Part 1: Introduction -1/22 Econometrics I Professor William Greene Stern School of Business Department of Economics
Dec 24, 2015
Part 1: Introduction1-1/22
Econometrics IProfessor William GreeneStern School of Business
Department of Economics
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Econometrics I
Part 1 - Paradigm
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Econometrics: Paradigm Theoretical foundations
Microeconometrics and macroeconometrics
Behavioral modeling: Optimization, labor supply, demand equations, etc.
Statistical foundations Mathematical Elements ‘Model’ building – the econometric
model Mathematical elements The underlying truth – is there one?
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Why Use This Framework? Understanding covariation Understanding the relationship:
Estimation of quantities of interest such as elasticities
Prediction of the outcome of interest The search for “causal” effects Controlling future outcomes using
knowledge of relationships
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Model Building in Econometrics
Role of the assumptions Parameterizing the model
Nonparametric analysis Semiparametric analysis Parametric analysis
Sharpness of inferences
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Application: Is there a relationship between investment and capital stock? (10 firms, 20 years)
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Nonparametric Regression
What are the assumptions? What are the conclusions?
Ni=1 i i
Ni=1 i
ii
0.2
Kernel Regression
w (z)yF(z)=
w (z)
x -z1w (z) K
.9 / N
K(t) (t)[1 (t)]
exp(t)(t)
1 exp(t)
s
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Semiparametric Regression Investmenti,t = a + b*Capitali,t + ui,t
Median[ui,t | Capitali,t] = 0
N
a,b i ii 1
Least Absolute Deviations
ˆˆ ˆ F(x)=a+bx
ˆa,b=ArgMin |y a-bx |
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Fully Parametric Regression
Investmenti,t = a + b*Capitali,t + ui,t
ui,t | Capitalj,s ~ N[0,2] for all i,j,s,t
Ii,t|Ci,t ~ N[a+bCit,2]
N 2a,b i ii 1
1
N N
i=1 i=1i i i
Least Squares Regression
ˆˆ ˆ F(x)=a+bx
ˆˆ a,b=ArgMin (y a bx )
1 1 1= y
x x x i
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Estimation Platforms
The “best use” of a body of data Sample data Nonsample information
The accretion of knowledge Model based
Kernels and smoothing methods (nonparametric) Moments and quantiles (semiparametric) Likelihood and M- estimators (parametric)
Methodology based (?) Classical – parametric and semiparametric Bayesian – strongly parametric
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Classical Inference
Population
Measurement
Econometrics Characteristics
Behavior PatternsChoices
Imprecise inference about the entire population – sampling theory and asymptotics
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Bayesian Inference
Population
Measurement
Econometrics Characteristics
Behavior PatternsChoices
Sharp, ‘exact’ inference about only the sample – the ‘posterior’ density.
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Data Structures
Observation mechanisms Passive, nonexperimental Active, experimental The ‘natural experiment’
Data types Cross section Pure time series Panel –
Longitudinal data – NLS Country macro data – Penn W.T.
Financial data
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Estimation Methods and Applications
Least squares etc. – OLS, GLS, LAD, quantile Maximum likelihood
Formal ML Maximum simulated likelihood Robust and M- estimation
Instrumental variables and GMM Bayesian estimation – Markov Chain Monte Carlo methods
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Trends in Econometrics
Small structural models vs. large scale multiple equation models
Non- and semiparametric methods vs. parametric Robust methods – GMM (paradigm shift) Unit roots, cointegration and macroeconometrics Nonlinear modeling and the role of software Behavioral and structural modeling vs. “reduced
form,” “covariance analysis” Pervasiveness of an econometrics paradigm Identification and “Causal” effects
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Course Objective
Develop the tools needed to read about with understanding and to do empirical research using the current body of techniques.
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Prerequisites
A previous course that used regression Mathematical statistics Matrix algebra
We will do some proofs and derivations We will also examine empirical applications
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Readings
Main text: Greene, W., Econometric Analysis, 7th Edition, Prentice Hall, 2012.
A few articles Notes and materials on the course website:
http://people.stern.nyu.edu/wgreene/Econometrics/Econometrics.htm
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http://people.stern.nyu.edu/wgreene/Econometrics/Econometrics.htm
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The Course Outline
No class on: Thursday, September 25
Midterm: October 21
Final: Take home due December 19
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Course Applications
Software NLOGIT provided, supported SAS, Stata, EViews optional, your choice R, Matlab, Gauss, others Questions and review as requested
Problem Sets: (more details later)
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Course Requirements
Problem sets: 5 (25%) Midterm, in class (30%) Final exam, take home (45%) Enthusiasm