Econometric Analysis Of Cross Section And Panel Data/

por WOOLDRIDGE, Jeffrey M.
[ Livros ] Publicado por : MIT Press, (Estados Unidos:) Detalhes físicos: 752 p. ISBN:262232197. Ano: 1960 Tipo de Material: Livros
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1 Introduction
1.1 Causal Relationships and Cetens Paribus Analysis
1.2 The Stochastic Setting and Asymptotic Analysis
1.2.1 Data Structures
1.2.2 Asymptotic Analysis
1.3 Some Examples
1.4 Why Not Fixed Explanatory Variables?

2 Conditional Expectations and Related Concepts in Econometrics
2.1 The Role of Conditional Expectations in Econometrics
2.2 Features of Conditional Expectations
2.2.1 Definition and Examples
2.2.2 Partial Effects, Elasticities, and Semielasticities
2.2.3 The Error Form of Models of Conditional Expectations
2.2.4 Some Properties of Conditional Expectations
2.2.5 Average Partial Effects
2.3 Linear Projections
Appendix 2A
2.A.1 Properties of Conditional Expectations
2.A.2 Properties of Conditional Variances
2.A.3 Properties of Linear Projections

3 Basic Asymptotic Theory
3.1 Convergence of Deterministic Sequences
3.2 Convergence in Probability and Bounded in Probability
3.3 Convergence in Distribution
3.4 Limit Theorems for Random Samples
3.5 Luniting Behavior of Estimators and Test Statistics
3.5.1 Asymptotic Properties of Estimators
3.5.2 Asymptotic Properties of Test Statistics

4 The Single-Equation Linear Model and OLS Estimation
4.1 Overview of the Single-Equation Linear Model
4.2 Asymptotic Properties of OLS
4.2.1 Consistency
4.2.2 Asymptotic Inference Using OLS
4.2.3 Heteroskedasticity-Robust Inference
4.2.4 Lagrange Multiplier (Score) Tests
4.3 OLS Solutions to the Omitted Variables Problem
4.3.1 OLS Ignoring the Omitted Variables
4.3.2 The Proxy Variable—OLS Solution
4.3.3 Modeis with Interactions in Unobservables
4.4 Properties of OLS under Measurement Error
4.4.1 Measurement Error in the Dependent Variable
4.4.2 Measurement Error in an Explanatory Variable

5 Instrumental Variables Estimation of Single-Equation Linear Modeis
5.1 Instrumental Variables and Two-Stage Least Squares
5.1.1 Motivation for Instrumental Variables Estimation
5.1.2 Multiple Instruments: Two-Stage Least Squares
5.2 General Treatment of 2SLS
5.2.1 Consistency
5.2.2 Asymptotic Normality of 2SLS
5.2.3 Asymptotic Efficiency of 2SLS
5.2.4 Hypothesis Testing with 2SLS
5.2.5 Heteroskedasticity-Robust Inference for 2SLS
5.2.6 Potential Pitfalls with 2SLS
5.3 IV Solutions to the Omitted Variables and Measurement Error
5.3.1 Leaving the Omitted Factors in the Error Term
5.3.2 Solutions Using Indicators of the Unobservable

6 Additional Single-Equation Topics
6.1 Estimation with Generated Regressors and Instruments
6.1.1 OLS with Generated Regressors
6.1.2 2SLS with Generated Instruments
6.1.3 Generated Instruments and Regressors
6.2 Some Specification Tests
6.2.1 Testing for Endogeneity
6.2.2 Testing Overidentifying Restrictions
6.2.3 Testing Functional Form
6.2.4 Testing for Heteroskedasticity
6.3 Single-Equation Methods under Other Sampling Schemes
6.3.1 Pooled Cross Sections over Time
6.3.2 Geographically Stratified Samples
6.3.3 Spatial Dependence
6.3.4 Cluster Samples
Appendix 6A

