# Chapter 10: Basic Linear Unobserved Effects Panel Data. Models:

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 10: Basic Linear Unobserved Effects Panel Data Models: Microeconomic Econometrics I Spring Motivation: The Omitted Variables Problem We are interested in the partial effects of the observable explanatory variables x j in the population regression function E(y x 1, x 2,..., x k, c) (10.1) An unobserved,time-constant variable is called an unobserved effect in panel data analysis. Such a data set is usually called a balanced panel because the same time periods are available for all cross section units. 1

2 10.2 Assumptions about the Unobserved Effects and Explanatory Variables Random or Fixed Effects? The basic unobserved effects model (UEM) can be written, for a randomly drawn cross section observation i, as y it = x it β + c i + u it, t = 1,2,..., T (10.11) In addition to unobserved effect, there are many other names given to c i in applications: unobserved component, latent variable, and unobserved heterogeneity are common. If i indexes individuals, then c i is sometimes called an individual effect or individual heterogeneity; analogous terms apply to families, firms, cities, and other cross-sectional units. The u it are called the idiosyncratic errors or idiosyncratic disturbances because these change across t as well as across i. Nevertheless, later we will label two different estimation methods random effects estimation and fixed effects estimation. 2

3 Strict Exogeneity Assumptions on the Explanatory Variables With an unobserved effect the most revealing form of the strict exogeneity assumption is E(y it x i1, x i2,..., x it, c i ) = E(y it x it, c i ) = x it β + c i (10.12) When assumption (10.12) holds, we say that the x it : t = 1,2,..., T are strictly exogenous conditional on the unobserved effect c i Some Examples of Unobserved Effects Panel Data Models 3

4 Example10.1(Program Evaluation): log(wage it ) = θ t + z it γ + δ 1 prog it + c i + u it (10.16) Example 10.2 (Distributed Lag Model): patents it = θ t + z it γ + δ 0 RD it + δ 1 RD i,t δ 5 RD i,t 5 + c i + u it (10.17) 4

5 Example 10.3 (Lagged Dependent Variable): log(wage it ) = β 1 log(wage i,t 1 ) + c i + u it, t = 1,2,..., T (10.18) 10.3 Estimating Unobserved Effects Models by Pooled OLS Under certain assumptions, the pooled OLS estimator can be used to obtain a consistent estimator of β in model (10.11). Write the model as y it = x it β + υ it, t = 1,2,..., T (10.21) where υ it c i + u it, t = 1,2,...T are the composite errors. 5

6 10.4 Random Effects Methods Estimation and Inference under the Basic Random Effects Assumptions As with pooled OLS, a random effects analysis puts c i into the error term. Assumption RE.1: 1. E(u it x i, c i ) = 0, t = 1,..., T. 2. E(c i x i ) = E(c i ) = 0 where x i (x i1, x i2,..., x it ). Assumption RE.2: rank E(X i Ω 1 X i ) = K. When Ω has the form (10.31), we say it has the random effects structure. Assumption RE.3: 1. E(u i u i x i, c i ) = σ 2 u I T. 2. E(c 2 i x i) = σ 2 c In a panel data context, the FGLS estimator that uses the variance matrix (10.33) is what is known as the random effects estimator: ( N ˆβ RE = X ˆΩ ) 1 ( N 1 i X i X ˆΩ ) 1 i y i i=1 i=1 (10.34) Example 10.4(RE Estimation of the Effects of Job Training Grants): log(ŝcrap) = d d union.215 grant.377 grant 1 (.243) (.109) (.132) (.411) (.148) (.205) 6

7 Robust Variance Matrix Estimator A General FGLS Analysis If the idiosyncratic errors u it : t = 1,2,..., T are generally heteroskedastic and serially correlated across t, a more general estimator of Ω can be used in FGLS: ˆΩ = N 1 N ˆv i ˆv i (10.38) i=1 7

8 Testing for the Presence of an Unobserved Effect From equation (10.37), we base a test of H 0 : σ 2 c = 0 on the null asymptotic distribution of N 1/2 N T 1 T i=1 t=1 s=t+1 ˆυ it ˆυ is (10.39) which is essentially the estimator ˆσ 2 c scaled up by N Fixed Effects Methods Consistency of the Fixed Effects Estimator Again consider the linear unobserved effects model for T time periods: y it = x it β + c i + u it, t = 1,..., T (10.41) 8

