管理经济学（第14版） 课件 第7章　需求估计和预测

Chapter07DemandEstimationandForecastingMANAGERIALECONOMICSFoundationsofBusinessAnalysisandStrategyFourteenthEditionCHRISTOPHERR.THOMAS©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.LearningOutcomes7.1Explainstrengthsandweaknessesofdirectmethodsofdemandestimation.7.2Specifyanempiricaldemandfunctionandexplainthemathematicalpropertiesofeachtype.7.3Employlinearregressionmethodologytoestimatethedemandfunctionforasingleprice-settingfirm.7.4Forecastsalesandpricesusingtime-seriesregressionanalysis.7.5Usedummyvariablesintime-seriesdemandanalysistoaccountforcyclicalorseasonalvariationinsales.7.6Discussandexplainseveralimportantproblemsthatarisewhenusingstatisticalmethodstoforecastdemand.2DirectMethodsofDemandEstimation1Consumerinterviewswhichrangefromstoppingshopperstospeakwiththemtoadministeringdetailedquestionnaires.Potentialproblemswithconsumerinterviews:Selectionofarepresentativesample,whichisasample(usuallyrandom)havingcharacteristicsthataccuratelyreflectthepopulationasawhole.Responsebias,whichisthedifferencebetweenresponsesgivenbyanindividualtoahypotheticalquestionandtheactiontheindividualtakeswhenthesituationactuallyoccurs.Inabilityoftherespondenttoansweraccurately.3DirectMethodsofDemandEstimation2MarketstudiesandexperimentsMarketstudiesattempttoholdeverythingconstantduringthestudyexceptthepriceofthegood.Labexperimentsusevolunteerstosimulateactualbuyingconditions.Fieldexperimentsobserveactualbehaviorofconsumers.4EmpiricalDemandFunctionsEmpiricaldemandfunctionsaredemandequationsderivedfromactualmarketdataandareusefulinmakingproductandpricingdecisions.𝑸=𝒇(P,M,PR,N)whereQisquantitydemanded,Pisthepriceofthegoodorservice,Misconsumerincome,PRisthepriceofsomerelatedgoodR,andNisthenumberofbuyers.5SpecificationofEmpiricalDemandFunctionsQ=a+bP+cM+dPR+eNInlinearform:b=ΔQ∕

ΔPc=ΔQ∕ΔMd=ΔQ∕ΔPRExpectedsignsofcoefficients:bisexpectedtobenegative.cispositivefornormalgoods;negativeforinferiorgoods.dispositiveforsubstitutes;negativeforcomplements.6LinearEmpiricalDemandFunctions:ElasticitiesQ=a+bP+cM+dPR+eNEstimatedelasticitiesofdemandarecomputedas:7NonlinearEmpiricalDemandSpecificationWhendemandisspecifiedinlog-linearform,thedemandfunctioncanbewrittenas:Toestimatealog-lineardemandfunction,converttonaturallogarithms:InQ=Ina+bInP+cInM+dInPR+eInNInthisform,elasticitiesareconstant:8EstimatingDemandforaPrice-SettingFirmToestimatethedemandfunctionforaprice-settingfirm:Step1: Specifyprice-settingfirm’sdemandfunctionStep2: Collectdataonthevariablesinthefirm’sdemandfunctionStep3: Estimatethefirm’sdemand9LinearEmpiricalDemandFunctions:CheckersPizza

1DependentVariable:QRSquareFRatiopValueonFObservations:240.9555101.900.0001VariableParameterEstimateStandardErrortRatiopValueIntercept1,183.80506.2982.340.0305P−213.42213.4863−15.830.0001M0.091090.012417.340.0001PAL101.30338.74782.610.0171PBMAC71.844827.09972.650.0158WhenP=$9.05,M=$26,614,PAL=$10.12,PBMac

