11 November 2007 1

Introduction Econometrics for

Mathematics Bachelor Students

Kees Jan van GarderenProgramme Director BSc & MSc in Econometrics

11 November 2007 2

Kees Jan van GarderenProgramme Director BSc & MSc in Econometrics BSc& MSc in Econometrics UvA, MSc title:

Fractionele Matrix Calculus PhD, Trinity College, Cambridge, title:

Inference in Curved Exponential Models uses non-Riemannian geometry in econometric/statistical models Research Interest : Econometrics

– Econometric Theory - Exact Distribution Theory – Approximations (Tilted or Saddlepoint, Edgeworth )– Inference and Curvature in Econometric Models– Income Inequality– Aggregation

Teaching– 2nd year Econometrics 1 and 2– M.Phil. Tinbergen Institute, Advanced Econometrics II

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Department of Quantitative Economics

Actuarial Science

Operations Research

Econometrics & Economic Theory (Mathematical Economics)

• UvA - Econometrics• CeNDEF (Center for Nonlinear Dynamics in Economics and Finance)

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Econometrics

T he ore tica l M o de lsG en era l E qu i lib riumP rod u ce r /C o nsum erD yna m ica l S ys te m s

M a th e m a tica lE con o m ics

U s in g D a taE s tim ationIn fe ren ce

E con om etr ics

O ptim iza tionD e te rm in is tic

S to cha s ticD iscre te

O p era tio n s R esea rch a nd M a na ge m e nt

A p p lica tion o f M a the m a tica l a n d S ta tist ica l T e ch n iq u es toE con om ic P ro b le m s

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Econometrics and Statistics

Regression Models

Linear & non-Linear

Multivariate Analysis

Cross-section

Likelihood Theory

Time Series

ARIMA

Non-Parametrics

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Econometrics and Statistics

Non Experimental (i.i.d) Data

sample selection (self-selection)

endogeneity, instrumental variables

Misspecified Models : diagnostics/ model choice

Structural Modelling

causal relationships : economic theory and insight

Identification : Structural <==> Reduced Form

moment conditions

Multivariate Time-series Analysis VARwith Non-stationary data Cointegration CVAR

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Three Examples

1. Modelling wages

a. Instrumental Variable regression

b. Heckman

2. Demand and Supply

3. Cointegration (modelling with non-stationary timeseries)

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Modelling Wages I : returns to schooling

Log(income) = + schooling + age + tenure +…+

E-views

Expected income determines length of schoolingPeople with high academic ability earn more and will go to school longer (pay-offs for them are higher)Inappropriate to attribute to schooling only.

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Regression with Instrumental Variables

y X

b XX 1Xy

XX 1XX

b ( XXn ) 1 X

n

E |X ? 0 E b | X?

Model

Estimator (OLS)

Unbiased? Consistent?

Gewone Kleinste Kwadraten

(via regressie of lineaire algebra)

ModelStochastics

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Regression with Instrumental Variables

1

' ' '

' 'IV

y X

Z y Z X Z

Z X Z y

plim 1n Z

0

plim 1n Z

X QZX

Z uncorrelated with

Z and X are correlated

Valid

Relevant

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Modelling Wages II : sex discrimination

Log(income) = + Male + age + …. +

. reg LGEARNCL COLLYEAR EXP ASVABC MALE ETHBLACK ETHHISP

------------------------------------------------------ LGEARNCL | Coef. Std. Err. t P>|t|-------------+---------------------------------------- COLLYEAR | .1380715 .0201347 6.86 0.000 EXP | .039627 .0085445 4.64 0.000 ASVABC | .0063027 .0052975 1.19 0.235 MALE | .3497084 .0673316 5.19 0.000 ETHBLACK | -.0683754 .1354179 -0.50 0.614 ETHHISP | -.0410075 .1441328 -0.28 0.776 _cons | 1.369946 .2884302 4.75 0.000------------------------------------------------------

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Modelling Wages II

Log(income) = + Male + age + …. +

Working = 1 : Z* > 0

= 0 : Z* 0

Z* = f( predicted earnings, children, married, ) +

If and correlated, then E[ | working ] 0

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Maximum Likelihood

. g COLLYEAR = 0

. replace COLLYEAR = S-12 if S>12(286 real changes made)

. g LGEARNCL = LGEARN if COLLYEAR>0(254 missing values generated)

. heckman LGEARNCL COLLYEAR EXP ASVABC MALE ETHBLACK ETHHISP, select(ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS)

