Econometric Methods and Applications II Chapter 2: Simultaneous equations. Econometric Methods and Applications II, Chapter 2, Slide 1

Size: px
Start display at page:

Download "Econometric Methods and Applications II Chapter 2: Simultaneous equations. Econometric Methods and Applications II, Chapter 2, Slide 1"

Transcription

1 Econometric Methods and Applications II Chapter 2: Simultaneous equations Econometric Methods and Applications II, Chapter 2, Slide 1

2 2.1 Introduction An example motivating the problem of simultaneous equations: Econometric Methods and Applications II, Chapter 2, Slide 2

3 2.1 Introduction Econometric Methods and Applications II, Chapter 2, Slide 3

4 2.1 Introduction Econometric Methods and Applications II, Chapter 2, Slide 4

5 2.1 Introduction Econometric Methods and Applications II, Chapter 2, Slide 5

6 2.2 IV assumptions IV assumptions: (2.1) Econometric Methods and Applications II, Chapter 2, Slide 6

7 2.2 IV assumptions Moment conditions and matrix notation: K Econometric Methods and Applications II, Chapter 2, Slide 7

8 2.2 IV assumptions Matrix notation (continued): Econometric Methods and Applications II, Chapter 2, Slide 8

9 2.3 IV estimation based on GMM Generalized Methods of Moments (GMM-particular estimation principle): (2.2) (2.2) (2.2) (2.3) This GMM estimator is consistent, but not efficient! Econometric Methods and Applications II, Chapter 2, Slide 9

10 2.3 IV estimation based on GMM Efficient GMM: (2.4) Econometric Methods and Applications II, Chapter 2, Slide 10

11 2.3 IV estimation based on GMM Consistency: 2.1: Econometric Methods and Applications II, Chapter 2, Slide 11

12 2.3 IV estimation based on GMM Asymptotic normality: 2.2: s Econometric Methods and Applications II, Chapter 2, Slide 12

13 2.3 IV estimation based on GMM The system 2SLS estimator: 2.4 Econometric Methods and Applications II, Chapter 2, Slide 13

14 2.3 IV estimation based on GMM GMM with asymptotically optimal weighting matrix: 2.3 Econometric Methods and Applications II, Chapter 2, Slide 14

15 2.3 IV estimation based on GMM Practical implementation of GMM with optimal weighting matrix: Econometric Methods and Applications II, Chapter 2, Slide 15

16 2.3 IV estimation based on GMM Three stage least squares estimation (3SLS): Econometric Methods and Applications II, Chapter 2, Slide 16

17 2.3 IV estimation based on GMM Equivalence of optimal GMM and 3SLS: Econometric Methods and Applications II, Chapter 2, Slide 17

18 2.3 IV estimation based on GMM Conditions for the efficiency of 3SLS: 2.4 Econometric Methods and Applications II, Chapter 2, Slide 18

19 2.4 Identification in the classical simultaneous equation model Notation and exclusion restriction: Econometric Methods and Applications II, Chapter 2, Slide 19

20 2.4 Identification in the classical simultaneous equation model Identification: A B A A Econometric Methods and Applications II, Chapter 2, Slide 20

21 2.4 Identification in the classical simultaneous equation model Structural and reduced form: Econometric Methods and Applications II, Chapter 2, Slide 21

22 2.4 Identification in the classical simultaneous equation model General system: Let M denote the total number of exogenous variables z in the system. Econometric Methods and Applications II, Chapter 2, Slide 22

23 2.4 Identification in the classical simultaneous equation model Condition for identification: 2.5 Econometric Methods and Applications II, Chapter 2, Slide 23

24 2.4 Identification in the classical simultaneous equation model Example with graphical illustration: q: quantity, p: price, i: income 0 1 pt 2it ut 0 1 pt vt ( 1 1 ) pt 0 0 2it ( vt ut ) pt v ut, it t E ( pt qt, i ) pt it, qt 0 1 pt vt. Econometric Methods and Applications II, Chapter 2, Slide 24

25 2.5 Identification of triangular systems based on control functions Triangular system: y1 1 y2 z1 1 u1, y2 z 2 u2. y1 is G1 1, y2 is G A triangular system is similar to a recursive system with simultaneity, with the exception that at least one or several of the endogenous variables are only determined by exogenous variables (but not by other endogenous variables). - Still, they appear in sets of equations determining other endogenous variables. - E.g., y2 is only determined by the exogenous variables z, but determines y1. Assumptions: E (u1 z ) 0, E (u2 z ) 0, E (u1 u2, z ) E (u1 u2 ). - A sufficient condition for E(u1 u2, z) E(u1 u2 ) is that (u1, u2 ) is independent of z. - Then, E ( y u, z ) y z E (u u, z ) y2 z1 1 E (u1 u2 ) 1 y2 z1 1 H1 (u2 ) if we knew H1 (u2 ) and u2, we could estimate 1 by a system estimation method, such as system OLS or FGLS. Econometric Methods and Applications II, Chapter 2, Slide 25

