1. 11 November 20071 Introduction Econometrics for Mathematics Bachelor Students Kees Jan van Garderen Programme Director BSc & MSc in Econometrics

2. 11 November 2007 2 Kees Jan van Garderen Programme 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 –2 nd year Econometrics 1 and 2 –M.Phil. Tinbergen Institute, Advanced Econometrics II

3. 11 November 2007 3 Department of Quantitative Economics Actuarial Science Operations Research Econometrics & Economic Theory (Mathematical Economics) UvA - Econometrics CeNDEF (Center for Nonlinear Dynamics in Economics and Finance)

4. 11 November 2007 4 Econometrics

5. 11 November 2007 5 Econometrics and Statistics Regression Models Linear & non-Linear Multivariate Analysis Cross-section Likelihood Theory Time Series ARIMA Non-Parametrics

6. 11 November 2007 6 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 VAR with Non-stationary data Cointegration CVAR

7. 11 November 2007 7 Three Examples 1.Modelling wages a.Instrumental Variable regression b.Heckman 2.Demand and Supply 3.Cointegration (modelling with non-stationary timeseries)

8. 11 November 2007 8 Modelling Wages I : returns to schooling Log(income) =   +   s chooling +   age +   tenure +…+  E-views Expected income determines length of schooling People with high academic ability earn more and will go to school longer (pay-offs for them are higher) Inappropriate to attribute to schooling only.

9. 11 November 2007 9 Regression with Instrumental Variables Model Estimator (OLS) Unbiased? Consistent? Gewone Kleinste Kwadraten (via regressie of lineaire algebra) Model Stochastics

10. 11 November 2007 10 Regression with Instrumental Variables

11. 11 November 2007 11 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 ------------------------------------------------------

12. 11 November 2007 12 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

13. 11 November 2007 13 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) = 95.83 Log likelihood = -509.1859 Prob > chi2 = 0.0000

14. 11 November 2007 14 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 ------------------------------------------------------------------------------

15. 11 November 2007 15 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 ------------------------------------------------------------------------------

16. 11 November 2007 16 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 €.

17. 11 November 2007 17 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 24681012 P 2 4 6 8 10 12 Q

18. 11 November 2007 18 Data : Price & Quantity Varying income Varying Cost only Instrumental Variable estimation 24681012 P 2 4 6 8 10 12 Q demand supply

19. 11 November 2007 19 Q =  - 0.9 P + 1.0 income +  1 ( demand ) Q = 3 + 1.5 P – 1.0 cost +  2 ( supply ) We can : Estimate 2 equations correctly from 1 set of data Lesson: Running regression can be very misleading Use economic theory and econometric techniques True relations Estimated relations

20. 11 November 2007 20 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.

21. 11 November 2007 21 Possibilities Minor Econometrics Deficiency Programme/Schakel programma B.Sc. in Econometrics and ORM or Actuarial Sciences M.Sc. in Econometrics (Financial Econometrics, Math Econ)

22. 11 November 2007 22 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

23. 11 November 2007 23 … 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

24. 11 November 2007 24 Tot spoedig ziens !? Kees Jan van Garderen Programme Director BSc & MSc Econometrics Faculty of Economics and Business University of Amsterdam Roetersstraat 11 1018 WB, Amsterdam Room E 3.25, Economics Building E-Building, central tower http://www.studeren.uva.nl/msc_econometrics http://studiegids.uva.nl/web/uva/sgs/en/p/241.html tel +31-20-525 4220 fax +31-20-525 4349 K.J.vanGarderen@uva.nl