Introduction Econometrics for Mathematics Bachelor Students

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Introduction Econometrics forMathematics
Bachelor Students

• Kees Jan van Garderen
• Programme Director BSc MSc in Econometrics

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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
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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 ltgt Reduced Form
• moment conditions
• Multivariate Time-series Analysis VAR with
  Non-stationary data Cointegration CVAR

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Three Examples

• Modelling wages
• Instrumental Variable regression
• Heckman
• Demand and Supply
• Cointegration (modelling with non-stationary
  timeseries)

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Modelling Wages I returns to schooling

• Log(income) b1 b2 schooling b3 age b4
  tenure e
• 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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Regression with Instrumental Variables
Model Estimator (OLS) Unbiased? Consistent?
Model Stochastics
Gewone Kleinste Kwadraten (via regressie of
lineaire algebra)
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Regression with Instrumental Variables
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Modelling Wages II sex discrimination

• Log(income) b1 b2 Male b3 age . e1
• . reg LGEARNCL COLLYEAR EXP ASVABC MALE ETHBLACK
  ETHHISP
• --------------------------------------------------
  ----
• LGEARNCL Coef. Std. Err. t
  Pgtt
• -------------------------------------------------
  ----
• 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) b1 b2 Male b3 age . e1
• Working 1 Z gt 0 0 Z ? 0
• Z f( predicted earnings, children, married,
  ) e2 If e1 and e2 correlated, then E e1
  working ? 0

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Maximum Likelihood

• . g COLLYEAR 0
• . replace COLLYEAR S-12 if Sgt12
• (286 real changes made)
• . g LGEARNCL LGEARN if COLLYEARgt0
• (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

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Maximum Likelihood

• --------------------------------------------------
  ----------------------------
• Coef. Std. Err. z
  Pgtz 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

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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
  Pgtz 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
• --------------------------------------------------
  ----------------------------

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Demand and Supply

• Q 5 - 0.9 P 1.0 income e 1
  ( demand )
•  
• Q Quantity (in kg),
• P Price (in )
• income in 000
• e N( 0, S ).

Q 3 1.5 P 1.0 cost e 2
( supply )   cost in 000 .
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Demand and Supply(unconventionally P(rices) on
horizontal axis)
Shift in supply
supply
demand
demand
Increase income
supply
demand
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Data Price Quantity
Varying income
Q
12
supply
10
8
6
4
2
demand
P
2
4
6
8
10
12
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True relations

• Q 5 - 0.9 P 1.0 income e1
  ( demand )

Q 3 1.5 P 1.0 cost e2
( 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

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Cointegration Money demand

• m-p g g2 y g3 Dp g4 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
  (1990100)
• P RPI Retail price index all items (1985100)
• 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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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 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)

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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 [phone]
• fax [phone]
• K.J.vanGarderen_at_uva.nl