RGDP (7.2) (7.1) 2010 1.000

100 120 140 160 20 40 60 80

E VALU INDEX

39 | Small Business Indicators of Macro-economic Performance: An Update 40 | Small Business Indicators of Macro-economic Performance: An Update The datadonotsupportthisview.According Index forthemanufacturingsector(ISM) Supply Management’sPurchasingManagers value above50indicatesthatactivityinthe viewed asaproxyforlargefirmsingeneral. turning pointsinthebusinesscycle.Anindex to businesstrendsinthebroadereconomyand to makeproducts.TheISMishighlysensitive the manufacturingindustry.TheInstitutefor to datafromtheCensusBureau’sStatis- responsible forprocuringthesuppliesneces- reflects thesentimentsofpurchasingagents popular measureofeconomicperformancein manufacturing sectorisincreasing;avalue sary fortheirrespectivemanufacturingfirms below 50indicatesthatitisdecreasing. is knowntobeausefulmeasureforgauging The manufacturing sector is sometimes

INDEX alsocomparesfavorablywitha RGDP = -8.202 + 0.126 UMCSENT 0.126 + -8.202 = %∆RGDP RGDP = -14.275 + 0.330 ISM 0.330 + -14.275 = %∆RGDP R R R u t 2 2 2 = 0.177 u 0.177 = =0.362, Adj. R =0.242, Adj. R 0.135,= Adj.R t-1 +ε 2 2 2 t = 0.122, F = 10.133, AIC = 5.103, SIC = 5.168, DW = 1.960 = 5.168,DW = 5.103,SIC 10.133,= = AIC 0.122,F = = 0.357, F = 78.206, AIC = 4.853, SIC = 4.895, DW = 1.694 = 4.895,DW = 4.853,SIC 78.206,= = AIC 0.357,F = 1.775 = 5.046,DW = 4.978,SIC 19.107,= = AIC 0.229,F = (0.000) (0.000) 2009, a small fraction. Conversely, manufac- (those with500ormoreemployees)madeup firms, asizeablepercentage,butnowherenear INDEX asameansofmakinglarge-versus- questionable practice. just 1.4percentofallmanufacturingfirmsin tics ofU.S.Businessesdataset,largefirms turing firmsmadeup21percentofalllarge facturer’s indexexplains36.2percentofmove- time period1973:Q4to2008:Q4,themanu- doing so, measuring its performance relative to as aproxyforthelargebusinesssectorand,in a majority.ThesedatasuggestthatusingISM equation 7.1, where INDEX explained 38.3 equation 7.1, where INDEX explained 38.3 percent ofmovementsinrealGDP. ments in real GDP (Equation 7.4). This result ments in real GDP (Equation 7.4). This result small businessperformancecomparisonisa is almost as good as INDEX’s performance in is almostasgoodINDEX’sperformancein In aregressionof%∆ RGDP on ISM over the RGDP onISMoverthe (7.3) (7.3) The small business sector produces almost C NFIB measuresappeartodobestpredicting created. Collectively,theactionsofsmallbusi- one-half oftheprivatesectorGDP,accounts future movements in inflationary and labor force, andtwo-thirdsofthenetnewjobs for roughlyhalfoftheprivatesectorlabor to importanteconomicmeasureslikeGDP ness ownershaveamajorimpactontheU.S. larly exceed0.60.R-squaredvaluesofregres- analysis, the R-squared values of regressions of economy. Theeconomicindicatorspioneered market indicators.Whenserialcorrelation growth, unemployment,inflation,business sions ofchangesinprivateemploymentorthe shown tohavestrongempiricalrelationships by NFIBanddescribedhereinhavebeen inflationary indicatorsonNFIBmeasuresregu- is accountedforandaddressedinregression inventories, andcapitalexpenditures.The oncluding

