6 Basic Econometrics

8/11/2019 6 Basic Econometrics

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Executive MBA 2007-

2008emba bridge- 2006/2007 1

Basic EconometricsBasic Econometrics

ChristopherChristopher GrigoriouGrigoriou

ExecutiveExecutive MBAMBA--HEC LausanneHEC Lausanne

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

ExecutiveExecutive MBAMBA HEC Lausanne 2007/2008HEC Lausanne 2007/2008


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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




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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


=> 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


0.620.62ssii

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



0.080.08ConstantConstant


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


(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::


ResultsResults

::

Conclusion:Conclusion:


ExerciseExercise::


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ExerciseExercise::


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


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6 Basic Econometrics