Iteration 0: log likelihood = -510.46251 Iteration 1: log likelihood = -509.65904 Iteration 2: log likelihood = -509.19041 Iteration 3: log likelihood = -509.18587 Iteration 4: log likelihood = -509.18587

Heckman selection model Number of obs = 540(regression model with sample selection) Censored obs = 254 Uncensored obs = 286 Wald chi2(6) = 95.83Log likelihood = -509.1859 Prob > chi2 = 0.0000

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Maximum Likelihood

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------LGEARNCL | COLLYEAR | .126778 .0196862 6.44 0.000 .0881937 .1653623 EXP | .0390787 .008101 4.82 0.000 .023201 .0549565 ASVABC | -.0136364 .0069683 -1.96 0.050 -.027294 .0000211 MALE | .4363839 .0738408 5.91 0.000 .2916586 .5811092 ETHBLACK | -.1948981 .1436681 -1.36 0.175 -.4764825 .0866862 ETHHISP | -.2089203 .159384 -1.31 0.190 -.5213072 .1034667 _cons | 2.7604 .4290092 6.43 0.000 1.919557 3.601242-------------+----------------------------------------------------------------select | ASVABC | .070927 .008141 8.71 0.000 .054971 .086883 MALE | -.3814199 .1228135 -3.11 0.002 -.6221298 -.1407099 ETHBLACK | .433228 .2184279 1.98 0.047 .0051172 .8613388 ETHHISP | 1.198633 .299503 4.00 0.000 .6116179 1.785648 SM | .0342841 .0302181 1.13 0.257 -.0249424 .0935106 SF | .0816985 .021064 3.88 0.000 .0404138 .1229832 SIBLINGS | -.0376608 .0296495 -1.27 0.204 -.0957729 .0204512 _cons | -4.716724 .5139176 -9.18 0.000 -5.723984 -3.709464-------------+---------------------------------------------------------------- /athrho | -.9519231 .2430548 -3.92 0.000 -1.428302 -.4755444 /lnsigma | -.4828234 .0727331 -6.64 0.000 -.6253776 -.3402692-------------+---------------------------------------------------------------- rho | -.7406524 .1097232 -.8913181 -.4426682 sigma | .6170388 .0448791 .5350593 .7115788 lambda | -.4570113 .0967091 -.6465576 -.267465------------------------------------------------------------------------------LR test of indep. eqns. (rho = 0): chi2(1) = 7.63 Prob > chi2 = 0.0058------------------------------------------------------------------------------

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Maximum Likelihood versus Linear regression

. heckman LGEARNCL COLLYEAR EXP ASVABC MALE ETHBLACK ETHHISP, select(ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS)

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------LGEARNCL | COLLYEAR | .126778 .0196862 6.44 0.000 .0881937 .1653623 EXP | .0390787 .008101 4.82 0.000 .023201 .0549565 ASVABC | -.0136364 .0069683 -1.96 0.050 -.027294 .0000211 MALE | .4363839 .0738408 5.91 0.000 .2916586 .5811092 ETHBLACK | -.1948981 .1436681 -1.36 0.175 -.4764825 .0866862 ETHHISP | -.2089203 .159384 -1.31 0.190 -.5213072 .1034667 _cons | 2.7604 .4290092 6.43 0.000 1.919557 3.601242-------------+----------------------------------------------------------------

. reg LGEARNCL COLLYEAR EXP ASVABC MALE ETHBLACK ETHHISP

------------------------------------------------------------------------------ LGEARNCL | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- COLLYEAR | .1380715 .0201347 6.86 0.000 .0984362 .1777068 EXP | .039627 .0085445 4.64 0.000 .022807 .0564469 ASVABC | .0063027 .0052975 1.19 0.235 -.0041254 .0167309 MALE | .3497084 .0673316 5.19 0.000 .217166 .4822509 ETHBLACK | -.0683754 .1354179 -0.50 0.614 -.334946 .1981952 ETHHISP | -.0410075 .1441328 -0.28 0.776 -.3247333 .2427183 _cons | 1.369946 .2884302 4.75 0.000 .8021698 1.937721------------------------------------------------------------------------------

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Demand and Supply

Q = - 0.9 P + 1.0 income + 1 ( demand )

 

Q : Quantity (in kg),

P : Price (in €)

income in ‘000 €

~ N( 0, ).

Q = 3 + 1.5 P – 1.0 cost + 2 ( supply )

 

cost in ‘000 €.