O bservations Consumer ConfidenceIndexandtheUniver- casting, policymaking,andcomprehending of headlinemacroeconomicindicatorsshould of consumersentiment,therelativeperfor- to theISMPurchasingManagersIndex,an to besuperiorboththeConferenceBoard’s times exceed0.70. encourage theirincreasedusebyforecasters, economic activityin“larger”firms.Thestrong as apredictorofchangesinrealGDPisshown unemployment rateonNFIBmeasuressome- policymakers, and other analysts forfore- performance ofNFIBmeasuresaspredictors how onevitalhalfoftheeconomyperforms. ment. TheNFIBOptimismIndexisalso mance oftheheadlineNFIBOptimismIndex shown to perform favorably when compared sity ofMichigan’sIndexConsumerSenti- indicator sometimesthoughttorepresent Compared withothermajorindicators

41 | Small Business Indicators of Macro-economic Performance: An Update Appendix A:

Small Business Economic Survey 42 | Small Business Indicators of Macro-economic Performance: An Update 43 | Small Business Indicators of Macro-economic Performance: An Update 44 | Small Business Indicators of Macro-economic Performance: An Update 45 | Small Business Indicators of Macro-economic Performance: An Update 46 | Small Business Indicators of Macro-economic Performance: An Update A When performingregressionanalysis,one N This involves not only checking the statistical This involvesnotonlycheckingthestatistical S

whether certainindependentvariablesshould whether thesechoicescollectivelyprovide variable, independentvariable(s),andfunc- of thestatisticalsignificanceregres- on twolevels.First,economictheoryand of thequestionsaresearchermustconcern the finalmodelspecification. for themost“appropriate”modelspecifica- tion. Broadly speaking,decidingthe“appro- tional formoftheequation,anddeciding explanatory variableswhoset-statisticsand endeavor includesselectingthedependent has onmeasuresofgoodness-of-fitormodel priateness” of a model specification occurs himself withismodelspecification.This -values, significance ofindividualt-statisticsandp-values, ments in the dependent variable regardless strictly upon the regression results to help strictly upontheregressionresultstohelp but also examining model selection criteria that but alsoexaminingmodelselectioncriteriathat significance havenonethelessbeenincludedin sometimes encounterregressionsinwhich selection criteria.For this reason,readerswill sion coefficients orthe impact their inclusion be includedinthemodelto“explain”move- included or omitted in the final specification. included oromittedinthefinalspecification. inform what explanatory variables should be p-values arenotsignificantatachosenlevelof intuition canberelieduponwhendeciding pecification otes ppendix The second approach is to rely (more) The secondapproachistorely(more)

R egardin B.

A nd

M S election odel Criterion (AIC),definedasAIC=e Lack ofanunderlyingdistributionalsomakes SIC measure. where oped which serve as a useful way of discerning oped whichserveasausefulwayofdiscerning of observations: cations. Theseselectioncriteriagenerally seek of selectingthemodelwithlowestAICor ciency orrobustnessofthesecriteria.Inlieu of anunderlyingdistributionnaturallymakes observations. Thesecondmodelselectioncrite- to minimize some function of the mean squared to minimizesomefunctionofthemeansquared to confirmtherobustnessofthesemeasures. throughout. The first is the Akaike Information throughout. ThefirstistheAkaikeInformation and selectingamongalternativemodelspecifi- error (MSE),definedasthesumofresid- uals from a regression divided by the number uals fromaregressiondividedbythenumber rion is the Schwarz Information Criterion (SIC), rion istheSchwarzInformationCriterion(SIC), ated withastatisticaldistribution.Thislack defined asSIC=T use theAICorSICmeasurestoselecta“best” proofs, montecarlosimulationshavebeenused statisticians andeconometricianshavedevel- model specificationfollowtheruleofthumb measures isthatneitherofthemareassoci- mated intheregressionandT graph refers to two such model selection criteria graph referstotwosuchmodelselectioncriteria statistical significance.Instead,analystswho it impossibletousethesemeasuresintestsof it impossible to mathematically prove the effi-

An interesting feature of the AIC and SIC p isthenumberofparameterstobeesti- MSE = (∑ (p/T) *MSE. e t 2 / is the number of isthenumberof T ). This mono- ( 2 p/T) * MSE, *MSE, A N All ofthedatausedinthisanalysisistime