7 Estimating Systems of Equations by OLS and GLS
7.1 Introduction
7.2 Some Examples
7.3 System OLS Estimation of a Multivariate Linear System
7.3.1 Preliminaries
7.3.2 Asymptotic Properties of System OLS
7.3.3 Testing Multiple Hypotheses
7.4 Consistency and Asymptotic Normality of Generalized Least Squares
7.4.1 Consistency
7.4.2 Asymptotic Normality
7.5 Feasible GLS
7.5.1 Asymptotic Properties
7.5.2 Asymptotic Variance of FGLS under a Standard Assumption
7.6 Testing Using FGLS
7.7 Seemingly Unrelated Regressions, Revisited
7.7.1 Comparison between OLS and FGLS for SUR Systems
7.7.2 Systems with Cross Equation Restrictions
7.7.3 Singular Variance Matrices in SUR Systems
7.8 The Linear Panei Data Model, Revisited
7.8.1 Assumptions for Pooled OLS
7.8.2 Dynamic Compieteness
7.8.3 A Note on Time Series Persistence
7.8.4 Robust Asymptotic Variance Matrix
7.8.5 Testing for Serial Correlation and Heteroskedasticity after Pooled OLS
7.8.6 Feasibie GLS Estimation under Strict Exogeneity

8 System Estimation by Instrumental Variables
8.1 Introduction and Exampies
8.2 A General Linear System of Equations
8.3 Generalized Method of Moments Estimation
8.3.1 A General Weighting Matrix
8.3.2 The System 2SLS Estimator
8.3.3 The Optimal Weighting Matrix
8.3.4 The Three-Stage Least Squares Estimator
8.3.5 Comparison between GMM 3SLS and Traditional 3SLS
8.4 Some Considerations When Choosing an Estimator
8.5 Testing Using GMM
8.5.1 Testing Classical Hypotheses
8.5.2 Testing Overidentification Restrictions
8.6 More Efficient Estimation and Optimai Instruments

9 Siinultaneous Equations Modeis
9.1 The Scope of Simultaneous Equations Modeis
9.2 Identiflcation in a Linear System
9.2.1 Exclusion Restrictions and Reduced Forms
9.2.2 General Linear Restrictions and Structural Equations
9.2.3 Unidentified, Just Identified, and Overidentified Equations
9.3 Estimation after Identification
9.3.1 The Robustness-Efficiency Trade-off
9.3.2 When Are 2SLS and 3SLS Equivalent?
9.3.3 Estimating the Reduced Form Parameters
9.4 Additional Topics in Linear SEMs
9.4.1 Using Cross Equation Restrictions to Achieve Identification
9.4.2 Using Covariance Restrictions to Achieve Identification
9.4.3 Subtieties Concerning Identification and Efficiency in Linear
9.5 SEMs Nonlinear in Endogenous Variables
9.5.1 Identification
9.5.2 Estimation
9.6 Different Instruments for Different Equations

10 Basic Linear Unobserved Effects Panei Data Modeis
10.1 Motivation: The Omitted Variables Problem
10.2 Assumptions about the Unobserved Effects and Explanatory Variables
10.2.1 Random or Fixed Effects?
10.2.2 Strict Exogeneity Assumptions on the Explanatory Variables
10.2.3 Some Examples of Unobserved Effects Panei Data Modeis
10.3 Estimating Unobserved Effects Modeis by Pooled OLS
10.4 Random Effects Methods
10.4.1 Estimation and Inference under the Basic Random Effects Assumptions
10.4.2 Robust Variance Matrix Estimator
10.4.3 A General FGLS Analysis
10.4.4 Testing for the Presence of an Unobserved Effect
10.5 Fixed Effects Methods
10.5.1 Consistency of the Fixed Effects Estimator
10.5.2 Asymptotic Inference with Fixed Effects
10.5.3 The Dummy Variable Regression
10.5.4 Serial Correlation and the Robust Variance Matrix Estimator
10.5.5 Fixed Effects GLS
10.5.6 Using Fixed Effects Estimation for Policy Analysis
10.6 First Differencing Methods
10.6.1 Inference
10.6.2 Robust Variance Matrix
10.6.3 Testing for Serial Correlation
10.6.4 Poiicy Analysis Using First Differencing
10.7 Comparison of Estimators
10.7.1 Fixed Effects versus First Differencing
10.7.2 The Relationship between the Random Effects and Fixed Effects Estimators
10.7.3 The Hausman Test Comparing the RE and FE Estimators

11 More Topics m Linear Unobserved Effects Modeis
11.1 Unobserved Effects Modeis without the Strict Exogeneity Assumption
11.1.1 Models under Sequential Moment Restrictio
11.1.2 Models with Strictly and Sequentially Exogenous Explanatory Variables
11.1.3 Modeis with Contemporaneous Correlation between Some Explanatory Variables and the Idiosyncratic Error
11.1.4 Summary of Modeis without Strictly Exogenous Explanatory Variables
11.2 Modeis with Individual-Specific Siopes
11.2.1 A Random Trend Model
11.2.2 General Modeis with Individual-Specific Siopes
11.3 GMM Approaches to Linear Unobserved Effects Models
11.3.1 Equivalence between 3SLS and Standard Panei Data Estimators
11.3.2 Chamberlain's Approach to Unobserved Effects Models
11.4 Hausman and Taylor-Type Models
11.5 Applying Panel Data Methods to Matched Pairs and Cluster Samples