9 Assumption FE.1: E(u it x i, c i ) = 0, t = 1,2,..., T. In this section we study the fixed effects transformation, also called the within transformation. The fixed effects (FE) estimator, denoted by ˆβFE,is the pooled OLS estimator from the regression ÿ it on ẍ it, t = 1,2,..., T; i = 1,2,..., N (10.48) This set of equations can be obtained by premultiplying equation (10.42) by a timedemeaning matrix. Assumption FE.2: rank( Tt=1 E(ẍ itẍit) ) [ ] = rank E(Ẍ i Ẍ i) = K. It is also called the within estimator because it uses the time variation within each cross section. The between estimator, which uses only variation between the cross section observations, is the OLS estimator applied to the time-averaged equation (10.45). 9

10 Asymptotic Inference with Fixed Effects Assumption FE.3: E(u i u i x i, c i ) = σ 2 u I T. To see how to estimate σ 2 u, we use equation (10.51) summed across t : T t=1 E(ü 2 it ) = (T 1)σ 2 u, and so [N(T 1)] 1 N Tt=1 i=1 E(ü 2 it ) = σ2 u.now, define the fixed effects residuals as û it = ÿ it ẍ it ˆβFE, t = 1,2,..., T; i = 1,2,..., N (10.55) which are simply the OLS residuals from the pooled regression (10.48). Example 10.5(FE Estimation of the Effects of Job Training Grants): log(ŝcrap) =.080 d d grant.422 grant 1 (.109) (.133) (.151) (.210) 10

11 The Dummy Variable Regression The estimator of β obtained from regression (10.57) is, in fact, the fixed effects estimator. This is why ˆβFE is sometimes referred to as the dummy variable estimator Serial Correlation and the Robust Variance Matrix Estimator Applying equation (7.26), the robust variance matrix estimator of ˆβFE is Ava ˆr( ˆβFE ) = (Ẍ Ẍ) 1( N Ẍ iûiû i Ẍ i) (Ẍ Ẍ) 1 (10.59) which was suggested by Arellano (1987) and follows from the general results of White (1984, Chapter 6). i=1 11

12 Example 10.5 (continued): log(ŝcrap) =.080 d d grant.422 grant 1 (.109) (.133) (.151) (.210) [.096] [.193] [.140] [.276] Fixed Effects GLS Assumption FEGLS.3: E(u i u i x i, c i ) = Λ, a T T positive definite matrix. The fixed effects GLS (FEGLS) estimator is defined by ˆβ FEGLS = ( N Ẍ ˆΩ 1 ) 1 ( N i Ẍ i Ẍ ˆΩ 1 ) i ÿ i i=1 i=1 where Ẍ i and ÿ i are defined with the last time period dropped. 12

13 Assumption FEGLS.2: ranke(ẍ i ˆΩ 1 Ẍ i ) = K Using Fixed Effects Estimation for Policy Analysis Consider the model y it = x it β + υ it = z it γ + δw it + υ it where υ it may or may not contain an unobserved effect. 13

14 10.6 First Differencing Methods Inference Assumption FD.1: Same as Assumption FE.1. Lagging the model (10.41) one period and subtracting gives y it = x it β + u it, t = 2,3,..., T (10.63) where y it = y it y i,t 1, x it = x it x i,t 1, and u it = u it u i,t 1. As with the FE transformation, this first-differencing transformation eliminates the unobserved effect c i. The first-difference (FD) estimator, ˆβF D, is the pooled OLS estimator from the regression y it on x it, t = 2,..., T; i = 1,2,..., N (10.65) Tt=2 ) Assumption FD.2: rank( E( x it x it) = K. Assumption FD.3: E(e i e i x i1,..., x it, c i ) = σ 2 e I T 1, where e i is the (T 1) 1 vector containing e it,t = 2,..., T. 14

15 Robust Variance Matrix If Assumption FD.3 is violated, then, as usual, we can compute a robust variance matrix. The estimator in equation (7.26) applied in this context is Avar( ˆ ˆβFD ) = ( X X) 1( N ) X i êi ê i X i ( X X) 1 (10.70) where X denotes the N(T 1) K matrix of stacked first differences of x it. i=1 Example 10.6 (FD Estimation of the Effects of Job Training Grants): log(scrap it ) = δ 1 + δ 2 d89 t + β 1 grant it + β 2 grant i,t 1 + u it 15

16 Testing for Serial Correlation The regression is based on T 2 time periods: ê it = ˆp 1 ê i,t 1 + error it, t = 3,4,..., T; i = 1,2,..., N (10.71) Example10.6 (continued): Policy Analysis Using First Differencing In this one case, prog i = prog i2,and the first-differenced equation can be written as y i2 = θ 2 + z i2 γ + δ 1 prog i2 + u i2 (10.72) 16

