Introduction Econometrics for Mathematics Bachelor Students Kees Jan

Introduction Econometrics for Mathematics Bachelor Students Kees Jan van Garderen Programme Director BSc & MSc in Econometrics 11 November 2007 1

Kees Jan van Garderen Programme Director BSc & MSc in Econometrics BSc& MSc in Econometrics Uv. A, MSc title: Fractionele Matrix Calculus Ph. D, 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 11 November 2007 2

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

Econometrics 11 November 2007 4

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

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 11 November 2007 6

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

Modelling Wages I : returns to schooling Log(income) = b 1 + b 2 schooling + b 3 age + b 4 tenure +…+ e 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. E-views 11 November 2007 8

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

Regression with Instrumental Variables 11 November 2007 10

Modelling Wages II : sex discrimination Log(income) = b 1 + b 2 Male + b 3 age + …. + e 1. 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 ---------------------------11 November 2007 11

Modelling Wages II Log(income) = b 1 + b 2 Male + b 3 age + …. + e 1 Working = 1 : Z* > 0 = 0 : Z* 0 Z* = f( predicted earnings, children, married, ) + e 2 If e 1 and e 2 correlated, then E[ e 1 | working ] 0 11 November 2007 12

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 Iteration 0: 1: 2: 3: 4: log log log likelihood likelihood = = = -510. 46251 -509. 65904 -509. 19041 -509. 18587 Heckman selection model (regression model with sample selection) Log likelihood = -509. 1859 11 November 2007 Number of obs Censored obs Uncensored obs Wald chi 2(6) Prob > chi 2 = = = 540 254 286 95. 83 0. 0000 13

Maximum Likelihood 1. ---------------------------------------2. | Coef. Std. Err. z P>|z| [95% Conf. Interval] 3. -------+--------------------------------4. LGEARNCL | 5. COLLYEAR |. 126778. 0196862 6. 44 0. 000. 0881937. 1653623 6. EXP |. 0390787. 008101 4. 82 0. 000. 023201. 0549565 7. ASVABC | -. 0136364. 0069683 -1. 96 0. 050 -. 027294. 0000211 8. MALE |. 4363839. 0738408 5. 91 0. 000. 2916586. 5811092 9. ETHBLACK | -. 1948981. 1436681 -1. 36 0. 175 -. 4764825. 0866862 10. ETHHISP | -. 2089203. 159384 -1. 31 0. 190 -. 5213072. 1034667 11. _cons | 2. 7604. 4290092 6. 43 0. 000 1. 919557 3. 601242 12. -------+--------------------------------13. select | 14. ASVABC |. 070927. 008141 8. 71 0. 000. 054971. 086883 15. MALE | -. 3814199. 1228135 -3. 11 0. 002 -. 6221298 -. 1407099 16. ETHBLACK |. 433228. 2184279 1. 98 0. 047. 0051172. 8613388 17. ETHHISP | 1. 198633. 299503 4. 00 0. 000. 6116179 1. 785648 18. SM |. 0342841. 0302181 1. 13 0. 257 -. 0249424. 0935106 19. SF |. 0816985. 021064 3. 88 0. 000. 0404138. 1229832 20. SIBLINGS | -. 0376608. 0296495 -1. 27 0. 204 -. 0957729. 0204512 21. _cons | -4. 716724. 5139176 -9. 18 0. 000 -5. 723984 -3. 709464 22. -------+--------------------------------23. /athrho | -. 9519231. 2430548 -3. 92 0. 000 -1. 428302 -. 4755444 24. /lnsigma | -. 4828234. 0727331 -6. 64 0. 000 -. 6253776 -. 3402692 25. -------+--------------------------------26. rho | -. 7406524. 1097232 -. 8913181 -. 4426682 27. sigma |. 6170388. 0448791. 5350593. 7115788 28. lambda | -. 4570113. 0967091 -. 6465576 -. 267465 29. ---------------------------------------30. LR test of indep. eqns. (rho = 0): chi 2(1) = 7. 63 Prob > chi 2 = 0. 0058 31. ---------------------------------------11 November 2007 14

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

Demand Supply Q = 5 - 0. 9 P + 1. 0 income Q = 3 + 1. 5 P +e 1 – 1. 0 cost + e ( demand ) 2 ( supply ) Q : Quantity (in kg), P : Price (in €) income in ‘ 000 € cost in ‘ 000 €. e ~ N( 0, S ). 11 November 2007 16

Demand Supply Shift in supply (unconventionally P(rices) on horizontal axis) supply Increase cost demand Increase income supply In coscreas at r t & e and inc om demand Q 12 solutions 10 8 6 4 demand 11 November 2007 2 2 4 6 8 10 P 1217

Data : Price & Quantity Varying Cost only Varying income In Va strum est riab ent im le al atio n Q 12 supply 10 8 6 4 2 2 11 November 2007 4 6 8 10 demand P 12 18

True relations e 1 – 1. 0 cost + e 2 Q = 5 - 0. 9 P + 1. 0 income Q = 3 + 1. 5 P + ( demand ) ( supply ) Estimated relations We can : • Estimate 2 equations correctly from 1 set of data Lesson: • Running regression can be very misleading • Use economic theory and econometric techniques 11 November 2007 19

Cointegration : Money demand m-p = g + g 2 y +g 3 Dp + g 4 R m -p y p R : real money balances in logs, : real transactions (i. e. GDP) in logs, : log price index, : interest rate GDP 90 : GDP(A) at current market prices index (1990=100) P : RPI: Retail price index all items (1985=100) M 4 : Money stock M 4 (end period) : level, Seasonally Adjusted R : Treasury Bills 3 month yield Q 1, . . . , Q 4: Quarter 1 to quarter 4 dummy. 11 November 2007 20

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

M. Sc. Econometrics /Mathematical Economics Blok I (15 EC) Adv Econometrics 1 General Equilibrium Th. Elective Blok III (15 EC) Field course (Fin. Ectr) Field course (Micr. Ectr) Field course (caput ME 2) Blok II (15 EC) Adv. Econometrics 2 Game Theory Elective Blok IV Master Thesis 11 November 2007 22

Deficiëntieprogramma Econometrie (35 ec) studenten met WO bachelor- of master Wiskunde of Natuurkunde of equivalente exacte opleiding … alvorens toegelaten te kunnen worden tot de MSc in Econometrics, de volgende deficiënties weggewerkt te hebben: steunvakken KRe. S 3 (5 ec) en KRe. S 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) 11 November 2007 23

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. van. Garderen@uva. nl 11 November 2007 24