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Basic EconometricsBasic Econometrics
ChristopherChristopher GrigoriouGrigoriou
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2007/20082007/2008
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OverviewOverview
Objectives of the dayObjectives of the day Interpreting Econometric ApplicationsInterpreting Econometric Applications
Understanding how it worksUnderstanding how it works
Program of the dayProgram of the dayIntroduction (why? how? basic concepts)Introduction (why? how? basic concepts)InterpretationsInterpretations
CaseCase--studystudy
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1.1. Introduction to EconometricsIntroduction to Econometrics=> What for ?=> What for ?
Impact AnalysisImpact Analysis
To evaluate the success/failure of aTo evaluate the success/failure of aproject, reform, law,project, reform, law,
To test any economic theoryTo test any economic theory
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1.1. Introduction to EconometricsIntroduction to Econometrics=> How ?=> How ?
Apply statistical methods to economicApply statistical methods to economic
datadata
Econometric approach:Econometric approach:-- Develop working model from anDevelop working model from an
economic theoryeconomic theory
-- Estimate model with real world data.Estimate model with real world data.
Real world data is not perfectReal world data is not perfect
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Some examplesSome examples
Keynesian Consumption FunctionKeynesian Consumption Function
Price and QuantityPrice and Quantity
Philips CurvePhilips Curve
Production FunctionProduction Function
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C =C = ++ ..II C = ConsumptionC = Consumption
= Intercept= Intercept
I = IncomeI = Income
= slope (how much C changes for a given= slope (how much C changes for a given
change in I)change in I)
Not an econometric modelNot an econometric model
Assumes a deterministic relationshipAssumes a deterministic relationship
Keynesian Consumption FunctionKeynesian Consumption Function
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C =C = + + II ++
= error term= error term
Error term captures several factors:Error term captures several factors:
omitted variablesomitted variables
measurement error in the dependent variablemeasurement error in the dependent variable
randomness of human behaviorrandomness of human behavior
Keynesian Consumption FunctionKeynesian Consumption Function
=> Econometric Model=> Econometric Model
Expected Results:Expected Results: > 0 and 0 0 and 0 < < 1< 1 represents the MPCrepresents the MPC
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Ordinary Least SquaresOrdinary Least Squares
Estimate from the least squaresEstimate from the least squares the line of best fit minimizes the sum of thethe line of best fit minimizes the sum of the
squared deviations of the points on the graphsquared deviations of the points on the graphfrom the points on the straight line.from the points on the straight line.
MinimizeMinimize ((CACAii -- CPCPii))22
CACAii = Actual Consumption for= Actual Consumption for obsobs ii CPCPii = Predicted Consumption for= Predicted Consumption for obsobs ii
How to estimate the model?How to estimate the model?=> Fit a line through the data.=> Fit a line through the data.
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Ordinary Least Squares optimization processOrdinary Least Squares optimization process
=>search for ao and a1 that minimize the sum of thesquared residual (=the global error of the model)
yi = ao + a1.xi + ui
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Suppose we get C = 1000 + 0.8I
= 1000
= 0.8
Sample income levels
I = 0, Consumption = 1000
I = 1000, Consumption = 1800
If I increases by 1 dollar, then C increases on averageby 0.8 dollars.
Interpretation (1)Interpretation (1)
These estimates are consistent with theory since >0 and 0
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Interpretation (2)Interpretation (2)
11-- Basic specification :Basic specification :YYii == ++ ..XXii ++ ..ZZii ++ ii = = marginal impact:marginal impact:=>=> anan increaseincrease ofof11 unityunity in Xin X impliesimplies ceterisceterisparibusparibus anan
increaseincrease ofof unitiesunities in Yin Y
22-- LogLog--log specification :log specification : lnlnYYii == ++ ..lnXlnXii ++ ..lnZlnZii ++ ii = = elasticityelasticity::
=>=> anan increaseincrease ofof11perper centcentin Xin X impliesimplies ceterisceterisparibusparibus ananincreaseincrease ofofpercentpercent in Yin Y
33-- semisemi--log :log : lnlnYYii == ++ ..XXii ++ ..ZZii ++ ii = = semisemi--elasticityelasticity::=>=> anan increaseincrease ofof11 unityunity in Xin X impliesimplies ceterisceterisparibusparibus anan
increaseincrease ofofperper centcentin Yin Y
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Other examples (1)Other examples (1)
Price and QuantityPrice and Quantity
Demand andDemand and elasticitieselasticities of demandof demand
lnln Q =Q = + + lnPlnP ++
Phillips CurvePhillips Curve
Relationship between change in money wages andRelationship between change in money wages andunemploymentunemployment
ww = f (= f (u)u)
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Production FunctionProduction Function
Relationship between inputs and outputs.Relationship between inputs and outputs.