26 2.5 Identification of triangular systems based on control functions Estimation: - Assume that H1 (u2 ) E (u1 u2 ) 1u2 (linearity) - Then, in a first stage, we can estimate y2 z 2 u2 by a standard system method to obtain ˆ2 and the estimated residuals, uˆi 2. - In a second stage, one estimates the structural equation of interest by plugging in the estimated first stage residuals: yi1 1 yi 2 zi1 1 1uˆi 2 ei, with ei being the estimation error due to the estimation of ˆ2. - System OLS or FGLS might be used for estimation, but the asymptotic variance has to be adjusted due to the first stage estimation (similar to two stage least squares). Econometric Methods and Applications II, Chapter 2, Slide 26

1 Outline. 1. Motivation. 2. SUR model. 3. Simultaneous equations. 4. Estimation

1 Outline. 1. Motivation. 2. SUR model. 3. Simultaneous equations. 4. Estimation 1 Outline. 1. Motivation 2. SUR model 3. Simultaneous equations 4. Estimation 2 Motivation. In this chapter, we will study simultaneous systems of econometric equations. Systems of simultaneous equations

More information

Chapter 14. Simultaneous Equations Models Introduction

Chapter 14. Simultaneous Equations Models Introduction Chapter 14 Simultaneous Equations Models 14.1 Introduction Simultaneous equations models differ from those we have considered in previous chapters because in each model there are two or more dependent

More information

Lecture: Simultaneous Equation Model (Wooldridge s Book Chapter 16)

Lecture: Simultaneous Equation Model (Wooldridge s Book Chapter 16) Lecture: Simultaneous Equation Model (Wooldridge s Book Chapter 16) 1 2 Model Consider a system of two regressions y 1 = β 1 y 2 + u 1 (1) y 2 = β 2 y 1 + u 2 (2) This is a simultaneous equation model

More information

Chapter 6. Panel Data. Joan Llull. Quantitative Statistical Methods II Barcelona GSE

Chapter 6. Panel Data. Joan Llull. Quantitative Statistical Methods II Barcelona GSE Chapter 6. Panel Data Joan Llull Quantitative Statistical Methods II Barcelona GSE Introduction Chapter 6. Panel Data 2 Panel data The term panel data refers to data sets with repeated observations over

More information

ECONOMETRICS FIELD EXAM Michigan State University May 9, 2008

ECONOMETRICS FIELD EXAM Michigan State University May 9, 2008 ECONOMETRICS FIELD EXAM Michigan State University May 9, 2008 Instructions: Answer all four (4) questions. Point totals for each question are given in parenthesis; there are 00 points possible. Within

More information

ECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria

ECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria ECONOMETRICS II (ECO 2401S) University of Toronto. Department of Economics. Spring 2013 Instructor: Victor Aguirregabiria SOLUTION TO FINAL EXAM Friday, April 12, 2013. From 9:00-12:00 (3 hours) INSTRUCTIONS:

More information

PhD/MA Econometrics Examination. January, 2015 PART A. (Answer any TWO from Part A)

PhD/MA Econometrics Examination. January, 2015 PART A. (Answer any TWO from Part A) PhD/MA Econometrics Examination January, 2015 Total Time: 8 hours MA students are required to answer from A and B. PhD students are required to answer from A, B, and C. PART A (Answer any TWO from Part

More information

Dealing With Endogeneity

Dealing With Endogeneity Dealing With Endogeneity Junhui Qian December 22, 2014 Outline Introduction Instrumental Variable Instrumental Variable Estimation Two-Stage Least Square Estimation Panel Data Endogeneity in Econometrics

More information

Econometric Analysis of Cross Section and Panel Data

Econometric Analysis of Cross Section and Panel Data Econometric Analysis of Cross Section and Panel Data Jeffrey M. Wooldridge / The MIT Press Cambridge, Massachusetts London, England Contents Preface Acknowledgments xvii xxiii I INTRODUCTION AND BACKGROUND

More information

Chapter 6: Endogeneity and Instrumental Variables (IV) estimator

Chapter 6: Endogeneity and Instrumental Variables (IV) estimator Chapter 6: Endogeneity and Instrumental Variables (IV) estimator Advanced Econometrics - HEC Lausanne Christophe Hurlin University of Orléans December 15, 2013 Christophe Hurlin (University of Orléans)

More information

Econometrics II - EXAM Answer each question in separate sheets in three hours

Econometrics II - EXAM Answer each question in separate sheets in three hours Econometrics II - EXAM Answer each question in separate sheets in three hours. Let u and u be jointly Gaussian and independent of z in all the equations. a Investigate the identification of the following

More information

Econometrics II - EXAM Outline Solutions All questions have 25pts Answer each question in separate sheets

Econometrics II - EXAM Outline Solutions All questions have 25pts Answer each question in separate sheets Econometrics II - EXAM Outline Solutions All questions hae 5pts Answer each question in separate sheets. Consider the two linear simultaneous equations G with two exogeneous ariables K, y γ + y γ + x δ

More information

Short Questions (Do two out of three) 15 points each

Short Questions (Do two out of three) 15 points each Econometrics Short Questions Do two out of three) 5 points each ) Let y = Xβ + u and Z be a set of instruments for X When we estimate β with OLS we project y onto the space spanned by X along a path orthogonal

More information

Generalized Method of Moments: I. Chapter 9, R. Davidson and J.G. MacKinnon, Econometric Theory and Methods, 2004, Oxford.