17 When z i2 is omitted, the estimate of δ 1 from equation (10.72) is the difference-indifferences (DID) estimator (see Problem 10.4): ˆ 1 = y t reat y c ortrol Comparison of Estimators Fixed Effects versus First Differencing With more than two time periods, a test of strict exogeneity is a test of H 0 : γ = 0 in the expanded equation y t = x t β + w t γ + u t, t = 2,..., T where w t is a subset of x t (that would exclude time dummies). 17

18 The Relationship between the Random Effects and Fixed Effects Estimators Using the fact that j T j T = T, we can write Ω under the random effects structure as Ω = σ 2 u I T + σ 2 c j T j T = σ2 u I T + Tσ 2 c j T( j T j T) 1 j T = σ2 u I T + Tσ 2 c P T = (σ 2 u + σ2 c )(P T + ηq T ) where P T I T Q T = j T ( j T j T) 1 j T and η σ2 u /(σ2 u + Tσ2 c ). Equation (10.76) shows that the random effects estimator is obtained by a quasitime demeaning: rather than removing the time average from the explanatory and dependent variables at each t, random effects removes a fraction of the time average. Example 10.7 (Job Training Grants): The Hausman Test Comparing the RE and FE Estimators 18

### Panel Data: Linear Models

Panel Data: Linear Models Laura Magazzini University of Verona laura.magazzini@univr.it http://dse.univr.it/magazzini Laura Magazzini (@univr.it) Panel Data: Linear Models 1 / 45 Introduction Outline What

### ON THE ROBUSTNESS OF FIXED EFFECTS AND RELATED ESTIMATORS IN CORRELATED RANDOM COEFFICIENT PANEL DATA MODELS

ON THE ROBUSTNESS OF FIXED EFFECTS AND RELATED ESTIMATORS IN CORRELATED RANDOM COEFFICIENT PANEL DATA MODELS Jeffrey M. Wooldridge THE INSTITUTE FOR FISCAL STUDIES DEPARTMENT OF ECONOMICS, UCL cemmap working

### SYSTEMS OF REGRESSION EQUATIONS

SYSTEMS OF REGRESSION EQUATIONS 1. MULTIPLE EQUATIONS y nt = x nt n + u nt, n = 1,...,N, t = 1,...,T, x nt is 1 k, and n is k 1. This is a version of the standard regression model where the observations

### FIXED EFFECTS AND RELATED ESTIMATORS FOR CORRELATED RANDOM COEFFICIENT AND TREATMENT EFFECT PANEL DATA MODELS

FIXED EFFECTS AND RELATED ESTIMATORS FOR CORRELATED RANDOM COEFFICIENT AND TREATMENT EFFECT PANEL DATA MODELS Jeffrey M. Wooldridge Department of Economics Michigan State University East Lansing, MI 48824-1038

### What s New in Econometrics? Lecture 8 Cluster and Stratified Sampling

What s New in Econometrics? Lecture 8 Cluster and Stratified Sampling Jeff Wooldridge NBER Summer Institute, 2007 1. The Linear Model with Cluster Effects 2. Estimation with a Small Number of Groups and

### Panel Data Models. Chapter 5. Financial Econometrics. Michael Hauser WS15/16

1 / 63 Panel Data Models Chapter 5 Financial Econometrics Michael Hauser WS15/16 2 / 63 Content Data structures: Times series, cross sectional, panel data, pooled data Static linear panel data models:

### Econometric Methods for Panel Data

Based on the books by Baltagi: Econometric Analysis of Panel Data and by Hsiao: Analysis of Panel Data Robert M. Kunst robert.kunst@univie.ac.at University of Vienna and Institute for Advanced Studies

### Correlated Random Effects Panel Data Models

INTRODUCTION AND LINEAR MODELS Correlated Random Effects Panel Data Models IZA Summer School in Labor Economics May 13-19, 2013 Jeffrey M. Wooldridge Michigan State University 1. Introduction 2. The Linear

### Clustering in the Linear Model

Short Guides to Microeconometrics Fall 2014 Kurt Schmidheiny Universität Basel Clustering in the Linear Model 2 1 Introduction Clustering in the Linear Model This handout extends the handout on The Multiple

### 2. Pooled Cross Sections and Panels. 2.1 Pooled Cross Sections versus Panel Data

2. Pooled Cross Sections and Panels 2.1 Pooled Cross Sections versus Panel Data Pooled Cross Sections are obtained by collecting random samples from a large polulation independently of each other at different

### Econometric Analysis of Cross Section and Panel Data Second Edition. Jeffrey M. Wooldridge. The MIT Press Cambridge, Massachusetts London, England

Econometric Analysis of Cross Section and Panel Data Second Edition Jeffrey M. Wooldridge The MIT Press Cambridge, Massachusetts London, England Preface Acknowledgments xxi xxix I INTRODUCTION AND BACKGROUND

### Department of Economics Session 2012/2013. EC352 Econometric Methods. Solutions to Exercises from Week 10 + 0.0077 (0.052)

Department of Economics Session 2012/2013 University of Essex Spring Term Dr Gordon Kemp EC352 Econometric Methods Solutions to Exercises from Week 10 1 Problem 13.7 This exercise refers back to Equation

### Introduction to Regression Models for Panel Data Analysis. Indiana University Workshop in Methods October 7, 2011. Professor Patricia A.