Y = f (K,L)Y = f (K,L)
Cobb Douglas Y =Cobb Douglas Y = AKAKaaLL
Wage equationWage equation
lnln W =W = 00
++ 11
EDUC +EDUC + 22
EXP +EXP + 33
GENDER +GENDER +
44RACE +RACE + ++ ii
Other examples (2)Other examples (2)
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General Terminology (1)General Terminology (1)
Pooled data: mixture of crossPooled data: mixture of cross--sectional and time series datasectional and time series data
Panel data: follow a microeconomic unit over timePanel data: follow a microeconomic unit over time
Quantitative data: continuous dataQuantitative data: continuous data
Qualitative data: categorical dataQualitative data: categorical data
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General Terminology (2)General Terminology (2)
YYiitt==
++
..XX
iitt++
iitt
Y: dependent variableY: dependent variable
X: independent or explanatoryX: independent or explanatory
: : ErrorError--termterm subscript i: refers tosubscript i: refers to ithith observationobservation
t: for time series data at time tt: for time series data at time t
CrossCross--sectional data: collected at 1 point in timesectional data: collected at 1 point in time
Time series data: collected over a period of timeTime series data: collected over a period of time
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WhatWhat dodowewe know?know?
FromFrom aa theoreticaltheoretical economiceconomic hypothesishypothesis to anto aneconometriceconometricvalidationvalidation
EconometricEconometric methodsmethods == evaluateevaluate anan averageaverage
relationshiprelationshipbetweenbetweenY and XY and XEstimatesEstimates areare donedonewithwith errorerror
TheThe OrdinaryOrdinaryLeast Squares:Least Squares: methodmethod aimingaiming
atat assessingassessing thethe parametersparameters thatthat minimizeminimize thisthiserrorerror
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StatisticalStatistical DefinitionDefinition Basic ConceptsBasic Concepts
TwoTwobasicbasicwaysways toto characterizecharacterize aa statisticalstatistical serieserie ::
-- centralcentral parameterparameter =>=> meanmean,, medianmedian
meanmean ::
-- dispersiondispersion parameterparameter => variance,=> variance,
standardstandard--deviationdeviation
standardstandard--deviationdeviation ::
1
1 i ni
ii
X Xn
=
=
=
2
1
1( )
1
i n
n i
i
X Xn
=
=
=
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ExampleExample: 2: 2 differentdifferent classroomsclassrooms
ExamExam ofofStatisticsStatistics
2 groups2 groupswithwith onon averageaverage exactlyexactlythethe samesame markmark => 11.5=> 11.5
WhatWhat informationinformation doesdoes itit provideprovide ononyouryour ownown resultresult??
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Class AClass A
5.911.5Mean
34.3Var.149.5Sum
72.258.511.52013
49711.518.512
30.255.511.51711
20.254.511.51610
12.253.511.5159
6.252.511.5148
0.250.511.5127
2.25-1.511.5106
6.25-2.511.595
20.25-4.511.57430.25-5.511.563
72.25-8.511.532
90.25-9.511.521
(Xi-mean)Xi-MeanMeanXiRank
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Class BClass B
1.0411.5Mean
1.08Var.149.5Sum
2.251.511.513132.251.511.51312
1111.512.511
1111.512.510
0.250.511.5129
0011.511.58
0011.511.57
0.25-0.511.5116
0.25-0.511.5115
0.25-0.511.5114
1-111.510.53
2.25-1.511.5102
2.25-1.511.5101
(Xi-mean)Xi-MeanMeanXiRank
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=> To=> To characterizecharacterize aa serieserieyouyou needneed TheThe meanmean ofofthethe serieserie (central(central parameterparameter))
TheThe standardstandard--deviationdeviation (dispersion)(dispersion)
=>=>ofofcourse,course, thethe answeranswer alsoalso
dependsdepends onon thethe dispersion (dispersion (standardstandard--deviationdeviation))
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SameSame thingthingwithwith a coefficienta coefficient estimateestimate=>=> thethe coefficientcoefficient isis anan averagedaveraged impactimpact
=>=> itsits significancesignificance dependsdepends onon itsits dispersiondispersion,,i.e.i.e. thethe accuracyaccuracyassociatedassociated toto thethe estimateestimate
DonDontt forgetforget!! thethe predictionspredictions areare donedonewithwith errorerror!!