=$1.1510LinearEmpiricalDemandFunctions:CheckersPizza2Elasticities:11Time-SeriesForecastsAtime-seriesmodelshowshowatime-orderedsequenceofobservationsonavariableisgenerated.Simplestformislineartrendforecasting.Salesineachtimeperiod(Qt)areassumedtobelinearlyrelatedtotime(t)12LinearTrendForecastingUseregressionanalysistoestimatevaluesofaandb.Ifb>0,salesareincreasingovertime.Ifb

<0,salesaredecreasingovertime.Ifb=0,salesareconstantovertime.Statisticalsignificanceofatrendisdeterminedbytestingorbyexaminingthep

valuefor13Figure7.1ALinearTrendForecastAccessthetextalternativeforslideimages.14Figure7.2ForecastingSalesforTerminatorPestControlAccessthetextalternativeforslideimages.15Seasonal(orCyclical)VariationSeasonal(orcyclical)variationistheregularvariationthattime-seriesdatafrequentlyexhibit,whichcanbiastheestimationofparametersinlineartrendforecasting.Toaccountforsuchvariation,dummyvariables

areaddedtothetrendequation.Dummyvariablestakeonlyvaluesof0and1.Shifttrendlineupordowndependingontheparticularseasonalpattern.Significanceofseasonalbehaviordeterminedbyusingttestorpvaluefortheestimatedcoefficientonthedummyvariable.16Figure7.3SalesWithSeasonalVariationAccessthetextalternativeforslideimages.17DummyVariablesToaccountforNseasonaltimeperiods,N−1dummyvariablesareadded.Eachdummyvariableaccountsforoneseasonaltimeperiod:Takesvalueofone(1)forobservationsthatoccurduringtheseasonassignedtothatdummyvariable.Takesvalueofzero(0)otherwise.18Figure7.4TheEffectofSeasonalVariationAccessthetextalternativeforslideimages.19Table7.1CreatingaDummyVariableQttD10203041506070819010011012113014015016120Table7.2QuarterlySalesDataforStatewideTruckingCompany(2022–2025)(1)Year(2)Quarter(3)Sales(4)t(5)D1(6)D2(7)D32022I$72,0001100II87,0002010III87,0003001IV150,00040002023I82,0005100II98,0006010III94,0007001IV162,00080002024I97,0009100II105,00010010III109,00011001IV176,000120002025I105,00013100II121,00014010III119,00015001IV180,0001600021SomeFinalWarningsThefurtherintothefutureaforecastismade,thewideristheconfidenceintervalorregionofuncertainty.Modelmisspecification,eitherbyexcludinganimportantvariableorbyusinganinappropriatefunctionalform,reducesreliabilityoftheforecast.Forecastsareincapableofpredictingsharpchangesthatoccurbecauseofstructuralchangesinthemarket.22Figure7.5ConfidenceIntervalsAccessthetextalternativeforslideimages.23Summary1Consumerinterviewsandmarketstudiesaretwodirectmethodsofdemandestimation.Problemscaninclude:(1)selectionofarepresentativesample;(2)responsebias;and(3)inabilityoftherespondenttoansweraccurately.Empiricaldemandfunctionsaredemandequationsderivedfromactualmarketdataandareextremelyusefulinmakingpricingandproductiondecisions.Thefirststeptoestimatingasingleprice-settingfirm’sdemandistospecifythedemandfunction;thesecondstepistocollectdata;thethirdstepistoestimatetheparametersusingthelinearregression.24Summary2Atime-seriesmodelshowshowatime-orderedsequenceofobservationsonavariableisgenerated.Thesimplestformoftime-seriesforecastingislineartrendforecasting.Seasonalorcyclicalvariationcanbiasresultsinlineartrendmodels;toaccountforthis,dummyvariablesareaddedtothetrendequation.Dummyvariablestakeavalueof1forthoseobservationsthatoccurduringtheseasonassignedtothatdummyvariable,andavalueof0otherwise.Whenmakingforecasts,analystsmustrecognizethelimitationsthatareinherentinforecasting.25EndofMainContent©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.AccessibilityContent:TextAlternativesforImages27Figure7.1ALinearTrendForecast