This dangerisreferredtointheeconometrics Time trends observed for a particular economic Time trendsobservedforaparticulareconomic finding arelationshipbetweentwoormore what unsatisfactory at an intuitive level due to what unsatisfactory at an intuitiveleveldueto variable(s) in the absence of other econometric variable(s) intheabsenceofothereconometric variable(s) intheregressionequation,thereby ordering isassociatedwiththedata.This certain complications in dataanalysis. Fore- complication found in cases when the depen- omitted fromtheanalysiswhicharedriving cases, thereareusuallyoneormorevariables of obtainingbiasedestimators throughregres- or-less constantgrowthrate overtime.While for which certain analytical techniques (other forward method for reducing the likelihood forward method for reducing the likelihood frequently thecase.Anexponentialtrend,for this phenomenon’soccurrence.Anadditional than includingtheomittedfactors)havebeen trends observedamongtheincludedvariables. the changesinothervariables(s).Inmany that changesinaparticularvariablearecausing trends may lead an observer to falsely conclude trend over time. Failuretoaccount for time time seriesvariablessimplybecauseallofthem time series need not be linear, although this is time seriesneednotbelinear,althoughthisis the knowledge that the econometric model is the knowledge thattheeconometricmodel is regression problem is to include a time trend regression problem is to include a time trend literature asthespuriousregressionproblem, adjustments willtypicallyyieldbiasedregres- dent variables.Failuretoincludeatimetrend essentially unrelatedtochangesintheindepen- dependent variablemaybecausedforreasons explicitly recognizing that changes in the data fromcross-sectionalandintroduces dent variable is trending is artificially high developed inordertomitigatetheriskof and adjustedR approximate a time series exhibiting a more- example, is a better tool when attempting to principal differencedistinguishingtimeseries most amongthesecomplicationsistheriskof sion coefficients of the independent variables. sion coefficientsoftheindependentvariables. series data,meaningthatasystemoftemporal sion analysis,itisnonetheless atleastsome- including atimetrendvariable(s) isastraight- otes ppendix One approach used to address the spurious One approachusedtoaddressthespurious

R 2 values. egardin

T ime R 2

S That is,thet The econometrician is then able to perform The econometricianisthen abletoperform differencing prior to regressing: subtracting the variable(s) may be satisfactory if the emphasis variable(s) maybesatisfactoryiftheemphasis value ofthevariableduringagiventimeperiod course, the expectation that the sample size is course, the expectation that the sample size is of calculated usingtheconventionalequationfor conventional equationforthet or not this approach is sufficient depends on or notthisapproach is sufficientdependson from regression analysis require key conditions from regressionanalysisrequirekeyconditions the asymptotic(largesample)propertiesofesti- the frequently sufficienttoavoidthespurious from itsvalueduringtheperiodimmediately totic condition differencing attempts to achieve totic conditiondifferencingattempts toachieve the analysis at hand. Including time trend the analysisathand.Includingtimetrend the regressionequation).Ultimately,whether tional statistical measures calculated during tional statisticalmeasurescalculatedduring tions arenotsatisfied.Insuchcases,thetradi- tion ofregressionresultsisnowdifferent. time seriesinlieuoftheoriginalwhen the case of a variable(s) trending over time is theoretically sound and “fully explained” model. not followthet regression analysis(t regressions isespeciallycommoninlargesample regression problem,althoughtheinterpreta- lies in forecasting, for instance, but it may not lies inforecasting,forinstance,butitmaynot and so on. When this occurs, meaningful results and soon.Whenthisoccurs,meaningfulresults linear timetrends,takingone“difference”is time addressed in the contextofstationarytime etc.) will not follow the assumed distribution. etc.) willnotfollowtheassumeddistribution. analysis whenclassicallinearmodelassump- address thespuriousregressionproblemin performing regressionanalysis.Inthecaseof preceding andthenusingthe“differenced” mators and test statistics are not only known, mators andteststatisticsarenotonlyknown, sufficiently large. If the conditions are met, then sufficiently large.Iftheconditionsaremet,then standard testsofstatisticalsignificance. but also approximate the relevant distributions. but alsoapproximatetherelevant distributions. be satisfactory if the desire is to construct a be satisfactoryifthedesireistoconstructa is incomplete (factors have been omitted from incomplete (factorshavebeenomittedfrom eries , a concept which is best weak dependence , aconceptwhich isbest to be fulfilled, including, of asymptotic theorytobefulfilled,including,of F Another approachthatcanbeusedto Differencing in the context of time series Differencing inthecontextoftimeseries In timeseriesanalysis,theprincipal asymp- -statistic willnotfollowtheF