Generalized Method of Moments: I. Chapter 9, R. Davidson and J.G. MacKinnon, Econometric Theory and Methods, 2004, Oxford. Generalized Method of Moments: I References Chapter 9, R. Davidson and J.G. MacKinnon, Econometric heory and Methods, 2004, Oxford. Chapter 5, B. E. Hansen, Econometrics, 2006. http://www.ssc.wisc.edu/~bhansen/notes/notes.htm

More information

08 Endogenous Right-Hand-Side Variables. Andrius Buteikis,

08 Endogenous Right-Hand-Side Variables. Andrius Buteikis, 08 Endogenous Right-Hand-Side Variables Andrius Buteikis, andrius.buteikis@mif.vu.lt http://web.vu.lt/mif/a.buteikis/ Introduction Consider a simple regression model: Y t = α + βx t + u t Under the classical

More information

ECON 4160: Econometrics-Modelling and Systems Estimation Lecture 9: Multiple equation models II

ECON 4160: Econometrics-Modelling and Systems Estimation Lecture 9: Multiple equation models II ECON 4160: Econometrics-Modelling and Systems Estimation Lecture 9: Multiple equation models II Ragnar Nymoen Department of Economics University of Oslo 9 October 2018 The reference to this lecture is:

More information

1. You have data on years of work experience, EXPER, its square, EXPER2, years of education, EDUC, and the log of hourly wages, LWAGE

1. You have data on years of work experience, EXPER, its square, EXPER2, years of education, EDUC, and the log of hourly wages, LWAGE 1. You have data on years of work experience, EXPER, its square, EXPER, years of education, EDUC, and the log of hourly wages, LWAGE You estimate the following regressions: (1) LWAGE =.00 + 0.05*EDUC +

More information

Applied Econometrics (MSc.) Lecture 3 Instrumental Variables

Applied Econometrics (MSc.) Lecture 3 Instrumental Variables Applied Econometrics (MSc.) Lecture 3 Instrumental Variables Estimation - Theory Department of Economics University of Gothenburg December 4, 2014 1/28 Why IV estimation? So far, in OLS, we assumed independence.

More information

SIMULTANEOUS EQUATION MODEL

SIMULTANEOUS EQUATION MODEL SIMULTANEOUS EQUATION MODEL ONE Equation Model (revisited) Characteristics: One dependent variable (Y): as a regressand One ore more independent variables (X): as regressors One way causality relationship:

More information

Simultaneous Equation Models (Book Chapter 5)

Simultaneous Equation Models (Book Chapter 5) Simultaneous Equation Models (Book Chapter 5) Interrelated equations with continuous dependent variables: Utilization of individual vehicles (measured in kilometers driven) in multivehicle households Interrelation

More information

A Course in Applied Econometrics Lecture 14: Control Functions and Related Methods. Jeff Wooldridge IRP Lectures, UW Madison, August 2008

A Course in Applied Econometrics Lecture 14: Control Functions and Related Methods. Jeff Wooldridge IRP Lectures, UW Madison, August 2008 A Course in Applied Econometrics Lecture 14: Control Functions and Related Methods Jeff Wooldridge IRP Lectures, UW Madison, August 2008 1. Linear-in-Parameters Models: IV versus Control Functions 2. Correlated

More information

Regression Analysis Tutorial 228 LECTURE / DISCUSSION. Simultaneous Equations

Regression Analysis Tutorial 228 LECTURE / DISCUSSION. Simultaneous Equations Regression Analysis Tutorial 228 LECTURE / DISCUSSION Simultaneous Equations Regression Analysis Tutorial 229 Simultaneous Equations Example 1 Gas consumption = " + $(thermostat setting) + 2(sq ft) + g

More information

ECONOMETRICS FIELD EXAM May 10,2013 Department ofeconomics, Michigan State University

ECONOMETRICS FIELD EXAM May 10,2013 Department ofeconomics, Michigan State University ECONOMETRICS FIELD EXAM May 10,2013 Department ofeconomics, Michigan State University Instructions: Answer all four (4) questions. Be sure to show your work or provide sufficient justification for your

More information

Econometrics. 8) Instrumental variables

Econometrics. 8) Instrumental variables 30C00200 Econometrics 8) Instrumental variables Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Thery of IV regression Overidentification Two-stage least squates

More information

Economics 308: Econometrics Professor Moody

Economics 308: Econometrics Professor Moody Economics 308: Econometrics Professor Moody References on reserve: Text Moody, Basic Econometrics with Stata (BES) Pindyck and Rubinfeld, Econometric Models and Economic Forecasts (PR) Wooldridge, Jeffrey

More information

ECO 310: Empirical Industrial Organization Lecture 2 - Estimation of Demand and Supply

ECO 310: Empirical Industrial Organization Lecture 2 - Estimation of Demand and Supply ECO 310: Empirical Industrial Organization Lecture 2 - Estimation of Demand and Supply Dimitri Dimitropoulos Fall 2014 UToronto 1 / 55 References RW Section 3. Wooldridge, J. (2008). Introductory Econometrics:

