Part 1: Introduction 1-1/22 Econometrics I Professor William Greene Stern School of Business...

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