A -statistic as calculated using the -statistic ascalculatedusingthe nalysi -distribution; theF -statistics, -distribution will -distribution will -distribution; -distribution; -statistic as -statistic as F -statistics, -statistics,

47 | Small Business Indicators of Macro-economic Performance: An Update 48 | Small Business Indicators of Macro-economic Performance: An Update { 48 In such tests, the null hypothesis is that a unit In suchtests,thenullhypothesis isthataunit well-known central limit theorem for time series well-known centrallimittheoremfortimeseries wish toreferWooldridge(2009). Processes which are not weakly dependent are Processes whicharenotweaklydependent order is the number of differences that must be order isthenumberofdifferencesthatmustbe root stationary processandcanbeusedinregres- for the law of large numbers and central limit for thelawoflargenumbersandcentrallimit tions are stable over time. A stationary time series tions arestableovertime.Astationarytimeseries that accounts for complicated dynamics in the that accountsforcomplicated dynamicsinthe time trendisoftenreferredtoasatrend- taken for a process to (likely) be made weakly taken foraprocessto(likely)bemadeweakly theorem toholdincross-sectionanalysis.) tant fortimeseriesregressionanalysisbecause not mean that it is nonstationary. Likewise, not. Simply because a series is trending does nonstationary, as well as weakly dependent or notions oftrending,stationarity,andweak are includedinthemodel. dependent seriesthatisstationaryaboutits dependency are separate and distinct. Trending dependent. Readersinterestedinamoreexten- all thatneedbeknownistheintegration discussion here by simply mentioning that such discussion herebysimplymentioningthatsuch assumption requiredinlargesamplecross- data issatisfied.Weakdependenceimpor- processes aredenotedbyI(x pendent” ash Augmented Dickey-Fuller (ADF) model istheAugmented Dickey-Fuller (ADF) mean thatitisweaklydependent.A , which tests for the presence of a unit root. test, whichtestsforthepresence ofaunitroot. stationarity requirement, ensures that the most stationarity requirement,ensuresthatthemost series canbe,weakdependence,alongwiththe strongly relatedtwodifferentvaluesinatime series processisonewhoseprobabilitydistribu- series. Generallyspeaking,astationarytime sion analysis provided appropriate time trends simply becauseaseriesisstationarydoesnot series arecapableofbeingbothstationaryor sive treatment of the concept of integration may sive treatmentoftheconceptintegrationmay said about such processes, but we will limit the said about suchprocesses,butwewilllimitthe section analysis.(Randomsamplingisrequired be unit is integratedoforderonereferredtoasaunit integration orderoftheprocess.Aprocessthat integrated to a higher order. Much could be integrated toahigherorder.Muchcouldbe it essentiallyreplacestherandomsampling if forany value oft x

t Wooldridge, Jeffrey M.,IntroductoryEconometrics: AModernApproach,4thedition,2009. = 1, 2, …} is said to be weakly dependent : t = 1, 2, …} is said to be weakly dependent , denoted I(0). integrated oforderzero, denoted I(0). A common test for weak dependence A commontestforweakdependence Weakly dependent processes are said to Weakly dependentprocessesaresaidto It should be remarked briefly thatthe . For the practitioner’s purposes, process. Forthepractitioner’spurposes,