More information

Using regression to study economic relationships is called econometrics. econo = of or pertaining to the economy. metrics = measurement

Using regression to study economic relationships is called econometrics. econo = of or pertaining to the economy. metrics = measurement EconS 450 Forecasting part 3 Forecasting with Regression Using regression to study economic relationships is called econometrics econo = of or pertaining to the economy metrics = measurement Econometrics

More information

4 Instrumental Variables Single endogenous variable One continuous instrument. 2

4 Instrumental Variables Single endogenous variable One continuous instrument. 2 Econ 495 - Econometric Review 1 Contents 4 Instrumental Variables 2 4.1 Single endogenous variable One continuous instrument. 2 4.2 Single endogenous variable more than one continuous instrument..........................

More information

Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity?

Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity? MPRA Munich Personal RePEc Archive Identification through Heteroscedasticity: What If We Have the Wrong Form of Heteroscedasticity? Tak Wai Chau The Chinese University of Hong Kong, Shanghai University

More information

L2: Two-variable regression model

L2: Two-variable regression model L2: Two-variable regression model Feng Li feng.li@cufe.edu.cn School of Statistics and Mathematics Central University of Finance and Economics Revision: September 4, 2014 What we have learned last time...

More information

Introduction to Economic Time Series

Introduction to Economic Time Series Econometrics II Introduction to Economic Time Series Morten Nyboe Tabor Learning Goals 1 Give an account for the important differences between (independent) cross-sectional data and time series data. 2

More information

Spatial Regression. 11. Spatial Two Stage Least Squares. Luc Anselin. Copyright 2017 by Luc Anselin, All Rights Reserved

Spatial Regression. 11. Spatial Two Stage Least Squares. Luc Anselin.  Copyright 2017 by Luc Anselin, All Rights Reserved Spatial Regression 11. Spatial Two Stage Least Squares Luc Anselin http://spatial.uchicago.edu 1 endogeneity and instruments spatial 2SLS best and optimal estimators HAC standard errors 2 Endogeneity and

More information

Wooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares

Wooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares Wooldridge, Introductory Econometrics, 4th ed. Chapter 15: Instrumental variables and two stage least squares Many economic models involve endogeneity: that is, a theoretical relationship does not fit

More information

Missing dependent variables in panel data models

Missing dependent variables in panel data models Missing dependent variables in panel data models Jason Abrevaya Abstract This paper considers estimation of a fixed-effects model in which the dependent variable may be missing. For cross-sectional units

More information

IV estimators and forbidden regressions

IV estimators and forbidden regressions Economics 8379 Spring 2016 Ben Williams IV estimators and forbidden regressions Preliminary results Consider the triangular model with first stage given by x i2 = γ 1X i1 + γ 2 Z i + ν i and second stage

More information

4 Instrumental Variables Single endogenous variable One continuous instrument. 2

4 Instrumental Variables Single endogenous variable One continuous instrument. 2 Econ 495 - Econometric Review 1 Contents 4 Instrumental Variables 2 4.1 Single endogenous variable One continuous instrument. 2 4.2 Single endogenous variable more than one continuous instrument..........................

More information

Lecture 6: Dynamic panel models 1

Lecture 6: Dynamic panel models 1 Lecture 6: Dynamic panel models 1 Ragnar Nymoen Department of Economics, UiO 16 February 2010 Main issues and references Pre-determinedness and endogeneity of lagged regressors in FE model, and RE model

More information

Linear IV and Simultaneous Equations

Linear IV and Simultaneous Equations Linear IV and Daniel Schmierer Econ 312 April 6, 2007 Setup Linear regression model Y = X β + ε (1) Endogeneity of X means that X and ε are correlated, ie. E(X ε) 0. Suppose we observe another variable

More information

1 Estimation of Persistent Dynamic Panel Data. Motivation

1 Estimation of Persistent Dynamic Panel Data. Motivation 1 Estimation of Persistent Dynamic Panel Data. Motivation Consider the following Dynamic Panel Data (DPD) model y it = y it 1 ρ + x it β + µ i + v it (1.1) with i = {1, 2,..., N} denoting the individual

More information

Instrumental variables estimation using heteroskedasticity-based instruments

Instrumental variables estimation using heteroskedasticity-based instruments Instrumental variables estimation using heteroskedasticity-based instruments Christopher F Baum, Arthur Lewbel, Mark E Schaffer, Oleksandr Talavera Boston College/DIW Berlin, Boston College, Heriot Watt

More information

Exogeneity tests and weak identification

Exogeneity tests and weak identification Cireq, Cirano, Départ. Sc. Economiques Université de Montréal Jean-Marie Dufour Cireq, Cirano, William Dow Professor of Economics Department of Economics Mcgill University June 20, 2008 Main Contributions

More information

Discussion of Sensitivity and Informativeness under Local Misspecification

Discussion of Sensitivity and Informativeness under Local Misspecification Discussion of Sensitivity and Informativeness under Local Misspecification Jinyong Hahn April 4, 2019 Jinyong Hahn () Discussion of Sensitivity and Informativeness under Local Misspecification April 4,

