Single-Equation GMM: Endogeneity Bias
|
|
- Dorthy Goodman
- 5 years ago
- Views:
Transcription
1 Single-Equation GMM: Lecture for Economics 241B Douglas G. Steigerwald UC Santa Barbara January 2012
2 Initial Question Initial Question How valuable is investment in college education? economics - measure value in terms of wage How would you determine the return on investment in college education?
3 Framework Stochastic Model What are the returns to a college education? Random variables of interest W - log of worker wage S - years of schooling A - age M - indicator for male R - indicator for white U - other factors that a ect wages Stochastic Model W = β 0 + β 1 S + β 2 A + β 3 A 2 + β 4 M + β 5 R + U
4 Initial Question Answered? Estimates Stochastic Model W = β 0 + β 1 S + β 2 A + β 3 A 2 + β 4 M + β 5 R + U ˆβ (and signi cantly di erent from zero) each additional year of schooling is worth an additional 8.4% in wages 4 years of college would increase wages by 38% ( ) the median full time worker earns about $550 per week in 2000 wage increase of 38% is $210 per week over 30 year work-life, earnings increase by $170,000 in present value (5% interest), makes public universities a good deal
5 Initial Question Answered? Potential Endogeneity W = β 0 + β 1 S + β 2 A + β 3 A 2 + β 4 M + β 5 R + U β 1 may not capture a causal impact on wages workers who obtained more education may have attributes that would have led to higher earnings even without additional education S is endogenous ) Cov (S, U) 6= 0 ˆβ 1 is biased and inconsistent What is the direction of bias in ˆβ 1? ˆβ 1 is biased upward, does not provide a helpful bound to argue for bene ts of education
6 Background Sources of Covariate-Error Correlation Focus on Cor (S, U) Endogeneity workers who would otherwise have high wage rates are more likely to obtain higher education U = µ + e µ - ability e - random shock S = αµ + w describes how schooling is correlated with ability in this application, likely that Cor (S, U) > 0 Measurement Error S = S + v S - actual schooling S - reported v - measurement error in all applications, Cor (S, U) < 0
7 Background Detail: Measurement Error Correlation Simplify population model W t = βst + U t S t = St + v t estimated model W t = βs t + (U t βv t ) v t is a component of S t ) Cor [S t, (U t βv t )] < 0 in large samples ˆβ tends to Cov (S t, v t ) β 1 Var (S t ) ˆβ = β + n t=1 S t [U t βv t ] n t=1 S 2 t Var (S = t ) β Var (St ) + Var (v t ) where Var (S t ) = Var (S t ) + Var (v t ) Cov (S t, v t ) = Var (v t ) Iron Law of Econometrics - measurement error leads to attenuation bias
8 Background Solutions Instrument z is a (valid) instrument if Cov (S, z) 6= 0 and Cov (U, z) = 0 instruments can address both sources of covariate-error correlation issue - instruments can be di cult to nd Measurement error assumption S = S + v assumptions regard v example: v is symmetric around 0 issue - does not address endogeneity
9 Background Instrument Solutions Standard Instrument Solution implicit model of endogeneity no speci ed model linking endogenous covariates to error yields classic instrumental variable (IV) estimator Model-Based Selection (Endogeneity) Correction explicit model of endogeneity clearly speci ed model linking endogenous covariates to error yields selection-corrected IV estimator
10 Background Standard Instrument Solution : Identi cation X (K 1) covariate vector Z (L1) instrument vector Identi cation Assumption (Rank Condition) The L K matrix E ZX T has rank K. Example X T = (1, S) Z T = (1, z) E ZX T = 1 E (S) E (z) E (Sz) Rank is K if determinant is not zero, Cov (S, z) 6= 0
11 Background Identi cation Identi cation Assumption (Order Condition) There are at least as many instruments as endogenous covariates: L K. Over identi cation rank condition satis ed and L > K Exact identi cation rank condition satis ed and L = K No identi cation L < K (rank condition cannot hold)
12 Initial Question Revisited Selection (Endogeneity) Correction Key - construct E [UjX, Z ] add to regression, remaining error uncorrelated with covariates Wage Regression Application data on twins (indexed by i) who share family characteristics Selection (Endogeneity) Model U i = µ + ε i µ = γs 1 + γs 2 + ω µ - latent family characteristics, correlated with S could relax assumption that γ is constant (use equation for twin 1 to identify γ 2 ) γ - selection e ect : γ > 0 ) families that would otherwise have high wages are more likely to educate their children
13 Initial Question Revisited Selection Correction wage regression (twin 1 C 0 1 = A 1, A 2 1, M 1, R 1 ) W 1 = β 0 + β 1 S 1 + C 0 1δ + (µ + ε 1 ) = β 0 + β 1 S 1 + C 0 1δ + (γs 1 + γs 2 + ω + ε 1 ) identi cation assumption E [U 1 jx, Z ] = γs 1 + γs 2 selection-corrected regression W 1 = β 0 + (β 1 + γ) S 1 + γs 2 + C 0 1δ + (ε 1 + ω) Variable OLS Include S 2 Own education (0.014) (0.015) Sibling s education (0.015) Twins data - endogeneity bias is negative!