. By imposing a limit on how ∞. Byimposingalimitonhow → , x t andx t+h ), wherex are“almost inde- 48 is the isthe (OLS) nolongerproducesbest,linear,unbi- OLS coefficientsarenow biased. Moreimpor- If not, then the series is differenced once and If not,thentheseriesisdifferencedonceand weakly dependentseries.Theneedforregres- way. Regressionsmaythereforeincludeaset why onefrequentlyobservesdifferencedseries will typicallyperformanADFtestandcheck ysis andreferstothephenomenonwhenerror changes of the original series. For example, changes oftheoriginalseries.Forexample, of timeseriesvariableswhichareexpressednot combination of weakly dependent and not combination ofweaklydependentandnot of differencedtimeserieswhichrepresenta outside certainforecastingprojectssincedoing of aunitroot.Inpractice,whendifferencing correlation inthe error terms. Serial corre- terms (conditionalupontheindependentvari- terms isacommonproblemintimeseries anal- time seriesdataofaneconomicindexarebetter tantly, traditionalOLSstandard errorsandtest tion of the ADF test is not especially common tion oftheADFtestisnotespeciallycommon time seriesregressions.However,strictapplica- to seeifthenullhypothesisisrejectedornot. to obtainaweaklydependentseries,ananalyst reliability oftimeseriesregressionresultssince root exists. Failure to reject the null hypothesis root exists.Failuretorejectthenullhypothesis not weakly dependent into ones that are explains not weakly dependent into ones that are explains null hypothesisoftheADFtestisrejected. lated withoneanother.Failuretocorrectfor lation, alsocalledautocorrelation,intheerror ables expressed as period-to-period percentage ables expressedasperiod-to-periodpercentage ables) intwodifferenttimeperiodsarecorre- expressed inpercentagechangetermsinsteadof ased estimators,asthevarianceestimatorsfor among independent and dependent variables in among independentanddependentvariablesin enced series.Thisprocessisrepeateduntilthe another ADFtestisperformedonthediffer- period-to-period differences. presence ofserialcorrelation. pret the results in an economically-meaningful pret theresultsinaneconomically-meaningful may beweaklydependent),butrathervari- motivates theinclusionintoregressionmodels means that one cannot rule out the presence means thatonecannotruleoutthepresence sion results to be economically meaningful also sion resultstobeeconomicallymeaningfulalso serial correlation will raisedoubtsabout the statistics (t, so canlimittheabilityof analyst to inter- benefit ofcorrectingtheproblemserial in terms of period-to-period differences (which in termsofperiod-to-perioddifferences(which its presencemeansthatordinaryleastsquares is not evidence that a unit root exists; it simply is notevidencethataunitrootexists;itsimply The desire to generate time series that are The desiretogeneratetimeseriesthatare Differencing hasthepotentialadded F, LM) arenolongervalidinthe A A The Augmented Dickey-Fuller (ADF) test is a The AugmentedDickey-Fuller(ADF)testisa

weak dependence among the data may elect to weak dependenceamongthedatamayelectto variables presentedindifferenced(∆)formor quarterly change (%∆) form reject the ADF cance level.Thosevariablesthatdonotreject common test for weak dependence in a time common testforweakdependenceinatime follows guidelines set forth in the Box-Jenkins follows guidelinessetforthintheBox-Jenkins the null hypothesisat the five percent signif- test nullhypothesisatthefivepercentsignifi- time seriesbeginningwiththeearliestdata tests onallvariables,bothdependentand the nullhypothesisofsubsequentADFtestson take differencesofthetimeseriestesteduntil that aunitrootexists.Ifthetestresultsfailto reject the null hypothesis, an analyst concerned reject thenullhypothesis,ananalystconcerned differenced series is rejected. Such an approach differenced seriesisrejected.Suchanapproach about potentialcomplicationsduetopossible point availablethrough2011:Q3.Nearlyall preceding sections.Testswererunforeach methodology fortimeseriesanalysis. series. The null hypothesis of an ADF test is series. ThenullhypothesisofanADFtestis independent, containedinregressionsthe ugmented ppendix Table 4belowgivestheresultsofADF

D D. ickey -F uller In deferencetosimplicityandeconomicintu- In fact, the weak dependenceamongthedatamaybe would suggestatleastonelevelofdifferencing For thosevariablespresentedintheiroriginal variables andincludingtheresultingdataseries values, lowerAIC/SICvalues). followed strictly.However,transformingthese found intheappendixontimeseriesanalysis. form (withnotransformationsapplied),many the nullattenpercentsignificancelevel. reject thenullatfivepercentsignificance differencing might prove beneficial (higher R even whenADFtestresultssuggestedthat above wouldinmanycasesmaketheeconomic level, butmanyalsodonot,northeyreject and potentialcomplicationsresultingfrom be applied,weretheBox-Jenkinsmethodology ition, thesevariableswereleftuntransformed interpretation oftheequationsmoredifficult. into theappropriateregressionequations icance levelrejectitatthetenpercentlevel.