12 M-Estimation
12.1 Introduction
12.2 Identification, Uniform Convergence, and Consistency
12.3 Asymptotic Normality
12.4 Two-Step M-Estimators
12.4.1 Consistency
12.4.2 Asymptotic Normality
12.5 Estimating the Asymptotic Variance
12.5.1 Estimation without Nuisance Parameters
12.5.2 Adjustments for Two-Step Estimation
12.6 Hypothesis Testing
12.6.1 Wald Tests
12.6.2 Score (or Lagrange Multiplier) Tests
12.6.3 Tests Based on the Change in the Objective Function
12.6.4 Behavior of the Statistics under Alternatives
12.7 Optimization Methods
12.7.1 The Newton-Raphson Method
12.7.2 The Berndt, Hall, Hall, and Hausman Algorithm
12.7.3 The Generalized Gauss-Newton Method
12.7.4 Concentrating Parameters out of the Objective Function
12.8 Simulation and Resampling Methods
12.8.1 Monte Carlo Simulation
12.8.2 Bootstrapping

13 Maximum Likelihood Methods
13.1 Introduction
13.2 Preliminaries and Examples
13.3 General Framework for Conditional MLE
13.4 Consistency of Conditional MLE
13.5 Asymptotic Normality and Asymptotic Variance Estimation
13.5.1 Asymptotic Normality
13.5.2 Estimating the Asymptotic Variance
13.6 Hypothesis Testing
13.7 Specilication Testing
13.8 Partial Likelihood Methods for Panel Data and Cluster Samples
13.8.1 Setup for Panel Data
13.8.2 Asymptotic Inference
13.8.3 Inference with Dynamically Complete Models
13.8.4 Inference under Cluster Sampling
13.9 Panel Data Modeis with Unobserved Effects
13.9.1 Modeis with Strictiy Exogenous Explanatory Variables
13.9.2 Modeis with Lagged Dependent Variables
13.10 Two-StepMLE
Appendix 13A

14 Generalized Method of Moments and Minimum Distance Estimation
14.1 Asymptotic Properties ofGMM
14.2 Estimation under Orthogonaiity Conditions
14.3 Systems of Noniinear Equations
14.4 Panei Data Applications
14.5 Efficient Estimation
14.5.1 A General Efficiency Framework
14.5.2 Efficiency of MLE
14.5.3 Efficient Choice of Instruments under Conditional Moment Restrictions
14.6 Classical Minimum Distance Estimation
Appendix 14A