More information

Econometrics Summary Algebraic and Statistical Preliminaries

Econometrics Summary Algebraic and Statistical Preliminaries Econometrics Summary Algebraic and Statistical Preliminaries Elasticity: The point elasticity of Y with respect to L is given by α = ( Y/ L)/(Y/L). The arc elasticity is given by ( Y/ L)/(Y/L), when L

More information

Econometrics. Week 8. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague

Econometrics. Week 8. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Econometrics Week 8 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 25 Recommended Reading For the today Instrumental Variables Estimation and Two Stage

More information

Financial Econometrics

Financial Econometrics Financial Econometrics Multivariate Time Series Analysis: VAR Gerald P. Dwyer Trinity College, Dublin January 2013 GPD (TCD) VAR 01/13 1 / 25 Structural equations Suppose have simultaneous system for supply

More information

Michael Lechner Causal Analysis RDD 2014 page 1. Lecture 7. The Regression Discontinuity Design. RDD fuzzy and sharp

Michael Lechner Causal Analysis RDD 2014 page 1. Lecture 7. The Regression Discontinuity Design. RDD fuzzy and sharp page 1 Lecture 7 The Regression Discontinuity Design fuzzy and sharp page 2 Regression Discontinuity Design () Introduction (1) The design is a quasi-experimental design with the defining characteristic

More information

A Course on Advanced Econometrics

A Course on Advanced Econometrics A Course on Advanced Econometrics Yongmiao Hong The Ernest S. Liu Professor of Economics & International Studies Cornell University Course Introduction: Modern economies are full of uncertainties and risk.

More information

Econometrics I Lecture 3: The Simple Linear Regression Model

Econometrics I Lecture 3: The Simple Linear Regression Model Econometrics I Lecture 3: The Simple Linear Regression Model Mohammad Vesal Graduate School of Management and Economics Sharif University of Technology 44716 Fall 1397 1 / 32 Outline Introduction Estimating

More information

Intermediate Econometrics

Intermediate Econometrics Intermediate Econometrics Heteroskedasticity Text: Wooldridge, 8 July 17, 2011 Heteroskedasticity Assumption of homoskedasticity, Var(u i x i1,..., x ik ) = E(u 2 i x i1,..., x ik ) = σ 2. That is, the

More information

Lecture 8: Instrumental Variables Estimation

Lecture 8: Instrumental Variables Estimation Lecture Notes on Advanced Econometrics Lecture 8: Instrumental Variables Estimation Endogenous Variables Consider a population model: y α y + β + β x + β x +... + β x + u i i i i k ik i Takashi Yamano

More information

Chapter 1. GMM: Basic Concepts

Chapter 1. GMM: Basic Concepts Chapter 1. GMM: Basic Concepts Contents 1 Motivating Examples 1 1.1 Instrumental variable estimator....................... 1 1.2 Estimating parameters in monetary policy rules.............. 2 1.3 Estimating

More information

Simple Linear Regression Model & Introduction to. OLS Estimation

Simple Linear Regression Model & Introduction to. OLS Estimation Inside ECOOMICS Introduction to Econometrics Simple Linear Regression Model & Introduction to Introduction OLS Estimation We are interested in a model that explains a variable y in terms of other variables

More information

Spatial Regression. 13. Spatial Panels (1) Luc Anselin. Copyright 2017 by Luc Anselin, All Rights Reserved

Spatial Regression. 13. Spatial Panels (1) Luc Anselin.  Copyright 2017 by Luc Anselin, All Rights Reserved Spatial Regression 13. Spatial Panels (1) Luc Anselin http://spatial.uchicago.edu 1 basic concepts dynamic panels pooled spatial panels 2 Basic Concepts 3 Data Structures 4 Two-Dimensional Data cross-section/space

More information

Standard Error of Technical Cost Incorporating Parameter Uncertainty

Standard Error of Technical Cost Incorporating Parameter Uncertainty Standard Error of Technical Cost Incorporating Parameter Uncertainty Christopher Morton Insurance Australia Group This presentation has been prepared for the Actuaries Institute 2012 General Insurance

More information

ECO Class 6 Nonparametric Econometrics

ECO Class 6 Nonparametric Econometrics ECO 523 - Class 6 Nonparametric Econometrics Carolina Caetano Contents 1 Nonparametric instrumental variable regression 1 2 Nonparametric Estimation of Average Treatment Effects 3 2.1 Asymptotic results................................

More information

ECON 4160, Spring term 2015 Lecture 7

ECON 4160, Spring term 2015 Lecture 7 ECON 4160, Spring term 2015 Lecture 7 Identification and estimation of SEMs (Part 1) Ragnar Nymoen Department of Economics 8 Oct 2015 1 / 55 HN Ch 15 References to Davidson and MacKinnon, Ch 8.1-8.5 Ch

More information

Econometrics I. Ricardo Mora

Econometrics I. Ricardo Mora Econometrics I Department of Economics Universidad Carlos III de Madrid Master in Industrial Economics and Markets Outline Motivation 1 Motivation 2 3 4 Motivation The Analogy Principle The () is a framework

More information

Heteroskedasticity. y i = β 0 + β 1 x 1i + β 2 x 2i β k x ki + e i. where E(e i. ) σ 2, non-constant variance.