More informationregardingtheADFtest T est p-values and

R esult t-statistics for some 2

49 | Small Business Indicators of Macro-economic Performance: An Update 50 | Small Business Indicators of Macro-economic Performance: An Update

TNOTE TBILL ∆INV ∆u ∆PRIVEMPL XLFCH

GTEX CXPLAN CXPAST CREDHARD CCI %∆RGDP %∆PRIVFIXED %∆PCE %∆NONRESPRIVFIX %∆NONRESEQUIP %∆GDPDFL %∆FSALPRIV %∆FSAL %∆ECI %∆CPICORE %∆CPI %∆CAPX SAL NJOBOP RATEPD ISM INDEX INVCH INVPLN INVSAT FEDFUNDS UMCSENT ESAL ESAL EMPCH EBCD Variable Name PLANP PLANP PHIGHER PASTP>5 PASTP PLOWER PLANWAGE PLANP>5 -1

-1 -1 -1

-1

A ugmented t-statistic -13.3886 -2.6884 -2.1204 -6.0915 -3.2909 -2.5229 -3.1825 -3.4925 -2.4084 -6.2403 -2.9853 -3.0309 -3.5923 -4.7067 -2.8015 -1.9851 -3.0442 -4.2851 -5.0022 -3.9361 -3.0176 -8.7464 -6.2897 -3.7450 -6.1182 -4.9204 -3.2737 -6.9904 -6.0577 -4.7808 -3.4015 -3.6143 -8.7327 -4.9453 -3.7442 -4.0065 -3.1123 -1.7664 -3.4255 -2.6848 -5.3653 -4.4415 -3.4792 -3.0432 -3.1762 D ickey T -4.0204 -4.0290 -4.0204 -4.0200 -4.0235 -4.0204 -4.0217 -4.0200 -4.0200 -4.0208 -4.0217 -4.0217 -4.0200 -4.0217 -4.0461 -4.0200 -4.0226 -4.0204 -4.0217 -4.0398 -4.0208 -4.0204 -4.0217 -4.0208 -4.0213 -4.0213 -4.0208 -4.0213 -4.1985 -4.0217 -4.0217 -4.0208 -4.0200 -4.0259 -4.0200 -4.0217 -4.0302 -4.0204 -4.0290 -4.0217 -4.0208 -4.0208 -4.0213 -4.0221 -4.0204 1% level able -F uller 4 Test criticalvalues T est -3.4401 -3.4442 -3.4401 -3.4399 -3.4416 -3.4401 -3.4407 -3.4399 -3.4399 -3.4403 -3.4407 -3.4407 -3.4399 -3.4407 -3.4524 -3.4399 -3.4411 -3.4401 -3.4407 -3.4494 -3.4403 -3.4401 -3.4407 -3.4403 -3.4405 -3.4405 -3.4403 -3.4405 -3.5236 -3.4407 -3.4407 -3.4403 -3.4399 -3.4427 -3.4399 -3.4407 -3.4448 -3.4401 -3.4442 -3.4407 -3.4403 -3.4403 -3.4405 -3.4409 -3.4401 5% level R esult 10% level -3.1445 -3.1469 -3.1445 -3.1443 -3.1453 -3.1445 -3.1448 -3.1443 -3.1443 -3.1446 -3.1448 -3.1448 -3.1443 -3.1448 -3.1517 -3.1443 -3.1451 -3.1445 -3.1448 -3.1499 -3.1446 -3.1445 -3.1448 -3.1446 -3.1447 -3.1447 -3.1446 -3.1447 -3.1929 -3.1448 -3.1448 -3.1446 -3.1443 -3.1460 -3.1443 -3.1448 -3.1472 -3.1445 -3.1469 -3.1148 -3.1446 -3.1446 -3.1447 -3.1450 -3.1445 p-value 0.2430 0.5294 0.0000 0.0717 0.3168 0.0919 0.0439 0.3737 0.0000 0.1399 0.1275 0.0339 0.0010 0.1992 0.6025 0.1239 0.0044 0.0003 0.0129 0.1320 0.0000 0.0000 0.0224 0.0000 0.0005 0.0747 0.0000 0.0000 0.0021 0.0551 0.0320 0.0000 0.0004 0.0226 0.0104 0.1073 0.7154 0.0518 0.2447 0.0001 0.0026 0.0000 0.0454 0.1243 0.0932

