Panel Data Econometrics

Common Factor Analysis for Empirical Researchers

Donggyu Sul

• Publisher: Routledge
• Year: 2019
• ISBN:
  9780429752971
• Edition: 1
• Topic: Betriebswirtschaft
• Subtopic: Business allgemein

In the last 20 years, econometric theory on panel data has developed rapidly, particularly for analyzing common behaviors among individuals over time. Meanwhile, the statistical methods employed by applied researchers have not kept up-to-date. This book attempts to fill in this gap by teaching researchers how to use the latest panel estimation methods correctly.

Almost all applied economics articles use panel data or panel regressions. However, many empirical results from typical panel data analyses are not correctly executed. This book aims to help applied researchers to run panel regressions correctly and avoid common mistakes. The book explains how to model cross-sectional dependence, how to estimate a few key common variables, and how to identify them. It also provides guidance on how to separate out the long-run relationship and common dynamic and idiosyncratic dynamic relationships from a set of panel data.

Aimed at applied researchers who want to learn about panel data econometrics by running statistical software, this book provides clear guidance and is supported by a full range of online teaching and learning materials. It includes practice sections on MATLAB, STATA, and GAUSS throughout, along with short and simple econometric theories on basic panel regressions for those who are unfamiliar with econometric theory on traditional panel regressions.

1
Basic Structure of Panel Data

This chapter is the most basic and important chapter in this book. I encourage readers to digest this first chapter carefully. This chapter provides the basic structure of a panel data, which can be decomposed into time invariant individual specific variables, time-varying common variables, and time-varying individual specific variables. We will study how to identify each component statistically. By doing so, we will learn the economic meaning of each component.

Let y_it be a data of interest for the i−th individual (or firm, region, group, country) at time t.¹ The i−th unit is called the cross-sectional unit. The total number of the cross-sectional unit is denoted as n. That is, i = 1, …, n. The range of the time index is denoted as t = 1, …, T. The variable y must have the same attributes across i over t. For example, a panel of household income includes only income data for each household during a certain time period.

In the end, we will consider the following general structure of a panel data.

$$\begin{array}{c}\hfill y_{it}=a_i+b_{it}t+{\lambda }_{it}^{\text{'}}{\theta }_t+y_{it}^o,\end{array}$$

(1.1)

(1.1)

where a_i is a time invariant term, b_it is a time-varying individual growth rate, λ_it is a vector of time-varying factor loading coefficients, θ_t is a vector of common factors, and $y_{it}^o$ is a leftover term or purely idiosyncractic term. However, we start from a basic and simple model by assuming that b_it = 0 for all i and t, and λ_it = 1 for all i and t. These assumptions lead to

$$\begin{array}{c}\hfill y_{it}=a_i+{\theta }_t+y_{it}^o.\end{array}$$

(1.2)

(1.2)

Later we will relax these strong assumptions one by one.

1.1 Meaning of fixed effect

In this section, we study the economic meaning of the time invariant terms – a_i (individual mean) and b_i (slope coefficient on the trend term). First, we consider the economic meaning of a_i with non-trended data.

1.1.1 Fixed effects with non-trended data

We rewrite (1.2) as

$$\begin{array}{c}\hfill y_{it}=a_i+y_{it}^{*},\end{array}$$

(1.3)

where a_i is a time invariant unobserved variable, and $y_{it}^{*}$ is a time-varying variable with a mean of zero and finite variance. In this section, the parameter of interest is a_i, which is often called “fixed effect” among applied ecometricians.² Nonetheless, this unobserved time invariant variable can be identified and estimated if the number of time series...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• CONTENTS
• List of figures
• List of tables
• Preface
• 1 Basic structure of panel data
• 2 Statistical models for cross-sectional dependence
• 3 Factor number identification
• 4 Decomposition of panel: estimation of common and idiosyncratic components
• 5 Identification of Common Factors
• 6 Static and dynamic relationships
• 7 Convergence
• 8 Appendix: basic panel regressions
• References
• Index