Introduction to Regression Models for Panel Data Analysis Indiana University Workshop in Methods October 7, 2011 Professor Patricia A. McManus Panel Data Analysis October 2011 What are Panel Data? Panel

### DEPARTMENT OF ECONOMICS. Unit ECON 12122 Introduction to Econometrics. Notes 4 2. R and F tests

DEPARTMENT OF ECONOMICS Unit ECON 11 Introduction to Econometrics Notes 4 R and F tests These notes provide a summary of the lectures. They are not a complete account of the unit material. You should also

### Heteroskedasticity and Weighted Least Squares

Econ 507. Econometric Analysis. Spring 2009 April 14, 2009 The Classical Linear Model: 1 Linearity: Y = Xβ + u. 2 Strict exogeneity: E(u) = 0 3 No Multicollinearity: ρ(x) = K. 4 No heteroskedasticity/

### Testing for Serial Correlation in Fixed-Effects Panel Data Models

Testing for Serial Correlation in Fixed-Effects Panel Data Models Benjamin Born Jörg Breitung In this paper, we propose three new tests for serial correlation in the disturbances of fixed-effects panel

### Instrumental Variables & 2SLS

Instrumental Variables & 2SLS y 1 = β 0 + β 1 y 2 + β 2 z 1 +... β k z k + u y 2 = π 0 + π 1 z k+1 + π 2 z 1 +... π k z k + v Economics 20 - Prof. Schuetze 1 Why Use Instrumental Variables? Instrumental

### . This specification assumes individual specific means with Ey ( ) = µ. We know from Nickell (1981) that OLS estimates of (1.1) are biased for S S

UNIT ROOT TESTS WITH PANEL DATA. Consider the AR model y = αy ( ), it it + α µ + ε i it i =,... N, t =,..., T. (.) where the ε 2 IN(0, σ ) it. This specification assumes individual specific means with

### ECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2

University of California, Berkeley Prof. Ken Chay Department of Economics Fall Semester, 005 ECON 14 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE # Question 1: a. Below are the scatter plots of hourly wages

### Instrumental Variables (IV) Instrumental Variables (IV) is a method of estimation that is widely used

Instrumental Variables (IV) Instrumental Variables (IV) is a method of estimation that is widely used in many economic applications when correlation between the explanatory variables and the error term

### Panel Data: Fixed and Random Effects

Short Guides to Microeconometrics Fall 2015 Kurt Schmidheiny Unversität Basel Panel Data: Fixed and Random Effects 1 Introduction In panel data, individuals (persons, firms, cities, ) are observed at several

### Variance of OLS Estimators and Hypothesis Testing. Randomness in the model. GM assumptions. Notes. Notes. Notes. Charlie Gibbons ARE 212.

Variance of OLS Estimators and Hypothesis Testing Charlie Gibbons ARE 212 Spring 2011 Randomness in the model Considering the model what is random? Y = X β + ɛ, β is a parameter and not random, X may be

### A Subset-Continuous-Updating Transformation on GMM Estimators for Dynamic Panel Data Models

Article A Subset-Continuous-Updating Transformation on GMM Estimators for Dynamic Panel Data Models Richard A. Ashley 1, and Xiaojin Sun 2,, 1 Department of Economics, Virginia Tech, Blacksburg, VA 24060;

### CHAPTER 6. SIMULTANEOUS EQUATIONS

Economics 24B Daniel McFadden 1999 1. INTRODUCTION CHAPTER 6. SIMULTANEOUS EQUATIONS Economic systems are usually described in terms of the behavior of various economic agents, and the equilibrium that

### Instrumental Variables & 2SLS

Instrumental Variables & 2SLS y 1 = β 0 + β 1 y 2 + β 2 z 1 +... β k z k + u y 2 = π 0 + π 1 z k+1 + π 2 z 1 +... π k z k + v Economics 20 - Prof. Schuetze 1 Why Use Instrumental Variables? Instrumental

### Employer-Provided Health Insurance and Labor Supply of Married Women

Upjohn Institute Working Papers Upjohn Research home page 2011 Employer-Provided Health Insurance and Labor Supply of Married Women Merve Cebi University of Massachusetts - Dartmouth and W.E. Upjohn Institute

### Lecture 3: Differences-in-Differences

Lecture 3: Differences-in-Differences Fabian Waldinger Waldinger () 1 / 55 Topics Covered in Lecture 1 Review of fixed effects regression models. 2 Differences-in-Differences Basics: Card & Krueger (1994).