“lead” otherindicatorsreleasedatalaterdate. A A G

48 Granger causalitytest.Tothisend,asacheck Granger causalitystressestheimportanceof It shouldbeemphasizedthatalthoughtest Knowledge thatmovementsinoneindicator where Economic indicators are valuable for reasons can (toacertaindegree)accuratelypredictthe other thantheinformationtheyconvey content. Grangercausalitytestscannomore test wasperformedwithl tests performedformanyoftheNFIBand regarding certainfacetsoftheeconomy.For results mayindicatethatacertainvariable x “Grangercauses”anothervariabley,this analysis naturallypresentthemselves.Thefirst ables forforecastingfutureinstancesofgovern- a valuablecommodityintherealmoffinance. default settingfortheeconometricsoftware econometric technique. determine “true”causalitythancananyother a measureofprecedence and information does notimplythatxcausesyinthenormal program used.Becausethetheorybehind ment economictimeseries,twomethodsof many observers,theprimaryvalueofeconomic government economicvariablescontained sense oftheword.Grangercausalityissimply behavior ofsubsequentlyreleasedindicatorsis better to use more rather than fewer lags in a past information,asageneralprincipal,itis indicators liesintheirabilitytopredictand in the above regression equations. An initial (y, x)={(∆PRIVEMPL,XLFCH), (∆PRIVEMPL,NJOBOP), (%∆PCE,PASTP), ∆PCE, PLANP),(%PCECORE, PLANP), (%∆GDPDFL, (%∆INV,INVCH), ∆CAPX, CXPAST)}. nd ppendix ranger When consideringthevalueofNFIBvari- Table 5givesresultsofGrangercausality y t =α l signifiesthenumberoflaggedperiods.

F 0 +α orecast 1 *y

t - 1 C +…α ausality

E. equalto2,the

A l *y nalysi t –l +β

T 1 *x est t

- 1 - +…β Granger causalitytests,withafewnotable with cases, theadditionoftwoadditionallagged coefficients onthelaggedx-valuesarestatis- content thatpastinstancesofNFIBvariables tion raised the for robustness,asecondtestwasperformed the currentinstanceofdependentvari- the nullhypothesisisrejectedforapartic- the variabley tion isstatedas: tion contentofthextimeserieshelpsin tically significant,signifyingthattheinforma- toward avarietyofdifferentpriceindices. tion content contained in PASTP and PLANP null hypothesisatthetenpercentsignif- real GDP,theunemploymentrate,andkey exceptions. x. able, approach istheGrangercausalitytest,inwhich ables. Acommontechniqueimplementingthis approach involves measuring theinformation ular level of significance. The threshold for as welllaggedvaluesofsomeothervariable prediction ofy.Formally,theregressionequa- particular interestisthevaluableinforma- have oncurrentinstancesofgovernmentvari- be “Grangercaused”byNFIBvariables.Of instances of icance levelforl inclusion into the table is rejection of the is thatthevariablex inflation indices,amongothers,areshownto

R y issaidtobe“Granger-caused”byxifthe The nullhypothesisineachofthesetests esult l y equalto4. t , isregressedonlaggedvaluesofitself l *x 48 t -l Majoreconomicindicatorslike x . Alowp and +ε p -values associated with the

equalto2.Inalmostall t , y doesnotGranger-cause in the regression equa- -value indicatesthat