Heteroskedasticity. y i = β 0 + β 1 x 1i + β 2 x 2i β k x ki + e i. where E(e i. ) σ 2, non-constant variance. Heteroskedasticity y i = β + β x i + β x i +... + β k x ki + e i where E(e i ) σ, non-constant variance. Common problem with samples over individuals. ê i e ˆi x k x k AREC-ECON 535 Lec F Suppose y i =

More information

13 Endogeneity and Nonparametric IV

13 Endogeneity and Nonparametric IV 13 Endogeneity and Nonparametric IV 13.1 Nonparametric Endogeneity A nonparametric IV equation is Y i = g (X i ) + e i (1) E (e i j i ) = 0 In this model, some elements of X i are potentially endogenous,

More information

SEM with observed variables: parameterization and identification. Psychology 588: Covariance structure and factor models

SEM with observed variables: parameterization and identification. Psychology 588: Covariance structure and factor models SEM with observed variables: parameterization and identification Psychology 588: Covariance structure and factor models Limitations of SEM as a causal modeling 2 If an SEM model reflects the reality, the

More information

Specification testing in panel data models estimated by fixed effects with instrumental variables

Specification testing in panel data models estimated by fixed effects with instrumental variables Specification testing in panel data models estimated by fixed effects wh instrumental variables Carrie Falls Department of Economics Michigan State Universy Abstract I show that a handful of the regressions

More information

Instrumental variables estimation using heteroskedasticity-based instruments

Instrumental variables estimation using heteroskedasticity-based instruments Instrumental variables estimation using heteroskedasticity-based instruments Christopher F Baum, Arthur Lewbel, Mark E Schaffer, Oleksandr Talavera Boston College/DIW Berlin, Boston College, Heriot Watt

More information

Correlation Analysis

Correlation Analysis Simple Regression Correlation Analysis Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the

More information

Economics 582 Random Effects Estimation

Economics 582 Random Effects Estimation Economics 582 Random Effects Estimation Eric Zivot May 29, 2013 Random Effects Model Hence, the model can be re-written as = x 0 β + + [x ] = 0 (no endogeneity) [ x ] = = + x 0 β + + [x ] = 0 [ x ] = 0

More information

Final Exam. Economics 835: Econometrics. Fall 2010

Final Exam. Economics 835: Econometrics. Fall 2010 Final Exam Economics 835: Econometrics Fall 2010 Please answer the question I ask - no more and no less - and remember that the correct answer is often short and simple. 1 Some short questions a) For each

More information

Econometrics A. Simple linear model (2) Keio University, Faculty of Economics. Simon Clinet (Keio University) Econometrics A October 16, / 11

Econometrics A. Simple linear model (2) Keio University, Faculty of Economics. Simon Clinet (Keio University) Econometrics A October 16, / 11 Econometrics A Keio University, Faculty of Economics Simple linear model (2) Simon Clinet (Keio University) Econometrics A October 16, 2018 1 / 11 Estimation of the noise variance σ 2 In practice σ 2 too

More information

Dynamic Panel Data Models

Dynamic Panel Data Models Models Amjad Naveed, Nora Prean, Alexander Rabas 15th June 2011 Motivation Many economic issues are dynamic by nature. These dynamic relationships are characterized by the presence of a lagged dependent

More information

Title. Description. var intro Introduction to vector autoregressive models

Title. Description. var intro Introduction to vector autoregressive models Title var intro Introduction to vector autoregressive models Description Stata has a suite of commands for fitting, forecasting, interpreting, and performing inference on vector autoregressive (VAR) models

More information

Simultaneous Equation Models Learning Objectives Introduction Introduction (2) Introduction (3) Solving the Model structural equations

Simultaneous Equation Models Learning Objectives Introduction Introduction (2) Introduction (3) Solving the Model structural equations Simultaneous Equation Models. Introduction: basic definitions 2. Consequences of ignoring simultaneity 3. The identification problem 4. Estimation of simultaneous equation models 5. Example: IS LM model

More information

Linear Regression. Junhui Qian. October 27, 2014

Linear Regression. Junhui Qian. October 27, 2014 Linear Regression Junhui Qian October 27, 2014 Outline The Model Estimation Ordinary Least Square Method of Moments Maximum Likelihood Estimation Properties of OLS Estimator Unbiasedness Consistency Efficiency

More information

Economics 241B Estimation with Instruments

Economics 241B Estimation with Instruments Economics 241B Estimation with Instruments Measurement Error Measurement error is de ned as the error resulting from the measurement of a variable. At some level, every variable is measured with error.