Y =Y = ++ XX ++
Given the error in the estimate or the inaccuracy in theGiven the error in the estimate or the inaccuracy in the
estimate (assessed by the dispersion)estimate (assessed by the dispersion) isis significantly different fromsignificantly different from zero?zero?
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EstimationEstimation ofofthethe educationeducation return (1)return (1)
OneOne ((perhapsperhapsyouyou?)?)wantswants toto knowknowthethe impactimpact ofofananadditionnaladditionnalyearyear ofofeducationeducation onon hishiswagewage
EconomicEconomic TheoryTheory: Mincer: Mincerss EquationEquation
EconometricEconometric point:point: howhowbigbig isis??
=>=> lwagelwageii
== ++..educeducii
++ ..experexperii++ .. expersqexpersq
ii++
ii
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=> 428 observations in=> 428 observations in thethe samplesample
=>=>RR--squaredsquared = 15.68%= 15.68%
OurOur modelmodel predictspredicts 15.68%15.68% ofofthethe fluctuationsfluctuations ofofthethewageswages
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lwage
educ
=
((averageaverage) coefficient) coefficient
=> 0.1075=> 0.1075
=>=>AnyAnyadditionaladditionalyearyear ofofeducationeducation impliesimplies onon
averageaverage anan increaseincrease ofof0.1075% in0.1075% in thethewagewage
NotNot onlyonlyaa meanmean (coefficient), but(coefficient), but alsoalso aa standardstandard
deviationdeviation (0.0141465)(0.0141465)asas anyanyotherother statisticalstatistical serieserie
TheThe standardstandard deviationdeviation providesprovides information oninformation on thethe
accuracyaccuracyofofthethe estimateestimate..
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Coefficient estimated with error
standard deviation
Confidence Interval :
95% chances for the coefficient to be in the interval( 2 = 0.07968 ; + 2 = 0.1352956)2 = 0.07968 ; + 2 = 0.1352956)
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IsIs significantlysignificantlydifferentdifferent fromfrom zerozero??
A testA test classicallyclassicallyusedused to compareto compare averagesaverages: t: t--test.test.
=>Compare the actual coeff.( ) with the restricted coeff.( )weighted by the dispersion (= a measure of theaccuracy of the estimate)
t
=
= 0.1075; = 0 !! = 0.01414 => 0.1075 7.600.01414
t = =
SoSowhatwhat??
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HH00
:: = 0= 0
ComputeCompute aa tt--statisticstatistic
|| tt--statisticstatistic || > 2 =>> 2 => rejectrejectHH00
=> => significantlysignificantlydifferentdifferent fromfrom zerozero ((whatwhatwewe expectedexpected!!)!!)
|| tt--statisticstatistic || < 2 =>< 2 => cannotcannot rejectrejectHH00=> => significantlysignificantlydifferentdifferent fromfrom zerozero ((nono impactimpact ofof
studyingstudying oneone moremoreyearyear onon mymywageswages !!)!!)
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11-- Coefficient =Coefficient = thethe impactimpact studiedstudied
22-- EitherEither thethe standardstandard deviationdeviation oror thethe tt--statisticstatistic ororthethe pp--value (value (criticalcritical probabilityprobability i.e.i.e. thethe type 1type 1errorerror))
33-- TT--test =>test => = 0 = 0 forfor eacheach coefficientcoefficient
44-- PP--valuevalue associatedassociated = Type 1= Type 1 errorerror..
WhateverWhatever thethe econometriceconometric resultsresults
&& thethe purposepurpose ofofthethe studystudy
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ComparingComparing thethe tt--statisticstatistic to 2 = a 5% typeto 2 = a 5% type--11 errorerror
A type IA type I errorerror == thetheprobabilityprobability toto rejectrejectH0H0 whilewhile ititss truetrue
=>i.e. 5% chances to=>i.e. 5% chances tobebewrongwrongwhenwhen rejectingrejectingHH00
A moreA more accurateaccuratewayway:: thethe pp--value =value = thethe exact type 1exact type 1 errorerror::
LessLess thanthan 1% chance to1% chance tobebewrongwrongwhenwhen rejectingrejectingHH00
((HH00
== thethe coefficientcoefficient isis notnot significantlysignificantlydifferentdifferent fromfrom zerozero ))
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CaseCase--StudyStudy:: FeldsteinFeldstein andand HoriokaHorioka (1980)(1980)
FromFrom thethe liberalisationliberalisation ofofthethe capitalcapital flightsflights=>=> howhowdiddid thethe capitalcapital reallyreallymovemove ??