51 | Small Business Indicators of Macro-economic Performance: An Update 52 | Small Business Indicators of Macro-economic Performance: An Update “in sample”data)regressionmodels,wherethe

with theactualdata.Themostinteresting ysis” arefunctionsofthe forecast error,the values. Agoodforecasting model willtendto values forthedependentvariable,andthen value NFIBvariablesholdtowardforecasting comparing the“outofsample”forecastvalues of interest,toforecastthenextnnumber future valuesofothereconomicindicators tors ofwhatis tocome.Theforecasting accu- difference betweenthepredicted andactual dependent variablesaregovernmentstatistics entails employingpreviouslyestimated(using upon howreliably pasttrendsactaspredic - minimize theseerrors. statistics computedduringsuch“forecastanal- At itscore,forecastingaccuracy depends The secondapproachofanalyzingthe ∆PRIVEMPL ∆PRIVEMPL ∆PRIVEMPL ∆u ∆u %∆CAPX %∆INV %∆INV %∆INV %∆GDPDFL %∆GDPDFL %∆PCECORE %∆PCECORE %∆PCE %∆PCE %∆CPICORE %∆CPICORE %∆CPI %∆CPI %∆ECIWAGSAL %∆ECIWAGSAL %∆FSALPRIV %∆FSAL %∆FSAL %∆FSAL %∆RGDP %∆RGDP %∆RGDP %∆RGDP y G ranger CXPAST INVPLN INVSAT INVCH PLANP PASTP PLANP PASTP PLANP PASTP PLANP PASTP PLANP PASTP PLANWAGE PASTWAGE NJOBOP XLFCH EMPCH XLFCH EMPCH ESAL NEARN ESAL SAL GTEX EBCD ESAL INDEX x C ausality T able 5 crisis, housingcrash,andensuingGreatReces- occurrences will obviouslyhaveadeleterious tory and behavior of economic trends tempo- the NFIBseries. Suchirregular,record-setting rarily orevenpermanently.Thefinancial racy ofaparticularmodelestimatedusing ness ownerscutwagesand prices andreduced event(s) constitutinganexogenousshockora past datacanbeverygoodforestimating“in most rapidratesonrecord, andsmallbusi- shock. Unemploymentrose tolevelsnotseen sion beginningin2007/8constituteonesuch structural breakoccurs,changingthetrajec- sample” futurevalues,especiallywhensome sample” valueswhichpreviouslyoccurred, but mayfarepoorlywhenprojecting“outof in decades,GDPcontracted atsomeofthe inventory atthequickestpace inthehistoryof T est 0.0848 3.E-05 0.0182 0.0514 0.0056 0.0002 0.0441 0.0231 0.0737 0.0059 0.0005 0.0002 0.0105 0.0007 0.0026 0.0168 0.0040 0.0008 3.E-14 0.0781 0.0586 0.0849 0.0510 0.0031 0.0213 0.0021 0.0855 0.0005 0.0005 l =2 R esult p-value 0.0384 8.E-05 0.0852 0.0390 0.0049 0.0021 0.0140 0.0387 0.0291 0.0003 0.0016 0.0038 0.0531 0.0014 0.0092 0.0638 5.E-13 2.E-11 1.E-12 0.1662 0.3845 0.0098 0.1689 0.0050 0.1438 0.0023 0.1838 0.0005 0.0035 l =4 the regressionmodelsdiscussedaboveproved end of2008. using theabovemodels,consideringthat models wereestimatedusingdatathroughthe impact onout-of-sampleforecastanalysis Despite theseconsiderations,severalof 2011:Q4). Inparticular,theinflationregres- of-sample (actual)values. out-of-sample estimates (2009:Q1 through to begoodpredictorswhenusedforecast measures provedtobegoodpredictorsofout- sions alongwithmodelsoflabormarket

53 | Small Business Indicators of Macro-economic Performance: An Update 1201 “F” Street, NW Suite 200 Washington, DC 20004 nfib.com