-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledsales,Qin2024and2029.Thehorizontalx-axisislabeledtime,tthatrangesfrom2014to2024inincrementsof1unitand2029.Thetendatapointsarescatteredandfollowalinearincreasingpattern.Asolidlinelabeledestimatedtrendlineisdrawnthatbestfitsthedatascatteredandpassesthroughtwopoints(2024,Qsubscript2024)and(2029,Qsubscript2029).Notethatalltheabove-mentionedvaluesareapproximate.Averticaldashedlineoriginatesfromthex-axisin2024and2029tothepointsjustaboveit.AhorizontallineoriginatesfrompointQsubscript2024andQsubscript2029onthey-axistothepointsattheright.Returntoparent-slidecontainingimages.28Figure7.2ForecastingSalesforTerminatorPestControl

-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledsales(homeservicedpermonth),Qsubscripttrangesfrom0to160inincrementsof20.Thehorizontalx-axisislabeledt,rangingfrom0to18inincrementsof1unit.Thefifteendatapointsarescatteredatpoints(0,45),(1,46),(2,56),(3,72),(4,67),(5,77),(6,66),(7,69),(8,79),(9,88),(10,91),(11,94),(12,104),(13,100),(14,113),and(15,120).AlineofbestfitlabeledtrendlineQsubscripttequals46.57plus4.5t.Itpassesthroughthepoint(2,56)andthreemorepointslabeledQcapsubscript16equals46.57plus4.53of16equals119,Qcapsubscript17equals46.57plus4.53of17equals123.6,andQcapsubscript18equals46.57plus4.53of18equals128.1.Attheright,atableisshownwithcolumnheadersMonth,t,andQsubscriptt.Thedataenteredinthetableareasfollows:January2023;1;46.February2023;2;56.March2023;3;72.April2023;4;67.May2023;5;77.June2023;6;66.July2023;7;69.August2023;8;79.September2023;9;88.October2023;10;91.November2023;11;95.December2023;12;104.January2024;13;100.February2024;14;113.March2024;15;120.Returntoparent-slidecontainingimages.29Figure7.3SalesWithSeasonalVariation

-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledassales,Qsubscriptt,andthehorizontalx-axisislabeledasyears,from2021to2024inincrementsof1.Eachyearisdividedintofourseasonslabeledas1,2,3,and4.Intheyear2021,thefirstpointislabeleddirectlyabove1.Thesecondpointislabeleddirectlyabove2andslightlybelowthefirstpoint.Thethirdpointislabeleddirectlyabove3andslightlyabovethesecondpoint.Thefourthpointislabeleddirectlyabove4andfaraboveallthefirstthreepoints.Intheyear2022,thefirstpointislabeleddirectlyabove1,andabovethefirstthreepointsintheyear2021.Thesecondpointislabeleddirectlyabove2andslightlyabovethefirstpoint.Thethirdpointislabeleddirectlyabove3andslightlybelowthesecondpoint.Thefourthpointislabeleddirectlyabove4andslightlyabovethefourthpointintheyear2021.Intheyear2023,thepointsarearrangedsimilarlyasintheyear2022andallthepointsareslightlyshiftedup.Intheyear2024,allthepointsarearrangedinexponentiallyincreasingorder.Returntoparent-slidecontainingimages.30Figure7.4TheEffectofSeasonalVariation

-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledassales,Qsubscripttandhastwopointsmarkedonit,aandaprime.Point'a'isclosetotheorigin.Thehorizontalx-axisislabeledastime,t.TwoincreasingparallellineslabeledQsubscripttequalsaprimeplusbtandQsubscripttequalsaplusbtaredrawnseparatedbyadistancelabeledc.Returntoparent-slidecontainingimages.31Figure7.5ConfidenceIntervals

-TextAlternativeReturntoparent-slidecontainingimages.PanelA:Theverticaly-axisislabeledassales,Qsubscriptt,andhasapointQbarmarkedonit.Thehorizontalx-axisislabeledastime,t.Threepointstsubscript1,tbar,andtsubscriptnaremarked.AnincreasinglinelabeledQsubscripttequalsaplusbt,start