### 2. What are the theoretical and practical consequences of autocorrelation?

Lecture 10 Serial Correlation In this lecture, you will learn the following: 1. What is the nature of autocorrelation? 2. What are the theoretical and practical consequences of autocorrelation? 3. Since

### C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)}

C: LEVEL 800 {MASTERS OF ECONOMICS( ECONOMETRICS)} 1. EES 800: Econometrics I Simple linear regression and correlation analysis. Specification and estimation of a regression model. Interpretation of regression

### 1 Introduction. 2 The Econometric Model. Panel Data: Fixed and Random Effects. Short Guides to Microeconometrics Fall 2015

Short Guides to Microeconometrics Fall 2015 Kurt Schmidheiny Unversität Basel Panel Data: Fixed and Random Effects 2 Panel Data: Fixed and Random Effects 1 Introduction In panel data, individuals (persons,

### Econometric Methods fo Panel Data Part II

Econometric Methods fo Panel Data Part II Robert M. Kunst University of Vienna April 2009 1 Tests in panel models Whereas restriction tests within a specific panel model follow the usual principles, based

### Exam and Solution. Please discuss each problem on a separate sheet of paper, not just on a separate page!

Econometrics - Exam 1 Exam and Solution Please discuss each problem on a separate sheet of paper, not just on a separate page! Problem 1: (20 points A health economist plans to evaluate whether screening

### Instrumental Variables Regression. Instrumental Variables (IV) estimation is used when the model has endogenous s.

Instrumental Variables Regression Instrumental Variables (IV) estimation is used when the model has endogenous s. IV can thus be used to address the following important threats to internal validity: Omitted

### What s New in Econometrics? Lecture 10 Difference-in-Differences Estimation

What s New in Econometrics? Lecture 10 Difference-in-Differences Estimation Jeff Wooldridge NBER Summer Institute, 2007 1. Review of the Basic Methodology 2. How Should We View Uncertainty in DD Settings?

### MODELS FOR PANEL DATA Q

Greene-2140242 book November 23, 2010 12:28 11 MODELS FOR PANEL DATA Q 11.1 INTRODUCTION Data sets that combine time series and cross sections are common in economics. The published statistics of the OECD

### Marketing Mix Modelling and Big Data P. M Cain

1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored

### UNIVERSITY OF WAIKATO. Hamilton New Zealand

UNIVERSITY OF WAIKATO Hamilton New Zealand Can We Trust Cluster-Corrected Standard Errors? An Application of Spatial Autocorrelation with Exact Locations Known John Gibson University of Waikato Bonggeun

### The Loss in Efficiency from Using Grouped Data to Estimate Coefficients of Group Level Variables. Kathleen M. Lang* Boston College.

The Loss in Efficiency from Using Grouped Data to Estimate Coefficients of Group Level Variables Kathleen M. Lang* Boston College and Peter Gottschalk Boston College Abstract We derive the efficiency loss

### Econometric Methods for Panel Data

Based on the books by Baltagi: Econometric Analysis of Panel Data and by Hsiao: Analysis of Panel Data Robert M. Kunst robert.kunst@univie.ac.at University of Vienna and Institute for Advanced Studies

### Wooldridge, Introductory Econometrics, 3d ed. Chapter 12: Serial correlation and heteroskedasticity in time series regressions

Wooldridge, Introductory Econometrics, 3d ed. Chapter 12: Serial correlation and heteroskedasticity in time series regressions What will happen if we violate the assumption that the errors are not serially

### 1. THE LINEAR MODEL WITH CLUSTER EFFECTS

What s New in Econometrics? NBER, Summer 2007 Lecture 8, Tuesday, July 31st, 2.00-3.00 pm Cluster and Stratified Sampling These notes consider estimation and inference with cluster samples and samples

### Examining the effects of exchange rates on Australian domestic tourism demand: A panel generalized least squares approach

19th International Congress on Modelling and Simulation, Perth, Australia, 12 16 December 2011 http://mssanz.org.au/modsim2011 Examining the effects of exchange rates on Australian domestic tourism demand:

