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

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Presentation on theme: "11 November 20071 Introduction Econometrics for Mathematics Bachelor Students Kees Jan van Garderen Programme Director BSc & MSc in Econometrics."— Presentation transcript:

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

2 11 November 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 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 Econometrics

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

6 11 November 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 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 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 Regression with Instrumental Variables Model Estimator (OLS) Unbiased? Consistent? Gewone Kleinste Kwadraten (via regressie of lineaire algebra) Model Stochastics

10 11 November Regression with Instrumental Variables

11 11 November 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 | EXP | ASVABC | MALE | ETHBLACK | ETHHISP | _cons |

12 11 November 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 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 = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Iteration 4: log likelihood = Heckman selection model Number of obs = 540 (regression model with sample selection) Censored obs = 254 Uncensored obs = 286 Wald chi2(6) = Log likelihood = Prob > chi2 =

14 11 November Maximum Likelihood | Coef. Std. Err. z P>|z| [95% Conf. Interval] LGEARNCL | COLLYEAR | EXP | ASVABC | MALE | ETHBLACK | ETHHISP | _cons | select | ASVABC | MALE | ETHBLACK | ETHHISP | SM | SF | SIBLINGS | _cons | /athrho | /lnsigma | rho | sigma | lambda | LR test of indep. eqns. (rho = 0): chi2(1) = 7.63 Prob > chi2 =

15 11 November 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 | EXP | ASVABC | MALE | ETHBLACK | ETHHISP | _cons | reg LGEARNCL COLLYEAR EXP ASVABC MALE ETHBLACK ETHHISP LGEARNCL | Coef. Std. Err. t P>|t| [95% Conf. Interval] COLLYEAR | EXP | ASVABC | MALE | ETHBLACK | ETHHISP | _cons |

16 11 November Demand and Supply Q =  P income +   1 ( demand ) Q : Quantity (in kg), P : Price (in €) income in ‘000 €   ~ N( 0,  ). Q = P – 1.0 cost +  2 ( supply ) cost in ‘000 €.

17 11 November 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 P Q

18 11 November Data : Price & Quantity Varying income Varying Cost only Instrumental Variable estimation P Q demand supply

19 11 November Q =  P income +  1 ( demand ) Q = 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 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 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 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 … 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 Tot spoedig ziens !? Kees Jan van Garderen Programme Director BSc & MSc Econometrics Faculty of Economics and Business University of Amsterdam Roetersstraat WB, Amsterdam Room E 3.25, Economics Building E-Building, central tower tel fax


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