14 Review Review Stochastic Model W i = β 0 + β 1 S i + U i What two issues lead to correlation between S i and U i? 1) endogeneity - latent ability that impacts both S i and U i 2) measurement error in S i What is the impact of the correlation on B OLS? biased and inconsistent What is needed to construct a consistent estimator? 1) instrument Z i Cor (Z i, S i ) 6= 0 Cor (Z i, U i ) = 0 2) assumption about measurement error
Regression. Econometrics II. Douglas G. Steigerwald. UC Santa Barbara. D. Steigerwald (UCSB) Regression 1 / 17
Regression Econometrics Douglas G. Steigerwald UC Santa Barbara D. Steigerwald (UCSB) Regression 1 / 17 Overview Reference: B. Hansen Econometrics Chapter 2.20-2.23, 2.25-2.29 Best Linear Projection is
More informationIntroduction: structural econometrics. Jean-Marc Robin
Introduction: structural econometrics Jean-Marc Robin Abstract 1. Descriptive vs structural models 2. Correlation is not causality a. Simultaneity b. Heterogeneity c. Selectivity Descriptive models Consider
More informationRegression Discontinuity
Regression Discontinuity STP Advanced Econometrics Lecture Douglas G. Steigerwald UC Santa Barbara March 2006 D. Steigerwald (Institute) Regression Discontinuity 03/06 1 / 11 Intuition Reference: Mostly
More informationSpeci cation of Conditional Expectation Functions
Speci cation of Conditional Expectation Functions Econometrics Douglas G. Steigerwald UC Santa Barbara D. Steigerwald (UCSB) Specifying Expectation Functions 1 / 24 Overview Reference: B. Hansen Econometrics
More informationEconomics 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 informationChapter 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 informationControlling for Time Invariant Heterogeneity
Controlling for Time Invariant Heterogeneity Yona Rubinstein July 2016 Yona Rubinstein (LSE) Controlling for Time Invariant Heterogeneity 07/16 1 / 19 Observables and Unobservables Confounding Factors
More informationEC402 - Problem Set 3
EC402 - Problem Set 3 Konrad Burchardi 11th of February 2009 Introduction Today we will - briefly talk about the Conditional Expectation Function and - lengthily talk about Fixed Effects: How do we calculate
More informationSingle-Equation GMM: Estimation
Sigle-Equatio GMM: Estimatio Lecture for Ecoomics 241B Douglas G. Steigerwald UC Sata Barbara Jauary 2012 Iitial Questio Iitial Questio How valuable is ivestmet i college educatio? ecoomics - measure value
More informationEnvironmental Econometrics
Environmental Econometrics Syngjoo Choi Fall 2008 Environmental Econometrics (GR03) Fall 2008 1 / 37 Syllabus I This is an introductory econometrics course which assumes no prior knowledge on econometrics;
More informationLecture: 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 informationChapter 2. Dynamic panel data models
Chapter 2. Dynamic panel data models School of Economics and Management - University of Geneva Christophe Hurlin, Université of Orléans University of Orléans April 2018 C. Hurlin (University of Orléans)
More informationEconometrics. 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 informationInstrumental Variables
Instrumental Variables Econometrics II R. Mora Department of Economics Universidad Carlos III de Madrid Master in Industrial Organization and Markets Outline 1 2 3 OLS y = β 0 + β 1 x + u, cov(x, u) =
More informationProblem 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 informationECONOMETRICS 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 informationNonparametric Density Estimation
Nonparametric Density Estimation Advanced Econometrics Douglas G. Steigerwald UC Santa Barbara D. Steigerwald (UCSB) Density Estimation 1 / 20 Overview Question of interest has wage inequality among women
More informationDealing 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 informationECO375 Tutorial 8 Instrumental Variables
ECO375 Tutorial 8 Instrumental Variables Matt Tudball University of Toronto Mississauga November 16, 2017 Matt Tudball (University of Toronto) ECO375H5 November 16, 2017 1 / 22 Review: Endogeneity Instrumental
More informationLecture notes to Stock and Watson chapter 12
Lecture notes to Stock and Watson chapter 12 Instrument variable regression Tore Schweder October 2008 TS () LN10 21/10 1 / 16 Outline Do SW: 11.6 Exogenous and endogenous regressors The problem of estimating
More informationWe begin by thinking about population relationships.