### Structural Econometric Modeling in Industrial Organization Handout 1

Structural Econometric Modeling in Industrial Organization Handout 1 Professor Matthijs Wildenbeest 16 May 2011 1 Reading Peter C. Reiss and Frank A. Wolak A. Structural Econometric Modeling: Rationales

### Spatial panel models

Spatial panel models J Paul Elhorst University of Groningen, Department of Economics, Econometrics and Finance PO Box 800, 9700 AV Groningen, the Netherlands Phone: +31 50 3633893, Fax: +31 50 3637337,

### DISCUSSION PAPER SERIES

DISCUSSION PAPER SERIES No. 3048 GMM ESTIMATION OF EMPIRICAL GROWTH MODELS Stephen R Bond, Anke Hoeffler and Jonathan Temple INTERNATIONAL MACROECONOMICS ZZZFHSURUJ Available online at: www.cepr.org/pubs/dps/dp3048.asp

### Econometrics. Week 9. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague

Econometrics Week 9 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 21 Recommended Reading For the today Simultaneous Equations Models Chapter 16 (pp.

### IMPACT EVALUATION: INSTRUMENTAL VARIABLE METHOD

REPUBLIC OF SOUTH AFRICA GOVERNMENT-WIDE MONITORING & IMPACT EVALUATION SEMINAR IMPACT EVALUATION: INSTRUMENTAL VARIABLE METHOD SHAHID KHANDKER World Bank June 2006 ORGANIZED BY THE WORLD BANK AFRICA IMPACT

### Fixed Effects Bias in Panel Data Estimators

DISCUSSION PAPER SERIES IZA DP No. 3487 Fixed Effects Bias in Panel Data Estimators Hielke Buddelmeyer Paul H. Jensen Umut Oguzoglu Elizabeth Webster May 2008 Forschungsinstitut zur Zukunft der Arbeit

### Panel Data Analysis in Stata

Panel Data Analysis in Stata Anton Parlow Lab session Econ710 UWM Econ Department??/??/2010 or in a S-Bahn in Berlin, you never know.. Our plan Introduction to Panel data Fixed vs. Random effects Testing

### ANALYSIS OF FACTOR BASED DATA MINING TECHNIQUES

Advances in Information Mining ISSN: 0975 3265 & E-ISSN: 0975 9093, Vol. 3, Issue 1, 2011, pp-26-32 Available online at http://www.bioinfo.in/contents.php?id=32 ANALYSIS OF FACTOR BASED DATA MINING TECHNIQUES

### Chapter 2. Dynamic panel data models

Chapter 2. Dynamic panel data models Master of Science in Economics - University of Geneva Christophe Hurlin, Université d Orléans Université d Orléans April 2010 Introduction De nition We now consider

### Econometrics Simple Linear Regression

Econometrics Simple Linear Regression Burcu Eke UC3M Linear equations with one variable Recall what a linear equation is: y = b 0 + b 1 x is a linear equation with one variable, or equivalently, a straight

### The University of Kansas

All Greek Summary Rank Chapter Name Total Membership Chapter GPA 1 Beta Theta Pi 3.57 2 Chi Omega 3.42 3 Kappa Alpha Theta 3.36 4 Kappa Kappa Gamma 3.28 *5 Pi Beta Phi 3.27 *5 Gamma Phi Beta 3.27 *7 Alpha

### Poor identification and estimation problems in panel data models with random effects and autocorrelated errors

Poor identification and estimation problems in panel data models with random effects and autocorrelated errors Giorgio Calzolari Laura Magazzini January 7, 009 Submitted for presentation at the 15th Conference

### Implementing Panel-Corrected Standard Errors in R: The pcse Package

Implementing Panel-Corrected Standard Errors in R: The pcse Package Delia Bailey YouGov Polimetrix Jonathan N. Katz California Institute of Technology Abstract This introduction to the R package pcse is

### Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model

Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be written

### Is Infrastructure Capital Productive? A Dynamic Heterogeneous Approach.

Is Infrastructure Capital Productive? A Dynamic Heterogeneous Approach. César Calderón a, Enrique Moral-Benito b, Luis Servén a a The World Bank b CEMFI International conference on Infrastructure Economics

### Do Supplemental Online Recorded Lectures Help Students Learn Microeconomics?*

Do Supplemental Online Recorded Lectures Help Students Learn Microeconomics?* Jennjou Chen and Tsui-Fang Lin Abstract With the increasing popularity of information technology in higher education, it has

### 1. The Classical Linear Regression Model: The Bivariate Case

Business School, Brunel University MSc. EC5501/5509 Modelling Financial Decisions and Markets/Introduction to Quantitative Methods Prof. Menelaos Karanasos (Room SS69, Tel. 018956584) Lecture Notes 3 1.