More information

Multiple Equation GMM with Common Coefficients: Panel Data

Multiple Equation GMM with Common Coefficients: Panel Data Multiple Equation GMM with Common Coefficients: Panel Data Eric Zivot Winter 2013 Multi-equation GMM with common coefficients Example (panel wage equation) 69 = + 69 + + 69 + 1 80 = + 80 + + 80 + 2 Note:

More information

Simple Linear Regression: The Model

Simple Linear Regression: The Model Simple Linear Regression: The Model task: quantifying the effect of change X in X on Y, with some constant β 1 : Y = β 1 X, linear relationship between X and Y, however, relationship subject to a random

More information

Instrumental Variables

Instrumental Variables Instrumental Variables Department of Economics University of Wisconsin-Madison September 27, 2016 Treatment Effects Throughout the course we will focus on the Treatment Effect Model For now take that to

More information

Motivation Non-linear Rational Expectations The Permanent Income Hypothesis The Log of Gravity Non-linear IV Estimation Summary.

Motivation Non-linear Rational Expectations The Permanent Income Hypothesis The Log of Gravity Non-linear IV Estimation Summary. Econometrics I Department of Economics Universidad Carlos III de Madrid Master in Industrial Economics and Markets Outline Motivation 1 Motivation 2 3 4 5 Motivation Hansen's contributions GMM was developed

More information

Multiple Linear Regression CIVL 7012/8012

Multiple Linear Regression CIVL 7012/8012 Multiple Linear Regression CIVL 7012/8012 2 Multiple Regression Analysis (MLR) Allows us to explicitly control for many factors those simultaneously affect the dependent variable This is important for

More information

Freeing up the Classical Assumptions. () Introductory Econometrics: Topic 5 1 / 94

Freeing up the Classical Assumptions. () Introductory Econometrics: Topic 5 1 / 94 Freeing up the Classical Assumptions () Introductory Econometrics: Topic 5 1 / 94 The Multiple Regression Model: Freeing Up the Classical Assumptions Some or all of classical assumptions needed for derivations

More information

FINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE -MODULE2 Midterm Exam Solutions - March 2015

FINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE -MODULE2 Midterm Exam Solutions - March 2015 FINANCIAL ECONOMETRICS AND EMPIRICAL FINANCE -MODULE2 Midterm Exam Solutions - March 205 Time Allowed: 60 minutes Family Name (Surname) First Name Student Number (Matr.) Please answer all questions by

More information

Econometrics. Week 4. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague

Econometrics. Week 4. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Econometrics Week 4 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 23 Recommended Reading For the today Serial correlation and heteroskedasticity in

More information

Analogy Principle. Asymptotic Theory Part II. James J. Heckman University of Chicago. Econ 312 This draft, April 5, 2006

Analogy Principle. Asymptotic Theory Part II. James J. Heckman University of Chicago. Econ 312 This draft, April 5, 2006 Analogy Principle Asymptotic Theory Part II James J. Heckman University of Chicago Econ 312 This draft, April 5, 2006 Consider four methods: 1. Maximum Likelihood Estimation (MLE) 2. (Nonlinear) Least

More information

Generalized Method of Moments (GMM) Estimation

Generalized Method of Moments (GMM) Estimation Econometrics 2 Fall 2004 Generalized Method of Moments (GMM) Estimation Heino Bohn Nielsen of29 Outline of the Lecture () Introduction. (2) Moment conditions and methods of moments (MM) estimation. Ordinary

More information

A Course in Applied Econometrics Lecture 18: Missing Data. Jeff Wooldridge IRP Lectures, UW Madison, August Linear model with IVs: y i x i u i,

A Course in Applied Econometrics Lecture 18: Missing Data. Jeff Wooldridge IRP Lectures, UW Madison, August Linear model with IVs: y i x i u i, A Course in Applied Econometrics Lecture 18: Missing Data Jeff Wooldridge IRP Lectures, UW Madison, August 2008 1. When Can Missing Data be Ignored? 2. Inverse Probability Weighting 3. Imputation 4. Heckman-Type

More information

ECON 4160, Autumn term 2017 Lecture 9

ECON 4160, Autumn term 2017 Lecture 9 ECON 4160, Autumn term 2017 Lecture 9 Structural VAR (SVAR) Ragnar Nymoen Department of Economics 26 Oct 2017 1 / 14 Parameter of interest: impulse responses I Consider again a partial market equilibrium

More information

Warwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation

Warwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation Warwick Economics Summer School Topics in Microeconometrics Instrumental Variables Estimation Michele Aquaro University of Warwick This version: July 21, 2016 1 / 31 Reading material Textbook: Introductory

More information

Identifying Causal Effects in Time Series Models

Identifying Causal Effects in Time Series Models Identifying Causal Effects in Time Series Models Aaron Smith UC Davis October 20, 2015 Slides available at http://asmith.ucdavis.edu 1 Identifying Causal Effects in Time Series Models If all the Metrics

More information

Uncertainty and Disagreement in Equilibrium Models

Uncertainty and Disagreement in Equilibrium Models Uncertainty and Disagreement in Equilibrium Models Nabil I. Al-Najjar & Northwestern University Eran Shmaya Tel Aviv University RUD, Warwick, June 2014 Forthcoming: Journal of Political Economy Motivation

More information

Problem Set # 1. Master in Business and Quantitative Methods

Problem Set # 1. Master in Business and Quantitative Methods Problem Set # 1 Master in Business and Quantitative Methods Contents 0.1 Problems on endogeneity of the regressors........... 2 0.2 Lab exercises on endogeneity of the regressors......... 4 1 0.1 Problems