FeldsteinFeldstein andand HoriokaHorioka (1980) :(1980) : correlationcorrelationbetweenbetweensavingssavings andand investmentsinvestments
TheThe impactimpact ofofeconomiceconomic policypolicydependsdepends onon thethe degreedegreeofofmobilitymobilityofofthethe capitalcapital
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Correlation between Savings and Investment
and the openness of the economy
1- Correlation between Savings and Investments close to 1:
Closed economyany increase in national savings induces an identical increase in investments=> low degree of capital mobility
2- Correlation between Savings and Investments close to 0:
Openned (integrated) economy:
National savings respond to investment opportunities on the world market/national investment is financed by savings from the rest of the world => highdegree of capital mobility
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EconometricEconometric modelmodel ((FeildsteinFeildstein andand HoriokaHorioka))
.
i i
ii i
I S
Y Y = + +
TestingTesting thethe correlationcorrelationbetweenbetween InvestmentsInvestments andand SavingsSavings
=>=>
TT--test ontest on thethe (i)(i) HH
00:: = 0 = 0
((iiii)) HH00
:: = 1 = 1
TheThe samplesample :: 19 countries19 countries ofofthethe OECDOECD
(a)(a) longlong--termterm effecteffect (1970(1970--1998)1998)(b)(b) shortshort--termterm ((threethree 1010yearyear periodsperiods))
19701970--1979; 19801979; 1980--1989; 19901989; 1990--19981998
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SavingSaving andand InvestmentInvestment: long: long periodperiod (1970(1970--98)98)
0.580.58RR-- SquaredSquared
1919ObservationsObservations
0.030.03((standardstandard--errorerror))
0.080.08ConstantConstant
0.130.13((standardstandard--errorerror))
0.620.62ssii
SavingSaving andand InvestmentInvestment::
19701970--1998199811-- IsIsbb significantlysignificantlydifferentdifferent fromfromzerozero?? HH
00:: = 0 = 0
tt--test (to comparetest (to compare meansmeans))
|| 4.854.85 || > 2> 2AtAt thethe 5%5% levellevelHH
00isis rejectedrejected
NoteNote thethe pp--value (value (computedcomputedbyby thethe
software)software) isis inferiorinferior to 1%to 1%
InIn thethe longlong--termtermwewe cannotcannotconcludeconclude to ato a perfectperfect degreedegree
ofofcapitalcapital mobilitymobility
0.62 04.85
0.13t
= = =
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SavingSaving andand InvestmentInvestment: long: long periodperiod (1970(1970--98)98)
0.580.58RR-- SquaredSquared
1919ObservationsObservations
0.030.03((standardstandard--errorerror))
0.080.08ConstantConstant
0.130.13((standardstandard--errorerror))
0.620.62ssii
SavingSaving andand InvestmentInvestment::
19701970--19981998 11-- IsIs significantlysignificantlydifferentdifferent fromfromoneone?? HH
00:: = 1 = 1
tt--test (to comparetest (to compare meansmeans))
|| 2.942.94 || > 2> 2AtAt thethe 5%5% levellevelHH
00isis rejectedrejected
NoteNote thethe pp--value (value (computedcomputedbyby thethe
software)software) isis inferiorinferior to 1%to 1%InIn thethe longlong--termtermwewe cannotcannot
concludeconclude toto closedclosed economieseconomies
0.62 12.94
0.13t
= = =
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SavingSaving andand InvestmentInvestment:: shortshort--termterm
ThreeThree
1010
yearyear
periodsperiods
19701970
--79; 198079; 1980
--89; 199089; 1990
--9898
0.400.650.820.82ssii
0.150.140.140.14((standardstandard--errorerror))
0.110.080.080.08ConstantConstant
0.030.030.030.03((standardstandard--errorerror))
0.300.550.610.61RR-- SquaredSquared
19191919ObservationsObservations
(3)
1990-1998
(2)
1980-1989
(1)
1970-1979
Periods
Saving and Investment
=>=>WhatWhat cancanyouyou saysayaboutabout opennessopenness ofofOECD countriesOECD countries
overover eacheach 1010yearyear periodsperiods??