Conditional Expectation Function (CEF) We begin by thinking about population relationships. CEF Decomposition Theorem: Given some outcome Y i and some covariates X i there is always a decomposition where
More informationApplied 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 informationx i = 1 yi 2 = 55 with N = 30. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations.
Exercises for the course of Econometrics Introduction 1. () A researcher is using data for a sample of 30 observations to investigate the relationship between some dependent variable y i and independent
More informationPanel Data. March 2, () Applied Economoetrics: Topic 6 March 2, / 43
Panel Data March 2, 212 () Applied Economoetrics: Topic March 2, 212 1 / 43 Overview Many economic applications involve panel data. Panel data has both cross-sectional and time series aspects. Regression
More information1 Correlation between an independent variable and the error
Chapter 7 outline, Econometrics Instrumental variables and model estimation 1 Correlation between an independent variable and the error Recall that one of the assumptions that we make when proving the
More informationECON Introductory Econometrics. Lecture 16: Instrumental variables
ECON4150 - Introductory Econometrics Lecture 16: Instrumental variables Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 12 Lecture outline 2 OLS assumptions and when they are violated Instrumental
More informationThe regression model with one stochastic regressor (part II)
The regression model with one stochastic regressor (part II) 3150/4150 Lecture 7 Ragnar Nymoen 6 Feb 2012 We will finish Lecture topic 4: The regression model with stochastic regressor We will first look
More informationEcon 300/QAC 201: Quantitative Methods in Economics/Applied Data Analysis. 18th Class 7/2/10
Econ 300/QAC 201: Quantitative Methods in Economics/Applied Data Analysis 18th Class 7/2/10 Out of the air a voice without a face Proved by statistics that some cause was just In tones as dry and level
More informationIntroductory Econometrics
Introductory Econometrics Violation of basic assumptions Heteroskedasticity Barbara Pertold-Gebicka CERGE-EI 16 November 010 OLS assumptions 1. Disturbances are random variables drawn from a normal distribution.
