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

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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

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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)

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11 November Econometrics

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

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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

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11 November 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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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.

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

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11 November Regression with Instrumental Variables

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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 |

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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

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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 =

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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 =

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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 |

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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 €.

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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

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

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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

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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.

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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)

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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

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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

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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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