Applied Econometrics Using the SAS System

Vivek Ajmani

• Publisher: Wiley-Interscience
• Year: 2011
• Print ISBN: 9780470129494
• eBook ISBN: 9781118210321
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

The first cutting-edge guide to using the SAS® system for the analysis of econometric data

Applied Econometrics Using the SAS® System is the first book of its kind to treat the analysis of basic econometric data using SAS®, one of the most commonly used software tools among today's statisticians in business and industry. This book thoroughly examines econometric methods and discusses how data collected in economic studies can easily be analyzed using the SAS® system.

In addition to addressing the computational aspects of econometric data analysis, the author provides a statistical foundation by introducing the underlying theory behind each method before delving into the related SAS® routines. The book begins with a basic introduction to econometrics and the relationship between classical regression analysis models and econometric models. Subsequent chapters balance essential concepts with SAS® tools and cover key topics such as:

• Regression analysis using Proc IML and Proc Reg
  
  

• Hypothesis testing
  
  

• Instrumental variables analysis, with a discussion of measurement errors, the assumptions incorporated into the analysis, and specification tests
  
  

• Heteroscedasticity, including GLS and FGLS estimation, group-wise heteroscedasticity, and GARCH models
  
  

• Panel data analysis
  
  

• Discrete choice models, along with coverage of binary choice models and Poisson regression
  
  

• Duration analysis models
  
  

Assuming only a working knowledge of SAS®, this book is a one-stop reference for using the software to analyze econometric data. Additional features include complete SAS® code, Proc IML routines plus a tutorial on Proc IML, and an appendix with additional programs and data sets. Applied Econometrics Using the SAS® System serves as a relevant and valuable reference for practitioners in the fields of business, economics, and finance. In addition, most students of econometrics are taught using GAUSS and STATA, yet SAS® is the standard in the working world; therefore, this book is an ideal supplement for upper-undergraduate and graduate courses in statistics, economics, and other social sciences since it prepares readers for real-world careers.

1

INTRODUCTION TO REGRESSION ANALYSIS

1.1 INTRODUCTION

The general purpose of regression analysis is to study the relationship between one or more dependent variable(s) and one or more independent variable(s). The most basic form of a regression model is where there is one independent variable and one dependent variable. For instance, a model relating the log of wage of married women to their experience in the work force is a simple linear regression model given by log(wage) = β₀ + β₁exper + ε, where β₀ and β₁ are unknown coefficients ande is random error. One objective here is to determine what effect (if any) the variable exper has on wage. In practice, most studies involve cases where there is more than one independent variable. As an example, we can extend the simple model relating log(wage) to exper by including the square of the experience (exper²) in the work force, along with years of education (educ). The objective here may be to determine what effect (if any) the explanatory variables (exper, exper², educ) have on the response variable log(wage). The extended model can be written as

where β₀, β₁, β₂, and β₃ are the unknown coefficients that need to be estimated, and ε is random error.

An extension of the multiple regression model (with one dependent variable) is the multivariate regression model where there is more than one dependent variable. For instance, the well-known Grunfeld investment model deals with the relationship between investment (I_it) with the true market value of a firm (F_it) and the value of capital (C_it) (Greene, 2003). Here, i indexes the firms and t indexes time. The model is given by I_it = β_0i + β_1iF_it + β_2iC_it + ε_it. As before, β_0i, β_i, and β_2i are unknown coefficients that need to be estimated and ε_it is random error. The objective here is to determine if the disturbance terms are involved in cross-equation correlation. Equation by equation ordinary least squares is used to estimate the model parameters if the disturbances are not involved in cross-equation correlations. A feasible generalized least squares method is used if there is evidence of cross-equation correlation. We will look at this model in more detail in our discussion of seemingly unrelated regression models (SUR) in Chapter 8.

Dependent variables can be continuous or discrete. In the Grunfeld investment model, the variable I_it is continuous. However, discrete responses are also very common. Consider an example where a credit card company solicits potential customers via mail. The response of the consumer can be classified as being equal to 1 or 0 depending on whether the consumer chooses to respond to the mail or not. Clearly, the outcome of the study (a consumer responds or not) isa discrete random variable. In this example, the response is a binary random variable. We will look at modeling discrete responses when we discuss discrete choice models in Chapter 10.

In general, a multiple regression model can be expressed as

(1.1)

where y is the dependent variable, β₀,…, β_k are the k + 1 unknown coefficients that need to be estimated, x₁,…, x_k are the k independent or explanatory variables, and ε is random error. Notice that the model is linear in parameters β₀,…,β_k and is therefore called a linear model. Linearity refers to how the parameters enter the model. For instance, the model

is also a linear model. However, the exponential model y = β₀ exp(–xβ₁) is a nonlinear model since the parameter β₁ enters the model in a nonlinear fashion through the exponential function.

1.1.1 Interpretation of the Parameters

One of the assumptions (to be discussed later) for the linear model is that the conditional expectation E(ε|x₁, …, x_k) equals zero. Under this assumption, the expectation, E(y|x₁,…,x_k) can be written as

That is, the regression model can be interpreted as the conditional expectation of y for given values of the explanatory variables x₁,…, x_k. In the Grunfeld example, we could discuss the expected investment for a given firm for known values of the firm's true market value and value of its capital. The intercept term, β₀, gives the expected value of y when all the explanatory variables are set at zero. In practice, this rarely makes sense since it is very uncommon to observe values of all the explanatory variables equal to zero. Furthermore, the expected value of y under such a case will often yield impossible results. The coefficient β_k is interpreted as the ...

Table of contents

• Cover
• Title page
• Copyright page
• Dedication
• Preface
• Acknowledgments
• 1: Introduction to Regression Analysis
• 2: Regression Analysis Using Proc IML and Proc Reg
• 3: Hypothesis Testing
• 4: Instrumental Variables
• 5: Nonspherical Disturbances and Heteroscedasticity
• 6: Autocorrelation
• 7: Panel Data Analysis
• 8: Systems of Regression Equations
• 9: Simultaneous Equations
• 10: Discrete Choice Models
• 11: Duration Analysis
• 12: Special Topics
• Appendix A: Basic Matrix Algebra for Econometrics
• Appendix B: Basic Matrix Operations in Proc IML
• Appendix C: Simulating the Large Sample Properties of the OLS Estimators
• Appendix D: Introduction to Bootstrap Estimation
• Appendix E: Complete Programs and Proc IML Routines
• References
• Index