More informationInstrumental Variables
Università di Pavia 2010 Instrumental Variables Eduardo Rossi Exogeneity Exogeneity Assumption: the explanatory variables which form the columns of X are exogenous. It implies that any randomness in the
More informationEstimation of a Local-Aggregate Network Model with. Sampled Networks
Estimation of a Local-Aggregate Network Model with Sampled Networks Xiaodong Liu y Department of Economics, University of Colorado, Boulder, CO 80309, USA August, 2012 Abstract This paper considers the
More information1 The Multiple Regression Model: Freeing Up the Classical Assumptions
1 The Multiple Regression Model: Freeing Up the Classical Assumptions Some or all of classical assumptions were crucial for many of the derivations of the previous chapters. Derivation of the OLS estimator
More informationLecture 4: Linear panel models
Lecture 4: Linear panel models Luc Behaghel PSE February 2009 Luc Behaghel (PSE) Lecture 4 February 2009 1 / 47 Introduction Panel = repeated observations of the same individuals (e.g., rms, workers, countries)
More informationInstrumental 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 informationBirkbeck Economics MSc Economics, PGCert Econometrics MSc Financial Economics Autumn 2009 ECONOMETRICS Ron Smith :
Birkbeck Economics MSc Economics, PGCert Econometrics MSc Financial Economics Autumn 2009 ECONOMETRICS Ron Smith : R.Smith@bbk.ac.uk Contents 1. Background 2. Exercises 3. Advice on Econometric projects
More informationEconometrics. 7) Endogeneity
30C00200 Econometrics 7) Endogeneity Timo Kuosmanen Professor, Ph.D. http://nomepre.net/index.php/timokuosmanen Today s topics Common types of endogeneity Simultaneity Omitted variables Measurement errors
More informationA Note on the Correlated Random Coefficient Model. Christophe Kolodziejczyk
CAM Centre for Applied Microeconometrics Department of Economics University of Copenhagen http://www.econ.ku.dk/cam/ A Note on the Correlated Random Coefficient Model Christophe Kolodziejczyk 2006-10 The
More informationNotes on Heterogeneity, Aggregation, and Market Wage Functions: An Empirical Model of Self-Selection in the Labor Market
Notes on Heterogeneity, Aggregation, and Market Wage Functions: An Empirical Model of Self-Selection in the Labor Market Heckman and Sedlacek, JPE 1985, 93(6), 1077-1125 James Heckman University of Chicago
More informationMore on Specification and Data Issues
More on Specification and Data Issues Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) Specification and Data Issues 1 / 35 Functional Form Misspecification Functional
More informationProblem Set #6: OLS. Economics 835: Econometrics. Fall 2012
Problem Set #6: OLS Economics 835: Econometrics Fall 202 A preliminary result Suppose we have a random sample of size n on the scalar random variables (x, y) with finite means, variances, and covariance.
More information4.8 Instrumental Variables
4.8. INSTRUMENTAL VARIABLES 35 4.8 Instrumental Variables A major complication that is emphasized in microeconometrics is the possibility of inconsistent parameter estimation due to endogenous regressors.
More informationIV Estimation WS 2014/15 SS Alexander Spermann. IV Estimation
SS 2010 WS 2014/15 Alexander Spermann Evaluation With Non-Experimental Approaches Selection on Unobservables Natural Experiment (exogenous variation in a variable) DiD Example: Card/Krueger (1994) Minimum
More informationApplied Quantitative Methods II
Applied Quantitative Methods II Lecture 10: Panel Data Klára Kaĺıšková Klára Kaĺıšková AQM II - Lecture 10 VŠE, SS 2016/17 1 / 38 Outline 1 Introduction 2 Pooled OLS 3 First differences 4 Fixed effects
More informationFinal 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 informationLecture Notes on Measurement Error
Steve Pischke Spring 2000 Lecture Notes on Measurement Error These notes summarize a variety of simple results on measurement error which I nd useful. They also provide some references where more complete
More information5. Erroneous Selection of Exogenous Variables (Violation of Assumption #A1)
5. Erroneous Selection of Exogenous Variables (Violation of Assumption #A1) Assumption #A1: Our regression model does not lack of any further relevant exogenous variables beyond x 1i, x 2i,..., x Ki and
More informationExercise Sheet 4 Instrumental Variables and Two Stage Least Squares Estimation
Exercise Sheet 4 Instrumental Variables and Two Stage Least Squares Estimation ECONOMETRICS I. UC3M 1. [W 15.1] Consider a simple model to estimate the e ect of personal computer (P C) ownership on the