### Econometrics Regression Analysis with Time Series Data

Econometrics Regression Analysis with Time Series Data João Valle e Azevedo Faculdade de Economia Universidade Nova de Lisboa Spring Semester João Valle e Azevedo (FEUNL) Econometrics Lisbon, May 2011

### MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

### The University of Kansas

Fall 2011 Scholarship Report All Greek Summary Rank Chapter Name Chapter GPA 1 Beta Theta Pi 3.57 2 Chi Omega 3.42 3 Kappa Alpha Theta 3.36 *4 Gamma Phi Beta 3.28 4 Kappa Kappa Gamma 3.28 6 Pi Beta Phi

### Panel Data Analysis Josef Brüderl, University of Mannheim, March 2005

Panel Data Analysis Josef Brüderl, University of Mannheim, March 2005 This is an introduction to panel data analysis on an applied level using Stata. The focus will be on showing the "mechanics" of these

### Chapter 1. Linear Panel Models and Heterogeneity

Chapter 1. Linear Panel Models and Heterogeneity Master of Science in Economics - University of Geneva Christophe Hurlin, Université d Orléans Université d Orléans January 2010 Introduction Speci cation

### Accounting for Time-Varying Unobserved Ability Heterogeneity within Education Production Functions

Accounting for Time-Varying Unobserved Ability Heterogeneity within Education Production Functions Weili Ding Queen s University Steven F. Lehrer Queen s University and NBER July 2008 Abstract Traditional

### Standard errors of marginal effects in the heteroskedastic probit model

Standard errors of marginal effects in the heteroskedastic probit model Thomas Cornelißen Discussion Paper No. 320 August 2005 ISSN: 0949 9962 Abstract In non-linear regression models, such as the heteroskedastic

### Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur

Regression Analysis Prof. Soumen Maity Department of Mathematics Indian Institute of Technology, Kharagpur Lecture - 7 Multiple Linear Regression (Contd.) This is my second lecture on Multiple Linear Regression

### Minimum LM Unit Root Test with One Structural Break. Junsoo Lee Department of Economics University of Alabama

Minimum LM Unit Root Test with One Structural Break Junsoo Lee Department of Economics University of Alabama Mark C. Strazicich Department of Economics Appalachian State University December 16, 2004 Abstract

### On Marginal Effects in Semiparametric Censored Regression Models

On Marginal Effects in Semiparametric Censored Regression Models Bo E. Honoré September 3, 2008 Introduction It is often argued that estimation of semiparametric censored regression models such as the

### OLS in Matrix Form. Let y be an n 1 vector of observations on the dependent variable.

OLS in Matrix Form 1 The True Model Let X be an n k matrix where we have observations on k independent variables for n observations Since our model will usually contain a constant term, one of the columns

### Chapter 3: The Multiple Linear Regression Model

Chapter 3: The Multiple Linear Regression Model Advanced Econometrics - HEC Lausanne Christophe Hurlin University of Orléans November 23, 2013 Christophe Hurlin (University of Orléans) Advanced Econometrics

### EC327: Advanced Econometrics, Spring 2007

EC327: Advanced Econometrics, Spring 2007 Wooldridge, Introductory Econometrics (3rd ed, 2006) Appendix D: Summary of matrix algebra Basic definitions A matrix is a rectangular array of numbers, with m

### 2. Linear regression with multiple regressors

2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression Assumptions

### Econometrics of Panel Data

Econometrics of Panel Data 1. Basics and Examples 2. The generalized least squares estimator 3. Fixed effects model 4. Random Effects model 1 1 Basics and examples We observes variables for N units, called

### Estimating the marginal cost of rail infrastructure maintenance. using static and dynamic models; does more data make a

Estimating the marginal cost of rail infrastructure maintenance using static and dynamic models; does more data make a difference? Kristofer Odolinski and Jan-Eric Nilsson Address for correspondence: The

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### An Introduction to Time Series Regression

An Introduction to Time Series Regression Henry Thompson Auburn University An economic model suggests examining the effect of exogenous x t on endogenous y t with an exogenous control variable z t. In

### Longitudinal (Panel and Time Series Cross-Section) Data

Longitudinal (Panel and Time Series Cross-Section) Data Nathaniel Beck Department of Politics NYU New York, NY 10012 nathaniel.beck@nyu.edu http://www.nyu.edu/gsas/dept/politics/faculty/beck/beck home.html

### PANEL DATA METHODS FOR FRACTIONAL RESPONSE VARIABLES WITH AN APPLICATION TO TEST PASS RATES

PANEL DATA METHODS FOR FRACTIONAL RESPONSE VARIABLES WITH AN APPLICATION TO TEST PASS RATES Leslie E. Papke Department of Economics Michigan State University East Lansing, MI 48824-1038 papke@msu.edu Jeffrey