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ExerciseExercise::
SavingSaving andand InvestmentInvestment:: shortshort--termtermThreeThree 1010yearyear periodsperiods 19701970--79; 198079; 1980--89; 199089; 1990--9898
WhatWhat cancanyouyou saysayaboutabout opennessopenness ofofOECD countriesOECD countries
forfor eacheach ofofthethe threethree periodsperiods??(for(for eacheach periodperiod:: perfectperfect capitalcapital mobilitymobility?? ClosedClosed economieseconomies?? EtcEtc))
WhatWhatwouldwouldyouyou saysayregardingregarding thethe evolutionevolution ofofthethe
capitalcapital mobilitymobilityoverover thethewholewhole periodperiod??
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ExerciseExercise::
SavingSaving andand InvestmentInvestment:: shortshort--termtermThreeThree 1010yearyear periodsperiods 19701970--79; 198079; 1980--89; 199089; 1990--9898
ResultsResults
::
Conclusion:Conclusion:
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ExerciseExercise::
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ExerciseExercise::
SavingSaving andand InvestmentInvestment:: shortshort--termtermThreeThree 1010yearyear periodsperiods 19701970--79; 198079; 1980--89; 199089; 1990--9898
ResultsResults::
PeriodPeriod 1 :1 : (i)(i) HH00 :: =0 => t = 5.93 => |t|>2 => rejection=0 => t = 5.93 => |t|>2 => rejection ofofHH00((iiii)) HH
00:: =1 => t ==1 => t = --1.32 => |t|1.32 => |t| nonnon--rejectionrejection ofofHH
00
Conclusion:Conclusion:-- NoneNone ofofthethe threethree periodsperiodswithwith aa perfectperfect capitalcapital mobilitymobility-- EvenEven aabehaviourbehaviour ofofclosedclosed economieseconomies overover thethe firstfirst periodperiod
=>=> A changeA change towardtowardopennessopenness overover thethe 22 lastlastperiodsperiods??
0.82=
0.65=
0.40=PeriodPeriod 3:3: (i)(i) HH00
:: =0 => t =2.67 => |t|>2 => rejection=0 => t =2.67 => |t|>2 => rejection ofofHH00
((iiii)) HH00
:: =1 => t ==1 => t = --4.04 => |t|>2 => rejection4.04 => |t|>2 => rejection ofofHH00
PeriodPeriod 2:2: (i)(i) HH00
:: =0 => t = 4.62 => |t|>2 => rejection=0 => t = 4.62 => |t|>2 => rejection ofofHH00
((iiii)) HH00
:: =1 => t ==1 => t = --2.46 => |t|>2 => rejection2.46 => |t|>2 => rejection ofofHH00
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=>=> A changeA change towardtowardopennessopenness overover thethe 22 lastlastperiodsperiods??
In other words
=> are the two coefficients significantly different?=> H0 : 8089 = 9098 ?
=> not exactly the same t-statistic as usualbecause the both terms are estimated (with error)
8089 9098
8089 9098
2 2
0.40 0.65* 1.2419 2
0.14 0.15t
= = = No significant decrease in over the two last periods, we cannotconclude to an increased liberalisation of the capital market for thissample of countries and these periods.
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ConclusionConclusion--WhatWhat havehavewewe learntlearnt??
- -
-
-
-
-
-
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ConclusionConclusion--WhatWhat havehavewewe learntlearnt??
11-- BasicBasic methodologymethodologyregardingregarding econometricseconometrics
-- EconomicEconomic problemproblem => data =>=> data => econometriceconometricvalidationvalidation
22-- CharacterizingCharacterizing aa statisticalstatistical serieserie-- CentralCentral parameterparameter, dispersion, dispersion charactercharacter
33-- TheThe mostmost commoncommon econometriceconometric estimatorestimator
-- OrdinaryOrdinaryLeastLeast Squares, conceptSquares, concept ofoferrorerror--termterm
44-- Reading/Reading/interpretinginterpreting econometriceconometric resultsresults
-- RR--squaredsquared, Marginal impact,, Marginal impact, elasticityelasticity,, semisemi--elasticityelasticity,,
confidenceconfidence intervalinterval, p, p--value,value,
55-- StatisticalStatistical testtest ofofthethe coefficientscoefficients
-- tt--test (test (studentstudent test):test): againstagainst a constant,a constant, againstagainst anotheranother estimateestimate
ExecutiveExecutive MBAMBA HEC Lausanne 2007/2008HEC Lausanne 2007/2008
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