More informationECONOMETRICS II (ECO 2401) Victor Aguirregabiria. Spring 2018 TOPIC 4: INTRODUCTION TO THE EVALUATION OF TREATMENT EFFECTS
ECONOMETRICS II (ECO 2401) Victor Aguirregabiria Spring 2018 TOPIC 4: INTRODUCTION TO THE EVALUATION OF TREATMENT EFFECTS 1. Introduction and Notation 2. Randomized treatment 3. Conditional independence
More informationGMM Estimation with Noncausal Instruments
ömmföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Papers GMM Estimation with Noncausal Instruments Markku Lanne University of Helsinki, RUESG and HECER and Pentti Saikkonen
More informationReturns to Tenure. Christopher Taber. March 31, Department of Economics University of Wisconsin-Madison
Returns to Tenure Christopher Taber Department of Economics University of Wisconsin-Madison March 31, 2008 Outline 1 Basic Framework 2 Abraham and Farber 3 Altonji and Shakotko 4 Topel Basic Framework
More informationTesting for Regime Switching: A Comment
Testing for Regime Switching: A Comment Andrew V. Carter Department of Statistics University of California, Santa Barbara Douglas G. Steigerwald Department of Economics University of California Santa Barbara
More informationApplied Econometrics. Lecture 3: Introduction to Linear Panel Data Models
Applied Econometrics Lecture 3: Introduction to Linear Panel Data Models Måns Söderbom 4 September 2009 Department of Economics, Universy of Gothenburg. Email: mans.soderbom@economics.gu.se. Web: www.economics.gu.se/soderbom,
More informationRecitation 1: Regression Review. Christina Patterson
Recitation 1: Regression Review Christina Patterson Outline For Recitation 1. Statistics. Bias, sampling variance and hypothesis testing.. Two important statistical theorems: Law of large numbers (LLN)
More informationMicroeconometrics: Clustering. Ethan Kaplan
Microeconometrics: Clustering Ethan Kaplan Gauss Markov ssumptions OLS is minimum variance unbiased (MVUE) if Linear Model: Y i = X i + i E ( i jx i ) = V ( i jx i ) = 2 < cov i ; j = Normally distributed
More informationInstrumental Variables. Ethan Kaplan
Instrumental Variables Ethan Kaplan 1 Instrumental Variables: Intro. Bias in OLS: Consider a linear model: Y = X + Suppose that then OLS yields: cov (X; ) = ^ OLS = X 0 X 1 X 0 Y = X 0 X 1 X 0 (X + ) =)
More informationEconometrics Lecture 1 Introduction and Review on Statistics
Econometrics Lecture 1 Introduction and Review on Statistics Chau, Tak Wai Shanghai University of Finance and Economics Spring 2014 1 / 69 Introduction This course is about Econometrics. Metrics means
More informationI 1. 1 Introduction 2. 2 Examples Example: growth, GDP, and schooling California test scores Chandra et al. (2008)...
Part I Contents I 1 1 Introduction 2 2 Examples 4 2.1 Example: growth, GDP, and schooling.......................... 4 2.2 California test scores.................................... 5 2.3 Chandra et al.
More informationFöreläsning /31
1/31 Föreläsning 10 090420 Chapter 13 Econometric Modeling: Model Speci cation and Diagnostic testing 2/31 Types of speci cation errors Consider the following models: Y i = β 1 + β 2 X i + β 3 X 2 i +
More informationThe returns to schooling, ability bias, and regression
The returns to schooling, ability bias, and regression Jörn-Steffen Pischke LSE October 4, 2016 Pischke (LSE) Griliches 1977 October 4, 2016 1 / 44 Counterfactual outcomes Scholing for individual i is
More informationAGEC 661 Note Fourteen
AGEC 661 Note Fourteen Ximing Wu 1 Selection bias 1.1 Heckman s two-step model Consider the model in Heckman (1979) Y i = X iβ + ε i, D i = I {Z iγ + η i > 0}. For a random sample from the population,
More informationWooldridge, Introductory Econometrics, 3d ed. Chapter 16: Simultaneous equations models. An obvious reason for the endogeneity of explanatory
Wooldridge, Introductory Econometrics, 3d ed. Chapter 16: Simultaneous equations models An obvious reason for the endogeneity of explanatory variables in a regression model is simultaneity: that is, one
More informationEconometrics. 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 informationHandout 12. Endogeneity & Simultaneous Equation Models
Handout 12. Endogeneity & Simultaneous Equation Models In which you learn about another potential source of endogeneity caused by the simultaneous determination of economic variables, and learn how to
More informationWhen is it really justifiable to ignore explanatory variable endogeneity in a regression model?