More information

E c o n o m e t r i c s

E c o n o m e t r i c s H:/Lehre/Econometrics Master/Lecture slides/chap 0.tex (October 7, 2015) E c o n o m e t r i c s This course 1 People Instructor: Professor Dr. Roman Liesenfeld SSC-Gebäude, Universitätsstr. 22, Room 4.309

More information

Eksamen på Økonomistudiet 2006-II Econometrics 2 June 9, 2006

Eksamen på Økonomistudiet 2006-II Econometrics 2 June 9, 2006 Eksamen på Økonomistudiet 2006-II Econometrics 2 June 9, 2006 This is a four hours closed-book exam (uden hjælpemidler). Please answer all questions. As a guiding principle the questions 1 to 4 have equal

More information

Repeated observations on the same cross-section of individual units. Important advantages relative to pure cross-section data

Repeated observations on the same cross-section of individual units. Important advantages relative to pure cross-section data Panel data Repeated observations on the same cross-section of individual units. Important advantages relative to pure cross-section data - possible to control for some unobserved heterogeneity - possible

More information

DSGE Methods. Estimation of DSGE models: GMM and Indirect Inference. Willi Mutschler, M.Sc.

DSGE Methods. Estimation of DSGE models: GMM and Indirect Inference. Willi Mutschler, M.Sc. DSGE Methods Estimation of DSGE models: GMM and Indirect Inference Willi Mutschler, M.Sc. Institute of Econometrics and Economic Statistics University of Münster willi.mutschler@wiwi.uni-muenster.de Summer

More information

Applied Health Economics (for B.Sc.)

Applied Health Economics (for B.Sc.) Applied Health Economics (for B.Sc.) Helmut Farbmacher Department of Economics University of Mannheim Autumn Semester 2017 Outlook 1 Linear models (OLS, Omitted variables, 2SLS) 2 Limited and qualitative

More information

Maximum Likelihood (ML) Estimation

Maximum Likelihood (ML) Estimation Econometrics 2 Fall 2004 Maximum Likelihood (ML) Estimation Heino Bohn Nielsen 1of32 Outline of the Lecture (1) Introduction. (2) ML estimation defined. (3) ExampleI:Binomialtrials. (4) Example II: Linear

More information

ECONOMETRIC THEORY. MODULE XVII Lecture - 43 Simultaneous Equations Models

ECONOMETRIC THEORY. MODULE XVII Lecture - 43 Simultaneous Equations Models ECONOMETRIC THEORY MODULE XVII Lecture - 43 Simultaneous Equations Models Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur 2 Estimation of parameters To estimate

More information

1 Motivation for Instrumental Variable (IV) Regression

1 Motivation for Instrumental Variable (IV) Regression ECON 370: IV & 2SLS 1 Instrumental Variables Estimation and Two Stage Least Squares Econometric Methods, ECON 370 Let s get back to the thiking in terms of cross sectional (or pooled cross sectional) data

More information

Spatial Regression. 15. Spatial Panels (3) Luc Anselin. Copyright 2017 by Luc Anselin, All Rights Reserved

Spatial Regression. 15. Spatial Panels (3) Luc Anselin.  Copyright 2017 by Luc Anselin, All Rights Reserved Spatial Regression 15. Spatial Panels (3) Luc Anselin http://spatial.uchicago.edu 1 spatial SUR spatial lag SUR spatial error SUR 2 Spatial SUR 3 Specification 4 Classic Seemingly Unrelated Regressions

More information

INTRODUCTION TO BASIC LINEAR REGRESSION MODEL

INTRODUCTION TO BASIC LINEAR REGRESSION MODEL INTRODUCTION TO BASIC LINEAR REGRESSION MODEL 13 September 2011 Yogyakarta, Indonesia Cosimo Beverelli (World Trade Organization) 1 LINEAR REGRESSION MODEL In general, regression models estimate the effect

More information

Asymptotic Properties and simulation in gretl

Asymptotic Properties and simulation in gretl Asymptotic Properties and simulation in gretl Quantitative Microeconomics R. Mora Department of Economics Universidad Carlos III de Madrid Outline 1 Asymptotic Results for OLS 2 3 4 5 Classical Assumptions

More information

DSGE-Models. Limited Information Estimation General Method of Moments and Indirect Inference

DSGE-Models. Limited Information Estimation General Method of Moments and Indirect Inference DSGE-Models General Method of Moments and Indirect Inference Dr. Andrea Beccarini Willi Mutschler, M.Sc. Institute of Econometrics and Economic Statistics University of Münster willi.mutschler@uni-muenster.de

More information

5.1 Model Specification and Data 5.2 Estimating the Parameters of the Multiple Regression Model 5.3 Sampling Properties of the Least Squares

5.1 Model Specification and Data 5.2 Estimating the Parameters of the Multiple Regression Model 5.3 Sampling Properties of the Least Squares 5.1 Model Specification and Data 5. Estimating the Parameters of the Multiple Regression Model 5.3 Sampling Properties of the Least Squares Estimator 5.4 Interval Estimation 5.5 Hypothesis Testing for

More information