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2 4 6 8 10 12P

2

4

6

8

10

12Q

2 4 6 8 10 12P

2

4

6

8

10

12Q

2 4 6 8 10 12P

2

4

6

8

10

12Q

Demand and Supply(unconventionally P(rices) on horizontal axis)

demand

supply

Increase cost

Increase income

Increase cost & inc

at random

demand

Shift in supply

demand

supply solutions

2 4 6 8 10 12P

2

4

6

8

10

12Q

11 November 2007 182 4 6 8 10 12P

2.55

7.510

12.515

Q

Data : Price & Quantity

2 4 6 8 10 12P

2

4

6

8

10

12

Q

Varying income

Varying Cost only

2 4 6 8 10 12P

2

4

6

8

10

Q

Instrumental

Variable estimation

2 4 6 8 10 12P

2

4

6

8

10

12Q

demand

supply

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Q = - 0.9 P + 1.0 income + 1 ( demand )

Q = 3 + 1.5 P – 1.0 cost + 2 ( supply )

Demand Equation Dependent Variable: Q Method: Two-Stage Least Squares Using cost as instrument to move the supply equation Sample: 1 100 Included observations: 100 Instrument list: COST INCOME

Variable Coefficient Std. Error t-Statistic Prob. C 0.122396 0.043038 2.843922 0.0054

P -0.864002 0.021714 -39.78930 0.0000 INCOME 0.959883 0.012300 78.03892 0.0000

R-squared 0.986776 Mean dependent var 2.402183 Adjusted R-squared 0.986503 S.D. dependent var 1.377962 S.E. of regression 0.160086 Sum squared resid 2.485870 Durbin-Watson stat 1.695308 Second-stage SSR 1.856418

Supply Equation

Dependent Variable: Q Method: Two-Stage Least Squares Using income as instrument to move demand equation Sample: 1 100 Included observations: 100 Instrument list: COST INCOME

Variable Coefficient Std. Error t-Statistic Prob. C -0.005513 0.043690 -0.126174 0.8999

P 1.474120 0.018785 78.47458 0.0000 COST -0.957523 0.012311 -77.78015 0.0000

R-squared 0.986688 Mean dependent var 2.402183 Adjusted R-squared 0.986413 S.D. dependent var 1.377962 S.E. of regression 0.160619 Sum squared resid 2.502439 Durbin-Watson stat 1.837763 Second-stage SSR 1.856418

We can :• Estimate 2 equations correctly from 1 set of dataLesson:• Running regression can be very misleading• Use economic theory and econometric techniques

True relations

Estimated relations

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Cointegration : Money demand

m-p = + 2 y +3 p + 4 R m -p : real money balances in logs, y : real transactions (i.e.GDP) in logs, p : log price index,R : interest rate GDP90 : GDP(A) at current market prices index (1990=100) P : RPI: Retail price index all items (1985=100)M4 : Money stock M4 (end period) : level, Seasonally Adjusted R : Treasury Bills 3 month yield Q1,...,Q4: Quarter 1 to quarter 4 dummy.

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Possibilities

Minor Econometrics

Deficiency Programme/Schakel programma

B.Sc. in Econometrics and ORM or Actuarial Sciences

M.Sc. in Econometrics (Financial Econometrics, Math Econ)

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M.Sc. Econometrics /Mathematical Economics

Blok I (15 EC)

Adv Econometrics 1

General Equilibrium Th.

Elective

Blok II (15 EC)

Adv. Econometrics 2

Game Theory

Elective

Blok III (15 EC)

Field course (Fin. Ectr)

Field course (Micr. Ectr)

Field course (caput ME2)

Blok IV

Master Thesis

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… alvorens toegelaten te kunnen worden tot de MSc in Econometrics, de volgende deficiënties weggewerkt te hebben:

steunvakken KReS 3 (5 ec) en KReS 4 (5 ec)

verbredingsvak Econometrie 3 (5 ec)

verbredingsvak Tijdreeksanalyse (5 ec)

verbredingsvak Wiskundige Economie B (5 ec)

Wiskundige Economie A (5 ec) en Inleiding Speltheorie (5 ec)

Deficiëntieprogramma Econometrie (35 ec) studenten met WO bachelor- of master Wiskunde

of Natuurkunde of equivalente exacte opleiding

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Tot spoedig ziens !?Kees Jan van GarderenProgramme Director BSc & MSc EconometricsFaculty of Economics and BusinessUniversity of AmsterdamRoetersstraat 111018 WB, Amsterdam

Room E 3.25, Economics BuildingE-Building, central tower

http://www.studeren.uva.nl/msc_econometricshttp://studiegids.uva.nl/web/uva/sgs/en/p/241.html

tel +31-20-525 4220fax +31-20-525 4349

K.J.vanGarderen@uva.nl