Discussion Paper: 2015/05 When is it really justifiable to ignore explanatory variable endogeneity in a regression model? Jan F. Kiviet www.ase.uva.nl/uva-econometrics Amsterdam School of Economics Roetersstraat
More informationOn the Power of Tests for Regime Switching
On the Power of Tests for Regime Switching joint work with Drew Carter and Ben Hansen Douglas G. Steigerwald UC Santa Barbara May 2015 D. Steigerwald (UCSB) Regime Switching May 2015 1 / 42 Motivating
More informationThe Augmented Solow Model Revisited
The Augmented Solow Model Revisited Carl-Johan Dalgaard Institute of Economics University of Copenhagen February, 2005 Abstract This note briefly discusses some recent (re-)investigations of the (augmented)
More informationUltra High Dimensional Variable Selection with Endogenous Variables
1 / 39 Ultra High Dimensional Variable Selection with Endogenous Variables Yuan Liao Princeton University Joint work with Jianqing Fan Job Market Talk January, 2012 2 / 39 Outline 1 Examples of Ultra High
More informationStatistics II. Management Degree Management Statistics IIDegree. Statistics II. 2 nd Sem. 2013/2014. Management Degree. Simple Linear Regression
Model 1 2 Ordinary Least Squares 3 4 Non-linearities 5 of the coefficients and their to the model We saw that econometrics studies E (Y x). More generally, we shall study regression analysis. : The regression
More informationContents. University of York Department of Economics PhD Course 2006 VAR ANALYSIS IN MACROECONOMICS. Lecturer: Professor Mike Wickens.
University of York Department of Economics PhD Course 00 VAR ANALYSIS IN MACROECONOMICS Lecturer: Professor Mike Wickens Lecture VAR Models Contents 1. Statistical v. econometric models. Statistical models
More informationLecture 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 informationApplied Quantitative Methods II
Applied Quantitative Methods II Lecture 4: OLS and Statistics revision Klára Kaĺıšková Klára Kaĺıšková AQM II - Lecture 4 VŠE, SS 2016/17 1 / 68 Outline 1 Econometric analysis Properties of an estimator
More informationPseudo panels and repeated cross-sections
Pseudo panels and repeated cross-sections Marno Verbeek November 12, 2007 Abstract In many countries there is a lack of genuine panel data where speci c individuals or rms are followed over time. However,
More informationLab 07 Introduction to Econometrics
Lab 07 Introduction to Econometrics Learning outcomes for this lab: Introduce the different typologies of data and the econometric models that can be used Understand the rationale behind econometrics Understand
More informationClub Convergence: Some Empirical Issues
Club Convergence: Some Empirical Issues Carl-Johan Dalgaard Institute of Economics University of Copenhagen Abstract This note discusses issues related to testing for club-convergence. Specifically some
More informationWhat Accounts for the Growing Fluctuations in FamilyOECD Income March in the US? / 32
What Accounts for the Growing Fluctuations in Family Income in the US? Peter Gottschalk and Sisi Zhang OECD March 2 2011 What Accounts for the Growing Fluctuations in FamilyOECD Income March in the US?
More information1 Static (one period) model
1 Static (one period) model The problem: max U(C; L; X); s.t. C = Y + w(t L) and L T: The Lagrangian: L = U(C; L; X) (C + wl M) (L T ); where M = Y + wt The FOCs: U C (C; L; X) = and U L (C; L; X) w +
More informationEmpirical Methods in Applied Microeconomics
Empirical Methods in Applied Microeconomics Jörn-Ste en Pischke LSE November 2007 1 Nonlinearity and Heterogeneity We have so far concentrated on the estimation of treatment e ects when the treatment e
More informationApplied Econometrics Lecture 1
Lecture 1 1 1 Università di Urbino Università di Urbino PhD Programme in Global Studies Spring 2018 Outline of this module Beyond OLS (very brief sketch) Regression and causality: sources of endogeneity
More informationWrite your identification number on each paper and cover sheet (the number stated in the upper right hand corner on your exam cover).
STOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods in Economics 2 Course code: EC2402 Examiner: Peter Skogman Thoursie Number of credits: 7,5 credits (hp) Date of exam: Saturday,
More informationExam D0M61A Advanced econometrics
Exam D0M61A Advanced econometrics 19 January 2009, 9 12am Question 1 (5 pts.) Consider the wage function w i = β 0 + β 1 S i + β 2 E i + β 0 3h i + ε i, where w i is the log-wage of individual i, S i is
More informationAbility Bias, Errors in Variables and Sibling Methods. James J. Heckman University of Chicago Econ 312 This draft, May 26, 2006
Ability Bias, Errors in Variables and Sibling Methods James J. Heckman University of Chicago Econ 312 This draft, May 26, 2006 1 1 Ability Bias Consider the model: log = 0 + 1 + where =income, = schooling,
More informationRegression with time series
Regression with time series Class Notes Manuel Arellano February 22, 2018 1 Classical regression model with time series Model and assumptions The basic assumption is E y t x 1,, x T = E y t x t = x tβ
More informationLecture Notes Part 7: Systems of Equations
17.874 Lecture Notes Part 7: Systems of Equations 7. Systems of Equations Many important social science problems are more structured than a single relationship or function. Markets, game theoretic models,
More informationECON 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 informationEndogeneity. Tom Smith
Endogeneity Tom Smith 1 What is Endogeneity? Classic Problem in Econometrics: More police officers might reduce crime but cities with higher crime rates might demand more police officers. More diffuse
More informationSimultaneous 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 informationThe College Premium in the Eighties: Returns to College or Returns to Ability
The College Premium in the Eighties: Returns to College or Returns to Ability Christopher Taber March 4, 2008 The problem of Ability Bias were A i is ability Y i = X i β + αs i + A i + u i If A i is correlated
More informationExercise sheet 3 The Multiple Regression Model
Exercise sheet 3 The Multiple Regression Model Note: In those problems that include estimations and have a reference to a data set the students should check the outputs obtained with Gretl. 1. Let the
More informationSimultaneous Equation Models
Simultaneous Equation Models Suppose we are given the model y 1 Y 1 1 X 1 1 u 1 where E X 1 u 1 0 but E Y 1 u 1 0 We can often think of Y 1 (and more, say Y 1 )asbeing determined as part of a system of
More informationChapter 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 informationEconometrics Problem Set 4
Econometrics Problem Set 4 WISE, Xiamen University Spring 2016-17 Conceptual Questions 1. This question refers to the estimated regressions in shown in Table 1 computed using data for 1988 from the CPS.
More informationMultiple Choice Questions (circle one part) 1: a b c d e 2: a b c d e 3: a b c d e 4: a b c d e 5: a b c d e
Economics 102: Analysis of Economic Data Cameron Fall 2005 Department of Economics, U.C.-Davis Final Exam (A) Tuesday December 16 Compulsory. Closed book. Total of 56 points and worth 40% of course grade.
More informationEcon 582 Fixed Effects Estimation of Panel Data
Econ 582 Fixed Effects Estimation of Panel Data Eric Zivot May 28, 2012 Panel Data Framework = x 0 β + = 1 (individuals); =1 (time periods) y 1 = X β ( ) ( 1) + ε Main question: Is x uncorrelated with?
More informationRecitation Notes 5. Konrad Menzel. October 13, 2006
ecitation otes 5 Konrad Menzel October 13, 2006 1 Instrumental Variables (continued) 11 Omitted Variables and the Wald Estimator Consider a Wald estimator for the Angrist (1991) approach to estimating
More informationEstimation of Dynamic Nonlinear Random E ects Models with Unbalanced Panels.
Estimation of Dynamic Nonlinear Random E ects Models with Unbalanced Panels. Pedro Albarran y Raquel Carrasco z Jesus M. Carro x June 2014 Preliminary and Incomplete Abstract This paper presents and evaluates
More informationDynamic Regression Models (Lect 15)
Dynamic Regression Models (Lect 15) Ragnar Nymoen University of Oslo 21 March 2013 1 / 17 HGL: Ch 9; BN: Kap 10 The HGL Ch 9 is a long chapter, and the testing for autocorrelation part we have already
More informationUNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Postponed exam: ECON4160 Econometrics Modeling and systems estimation Date of exam: Wednesday, January 8, 2014 Time for exam: 09:00 a.m. 12:00 noon The problem
More information4 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 informationEconometrics I KS. Module 2: Multivariate Linear Regression. Alexander Ahammer. This version: April 16, 2018
Econometrics I KS Module 2: Multivariate Linear Regression Alexander Ahammer Department of Economics Johannes Kepler University of Linz This version: April 16, 2018 Alexander Ahammer (JKU) Module 2: Multivariate
More informationow variables (sections A1. A3.); 2) state-level average earnings (section A4.) and rents (section
A Data Appendix This data appendix contains detailed information about: ) the construction of the worker ow variables (sections A. A3.); 2) state-level average earnings (section A4.) and rents (section
More information