PanelDataNotes-14

PanelDataNotes-14 - Econometric Analysis of Panel Data...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business Econometric Analysis of Panel Data 14. Nonlinear Models And Nonlinear Optimization Agenda Nonlinear Models Estimation Theory for Nonlinear Models Estimators Properties M Estimation Nonlinear Least Squares Maximum Likelihood Estimation GMM Estimation Minimum Distance Estimation Minimum Chi-square Estimation Computation Nonlinear Optimization Nonlinear Least Squares Newton-like Algorithms; Gradient Methods (Background: JW, Chapters 12-14, Greene, Chapters 16-18) What is a Model? Unconditional characteristics of a population Conditional moments: E[g(y)|x]: median, mean, variance, quantile, correlations, probabilities Conditional probabilities and densities Conditional means and regressions Fully parametric and semiparametric specifications Parametric specification: Known up to parameter Parameter spaces Conditional means: E[ y | x ] = m ( x , ) What is a Nonlinear Model? Model: E[g(y)| x ] = m( x , ) Objective: Learn about from y , X Usually estimate Linear Model: Closed form; = h( y , X ) Nonlinear Model Not wrt m( x , ). E.g., y=exp( x + ) Wrt estimator: Implicitly defined. h( y , X, )=0, E.g., E[y|x]= exp( x ) What is an Estimator? Point and Interval Classical and Bayesian f(data| model) I( ) sampling variability = = E[ | data,prior f( )] expectation from posterior I( ) narrowest interval from posterior density containing the specified probability (mass) = = = Parameters Model parameters The parameter space Interior of the parameter space Estimators of parameters The true parameter(s) i i i i i i i i i exp( y / ) Example : f(y | ) , exp( ) Model parameters : Conditional Mean: E(y | ) exp( )- = = = = i i x x x x The Conditional Mean Function 2 y,x m(x, ) E[y | x] for some in . A property of the conditional mean: E (y m(x, )) is minimized by E[y | x] (Proof, pp. 343-344, JW) = - M Estimation Classical estimation method n i i=1 n 2 i i i i=1 1 arg min q( , ) n Example : Nonlinear Least squares 1 arg min [y -E(y | , )] n = = data x An Analogy Principle for M Estimation n i i 1 n P i i 1 1 The estimator minimizes q= q(data , ) n The true parameter minimizes q* = E[q(data, )] The weak law of large numbers: 1 q= q(data , ) q* = E[q(data, )] n = = Estimation n P i i 1 P P 1 q= q(data , ) q*=E[q(data, )] n Estimator minimizes q True parameter minimizes q*...
View Full Document

This note was uploaded on 01/05/2012 for the course B 55.9912 taught by Professor Willamgreene during the Fall '11 term at NYU.

Page1 / 84

PanelDataNotes-14 - Econometric Analysis of Panel Data...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online