Measurement Error in Linear Multiple Regression Models Ulf H Olsson Professor Dep. Of Economics.

Slides:

Advertisements

Similar presentations

PANEL DATA 1. Dummy Variable Regression 2. LSDV Estimator

Advertisements

Økonometri The regression model OLS Regression Ulf H. Olsson Professor of Statistics.

Christopher Dougherty EC220 - Introduction to econometrics (chapter 11) Slideshow: model c assumptions Original citation: Dougherty, C. (2012) EC220 -

Economics 20 - Prof. Anderson1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u 7. Specification and Data Problems.

MEASUREMENT ERROR 1 In this sequence we will investigate the consequences of measurement errors in the variables in a regression model. To keep the analysis.

1 ASSUMPTIONS FOR MODEL C: REGRESSIONS WITH TIME SERIES DATA Assumptions C.1, C.3, C.4, C.5, and C.8, and the consequences of their violations are the.

Factor Analysis Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics Regression examples Ulf H. Olsson Professor of Statistics.

CHAPTER 3 ECONOMETRICS x x x x x Chapter 2: Estimating the parameters of a linear regression model. Y i = b 1 + b 2 X i + e i Using OLS Chapter 3: Testing.

GRA 6020 Multivariate Statistics The regression model OLS Regression Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics.

Linear Regression with One Regression

Econ Prof. Buckles1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u 1. Estimation.

Økonometri The regression model OLS Regression Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics Ulf H. Olsson Professor of Statistics.

FIN357 Li1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u 1. Estimation.

Multiple Regression Analysis

The LISREL MODEL and Ordinal Variables Ulf H. Olsson Professor of Statistics.

FIN357 Li1 The Simple Regression Model y =  0 +  1 x + u.

Multiple Regression Analysis

FIN357 Li1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u 1. Estimation.

GRA 6020 Multivariate Statistics The regression model OLS Regression Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics The Structural Equation Model Ulf H. Olsson Professor of Statistics.

Economics 310 Lecture 18 Simultaneous Equations There is a two-way, or simultaneous, relationship between Y and (some of) the X’s, which makes the distinction.

Met 2651 Instrument variabler (sider: 539,543, 544,545,549,550,551,559,560,561,564) Ulf H. Olsson Professor of Statistics.

1 Prof. Dr. Rainer Stachuletz Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u 3. Asymptotic Properties.

GRA 6020 Multivariate Statistics Ulf H. Olsson Professor of Statistics.

Met Multivartate Statistics Ho-Testing OLS-regression LISREL IS GREEK TO ME The SEM model LISREL SOFTWARE Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics Regression examples Ulf H. Olsson Professor of Statistics.

1.The independent variables do not form a linearly dependent set--i.e. the explanatory variables are not perfectly correlated. 2.Homoscedasticity --the.

GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics.

Empirical Estimation Review EconS 451: Lecture # 8 Describe in general terms what we are attempting to solve with empirical estimation. Understand why.

Regression, Factor Analysis and SEM Ulf H. Olsson Professor of Statistics.

Measurement Models and Correlated Errors and Correlated disturbance Terms Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics The regression model Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics The regression model OLS Regression Ulf H. Olsson Professor of Statistics.

Multivariate Regression Analysis Estimation. Why Multiple Regression? Suppose you want to estimate the effect of x1 on y, but you know the following:

Christopher Dougherty EC220 - Introduction to econometrics (chapter 8) Slideshow: measurement error Original citation: Dougherty, C. (2012) EC220 - Introduction.

CONSEQUENCES OF AUTOCORRELATION

Error Component Models Methods of Economic Investigation Lecture 8 1.

Managerial Economics Demand Estimation. Scatter Diagram Regression Analysis.

MTH 161: Introduction To Statistics

1 Multiple Regression Analysis y =  0 +  1 x 1 +  2 x  k x k + u.

M.Sc. in Economics Econometrics Module I Topic 7: Censored Regression Model Carol Newman.

Copyright © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin The Two-Variable Model: Hypothesis Testing chapter seven.

General ideas to communicate Dynamic model Noise Propagation of uncertainty Covariance matrices Correlations and dependencs.

Chapter 4 The Classical Model Copyright © 2011 Pearson Addison-Wesley. All rights reserved. Slides by Niels-Hugo Blunch Washington and Lee University.

Chapter 22: Building Multiple Regression Models Generalization of univariate linear regression models. One unit of data with a value of dependent variable.

5. Consistency We cannot always achieve unbiasedness of estimators. -For example, σhat is not an unbiased estimator of σ -It is only consistent -Where.

1. The independent variables do not form a linearly dependent set--i.e. the explanatory variables are not perfectly correlated. 2. Homoscedasticity--the.

Multiple Regression Analysis Regression analysis with two or more independent variables. Leads to an improvement.

1 STOCHASTIC REGRESSORS Until now we have assumed that the explanatory variables in a regression model are nonstochastic, that is, that they do not have.

AUTOCORRELATION 1 Assumption B.5 states that the values of the disturbance term in the observations in the sample are generated independently of each other.

Psychology 202a Advanced Psychological Statistics November 3, 2015.

Mediation: Assumptions David A. Kenny davidakenny.net.

8- Multiple Regression Analysis: The Problem of Inference The Normality Assumption Once Again Example 8.1: U.S. Personal Consumption and Personal Disposal.

Chapter 4. The Normality Assumption: CLassical Normal Linear Regression Model (CNLRM)

Regression Overview. Definition The simple linear regression model is given by the linear equation where is the y-intercept for the population data, is.

Ch3: Model Building through Regression

REGRESSION DIAGNOSTIC I: MULTICOLLINEARITY

Regression Assumptions of OLS.

The regression model in matrix form

Some issues in multivariate regression

Simultaneous equation models Prepared by Nir Kamal Dahal(Statistics)

MULTIVARIATE REGRESSION MODELS

Simple Linear Regression

Linear Panel Data Models

Linear Regression Summer School IFPRI

Econometric Analysis of Panel Data

Cases. Simple Regression Linear Multiple Regression.

Presentation transcript:

Measurement Error in Linear Multiple Regression Models Ulf H Olsson Professor Dep. Of Economics

Ulf H. Olsson The stadard linear multiple regression Model

Ulf H. Olsson Measurement Error/Errors-in-variables

Ulf H. Olsson The consequences of neglecting the measurent error

Ulf H. Olsson The consequences of neglecting the measurent error The probability limits of the two estimators when there is measurement error present: The disturbance term shares a stochastic term (V) with the regressor matrix => u is correlated with X and hence E(u|X)  0

Ulf H. Olsson The consequences of neglecting the measurent error Lack of orthogonality – crucial assumption underlying the use of OLS is violated !

Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b

Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b

Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b Bias towards zero (attenuation) for g=1 In multiple regression context things are less clear cut. Not all estimates are necessarilly biased towards zero, but there is an overall attenuation effect.

Ulf H. Olsson The consequences of neglecting the measurent error In the limit we find:

Ulf H. Olsson The consequences of neglecting the measurent error The estimator is biased upward

Ulf H. Olsson The consequences of neglecting the measurent error

Ulf H. Olsson The consequences of neglecting the measurent error