### Least Squares Estimation

Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David

### Multiple Choice Models II

Multiple Choice Models II Laura Magazzini University of Verona laura.magazzini@univr.it http://dse.univr.it/magazzini Laura Magazzini (@univr.it) Multiple Choice Models II 1 / 28 Categorical data Categorical

### sftfe: A Stata command for fixed-effects stochastic frontier models estimation

sftfe: A Stata command for fixed-effects stochastic frontier models estimation Federico Belotti Giuseppe Ilardi CEIS, University of Rome Tor Vergata Bank of Italy 2014 Italian Stata Users Group Meeting

### Simultaneous Equations

Simultaneous Equations 1 Motivation and Examples Now we relax the assumption that EX u 0 his wil require new techniques: 1 Instrumental variables 2 2- and 3-stage least squares 3 Limited LIML and full

### A Basic Introduction to Missing Data

John Fox Sociology 740 Winter 2014 Outline Why Missing Data Arise Why Missing Data Arise Global or unit non-response. In a survey, certain respondents may be unreachable or may refuse to participate. Item

### 16 : Demand Forecasting

16 : Demand Forecasting 1 Session Outline Demand Forecasting Subjective methods can be used only when past data is not available. When past data is available, it is advisable that firms should use statistical

### An Investigation of the Statistical Modelling Approaches for MelC

An Investigation of the Statistical Modelling Approaches for MelC Literature review and recommendations By Jessica Thomas, 30 May 2011 Contents 1. Overview... 1 2. The LDV... 2 2.1 LDV Specifically in

### Sales forecasting # 1

Sales forecasting # 1 Arthur Charpentier arthur.charpentier@univ-rennes1.fr 1 Agenda Qualitative and quantitative methods, a very general introduction Series decomposition Short versus long term forecasting

### A General Approach to Variance Estimation under Imputation for Missing Survey Data

A General Approach to Variance Estimation under Imputation for Missing Survey Data J.N.K. Rao Carleton University Ottawa, Canada 1 2 1 Joint work with J.K. Kim at Iowa State University. 2 Workshop on Survey

α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =

### Capturing Cross-Sectional Correlation with Time Series: with an Application to Unit Root Test

Capturing Cross-Sectional Correlation with Time Series: with an Application to Unit Root Test Chor-yiu SIN Wang Yanan Institute of Studies in Economics (WISE) Xiamen University, Xiamen, Fujian, P.R.China,

### 1. When Can Missing Data be Ignored?

What s ew in Econometrics? BER, Summer 2007 Lecture 12, Wednesday, August 1st, 11-12.30 pm Missing Data These notes discuss various aspects of missing data in both pure cross section and panel data settings.

### 1. Review of the Basic Methodology

What s New in Econometrics? NBER, Summer 2007 Lecture 10, Tuesday, July 31st, 4.30-5.30 pm Difference-in-Differences Estimation These notes provide an overview of standard difference-in-differences methods

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### RUNNING A PROPER REGRESSION ANALYSIS. V G R CHANDRAN GOVINDARAJU UITM Website:

RUNNING A PROPER REGRESSION ANALYSIS V G R CHANDRAN GOVINDARAJU UITM Email: vgrchan@gmail.com Website: www.vgrchandran.com/default.html Topics Running a proper regression analysis First half of the day:

### The Effect of R&D Expenditures on Stock Returns, Price and Volatility

Master Degree Project in Finance The Effect of R&D Expenditures on Stock Returns, Price and Volatility A study on biotechnological and pharmaceutical industry in the US market Aleksandra Titi Supervisor:

### Econometric analysis of the Belgian car market

Econometric analysis of the Belgian car market By: Prof. dr. D. Czarnitzki/ Ms. Céline Arts Tim Verheyden Introduction In contrast to typical examples from microeconomics textbooks on homogeneous goods

### Premium Copayments and the Trade-off between Wages and Employer-Provided Health Insurance. February 2011

PRELIMINARY DRAFT DO NOT CITE OR CIRCULATE COMMENTS WELCOMED Premium Copayments and the Trade-off between Wages and Employer-Provided Health Insurance February 2011 By Darren Lubotsky School of Labor &

### problem arises when only a non-random sample is available differs from censored regression model in that x i is also unobserved

4 Data Issues 4.1 Truncated Regression population model y i = x i β + ε i, ε i N(0, σ 2 ) given a random sample, {y i, x i } N i=1, then OLS is consistent and efficient problem arises when only a non-random