15 Discrete Response Models
15.1 Introduction
15.2 The Linear Probability Model for Binary Response
15.3 Index Models for Binary Response: Probit and Logit
15.4 Maximum Likelihood Estimation of Binary Response Index Models
15.5Testing m Binary Response Index Modeis
15.5.1 Testing Multipie Exclusion Restrictions
15.5.2 Testing Nonlinear Hypotheses about
15.5.3 Tests against More General Alternatives
15.6 Reporting the Results for Probit and Logit
15.7 Specification Issues in Binary Response Models
15.7.1 Neglected Heterogeneity
15.7.2 Continuous Endogenous Expianatory Variables
15.7.3 A Binary Endogenous Explanatory Variable
15.7.4 Heteroskedasticity and Nonnormality in the Latent Variable Model
15.7.5 Estimation under Weaker Assumptions
15.8 Binary Response Models for Panel Data and Cluster Samples
15.8.1 Pooled Probit and Logit
15.8.2 Unobserved Effects Probit Models under Strict Exogeneity
15.8.3 Unobserved Effects Logit Models under Strict Exogeneity
15.8.4 Dynamic Unobserved Effects Models
15.8.5 Semiparametric Approaches
15.8.6 Cluster Samples
15.9 Multinomial Response Models
15.9.1 Multinomial Logit
15.9.2 Probabilistic Choice Models
15.10 Ordered Response Models
15.10.1 Ordered Logit and Ordered Probit
15.10.2 Applying Ordered Probit to Interval-Coded Data
16 Comer Solution Outcomes and Censored Regression Models
16.1 Introduction and Motivation
16.2 Derivations of Expected Values
16.3 Inconsistency of OLS
16.4 Estimation and Inference with Censored Tobit
16.5 Reporting the Results
16.6 Specffication Issues in Tobit Models
16.6.1 Neglected Heterogeneity
16.6.2 Endogenous Explanatory Variables
16.6.3 Heteroskedasticity and Nonnormality in the Latent Variable Model
16.6.4 Estimation under Conditional Median Restrictions
16.7 Some Alternatives to Censored Tobit for Comer Solution Outcomes
16.8 Applying Censored Regression to Panel Data and Cluster Samples
16.8.1 Pooled Tobit
16.8.2 Unobserved Effects Tobit Models under Strict Exogeneity
16.8.3 Dynamic Unobserved Effects Tobit Models
17 Sample Selection, Attrition, and Stratified Sampling
17.1 Introduction
17.2 When Can Sample Selection Be Ignored?
17.2.1 Linear Models: OLS and 2SLS
17.2.2 Nonlinear Models
17.3 Selection on the Basis of the Response Variable: Truncated Regression
17.4 A Probit Selection Equation
17.4.1 Exogenous Explanatory Variables
17.4.2 Endogenous Explanatory Variables
17.4.3 Binary Response Model with Sample Selection
17.5 A Tobit Selection Equation
17.5.1 Exogenous Explanatory Variables
17.5.2 Endogenous Explanatory Variables
17.6 Estimating Structural Tobit Equations with Sample Selection
17.7 Sample Selection and Attrition in Linear Panel Data Models
17.7.1 Fixed Effects Estimation with Unbalanced Panels
17.7.2 Testing and Correcting for Sample Selection Bias
17.7.3 Attention
17.8 Stratified Sampling
17.8.1 Standard Stratified Sampling and Variable Probability Sampling
17.8.2 Weighted Estimators to Account for Stratification
17.8.3 Stratification Based on Exogenous Variables
18 Estimating Average Treatment Effects
18.1 Introduction
18.2 A Counterfactual Setting and the Self-Selection Problem
18.3 Methods Assuming Ignorability of Treatment
18.3.1 Regression Methods
18.3.2 Methods Based on the Propensity Score
18.4 Instrumental Variables Methods
18.4.1 Estimating the ATE Using IV
18.4.2 Estimating the Local Average Treatment Effect by IV
18.5 Further Issues
18.5.1 Special Considerations for Binary and Comer Solution Responses
18.5.2 Panel Data
18.5.3 Nonbinary Treatments
18.5.4 Multiple Treatments
19 Count Data and Related Models
19.1 Why Count Data Models?
19.2 Poisson Regression Models with Cross Section Data
19.2.1 Assumptions Used for Poisson Regression
19.2.2 Consistency of the Poisson QMLE
19.2.3 Asymptotic Normality of the Poisson QMLE
19.2.4 Hypothesis Testing
19.2.5 Specification Testing
19.3 Other Count Data Regression Models
19.3.1 Negative Binomial Regression Models
19.3.2 Binomial Regression Models
19.4 Other QMLEs in the Linear Exponential Family
19.4.1 Exponential Regression Models
19.4.2 Fractional Logit Regression
19.5 Endogeneity and Sample Selection with an Exponential Regression Function
19.5.1 Endogeneity
19.5.2 Sample Selection
19.6 Panel Data Methods
19.6.1 Pooled QMLE
19.6.2 Specifying Models of Conditional Expectations with Unobserved Effects
19.6.3 Random Effects Methods
19.6.4 Fixed Effects Poisson Estimation
19.6.5 Relaxing the Strict Exogeneity Assumption
20 Duration Analysis
20.1 Introduction
20.2 Hazard Functions
20.2.1 Hazard Functions without Covariates
20.2.2 Hazard Functions Conditional on Time-Invariant Covariates
20.2.3 Hazard Functions Conditional on Time-Varying Covariates
20.3 Analysis of Single-Spell Data with Time-Invariant Covariates
20.3.1 Flow Sampling
20.3.2 Maximum Likelihood Estimation with Censored Flow Data
20.3.3 Stock Sampling
20.3.4 Unobserved Heterogeneity
20.4 Analysis of Grouped Duration Data
20.4.1 Time-Invariant Covariates
20.4.2 Time-Varying Covariates
20.4.3 Unobserved Heterogeneity
20.5 Further Issues
20.5.1 Cox's Partia] Likelihood Method for the Proportional Hazard Model
20.5.2 Multiple-Spell Data
20.5.3 Competing Risks Modeis

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