Econometrics for Daily Lives, Volume II

Tam Bang Vu

• Publisher: Business Expert Press
• Year: 2018
• Print ISBN: 9781631576881
• eBook ISBN: 9781631576898
• Topic: Economics
• Subtopic: Econometrics
• Index: Economics

This volume deals with advanced topics and specific problems in applied econometrics. Part III introduces advanced topics in econometric theory and contains three chapters. Chapter 7 deals with modeling issues and some phenomena that occur when the dataset you have collected has certain problems that need special attention for your results to be reliable. Chapter 8 analyzes the concepts and models that are not linear in their forms. Chapter 9 introduces several interesting models in advanced time-series techniques when a dataset is not stationary. Part IV applies the theoretical concepts learned in the previous chapters into empirical research. This part also consists of three chapters. Chapter 10 discusses the problem of selection bias and correcting methods. Chapter 11 introduces the regression discontinuity design and differences-in-differences models. Chapter 12 presents steps to carry out an empirical research project and provides strategies to avoid pitfalls in applied econometrics.

PART III

Advanced Topics

This part contains three chapters:

• Chapter 7: Modeling Issues and Endogeneity

• Chapter 8: Nonlinearity and Limited Dependent Variables

• Chapter 9: Advanced Time Series Techniques

CHAPTER 7

Modeling Issues and Endogeneity

Touro shares an anecdote with us. His company sent him to China last week to carry out a study on demand for travel from Chinese residents. However, his colleagues in China warned him that China’s data have a great deal of measurement errors. He is wondering how we can control for this problem. Prof. Metric tells him not to worry, because we will discuss the issue this week. He says that upon finishing with this chapter, we will be able to:

1. Analyze several modeling issues in regression.

2. Explain cases when endogeneity occurs.

3. Detect endogeneity problems and perform the correction procedure.

4. Apply Excel tools into estimating the related models.

We will discuss the modeling issues first because some of them are related to the endogeneity problem.

Modeling Issues

Model Specification

Unless we develop an econometric model based on a theoretical model, there will always be the possibility of having fewer or more variables than needed.

Omitted Variables

An omitted variable will significantly bias the regression coefficients. Given a model

If all coefficient estimates of this model are significant, but we accidentally omit x_i2, then there are two consequences:

1. The coefficient estimates will be biased.

2. The variances will be incorrect, so the test results will be invalid.

For example, given the model:

where DUR is durable expenditures, WAGE is average weekly wage, ASSETP is average asset price, and DURP is durable price. If a₁, a₂, a₃, and a₄ are all significant, but we accidentally eliminate ASSETP, then there is an omitted-variable problem.

Irrelevant Variables

Including irrelevant variables will not significantly bias the regression coefficients, but the Ordinary Least Squares (OLS) procedure may provide incorrect variances of the coefficient estimates, so the tests are less reliable as discussed in Kmenta (2000). For example, if we accidentally add average stock price (STOCKP), having forgotten that we already included it in the ASSETP variable sometime in the past, then TOCKP is an irrelevant variable to Equation (7.2) and the model becomes:

The presence of the irrelevant variable, STOCKP, will not bias the coefficient estimates of the relevant variables, but their variances might be incorrect, so the test results will be less reliable.

We now see that choosing a correct model is crucial. Prof. Metric says that we might want to use a piecewise-downward approach starting from all theoretically possible variables with all available data. We then use F- and t-tests to eliminate the highly insignificant variables. He says that we can also use a piecewise-upward approach, which starts from a single explanatory variable. However, the downward approach is preferable, because this approach avoids the omitted variable problem that might arise if you use the piecewise-upward approach.

The Effect of Scaling the Data

Prof. Metric points out three cases of scaling the data.

1. Changing the scale of x: The only factor affected is the standard error, but it changes by the same proportion, so the t-statistic and R² are unaffected. The interpretation changes according to the new unit.

2. Change in the scale of y: The standard error is scaled up or down, but it also changes by the same proportion, so the t-statistic and R² are unaffected. The interpretation changes according to the new unit.

3. Scale of x and y are changed by the same factor, then there is no change in the regression results for b₂ and its standard error. The t-statistic and R² are unaffected. The interpretation changes according to the new unit.

We then work on an example of a spending model:

SPEND = 61.7 + 12.4 INCOMER² = 0.685

(se) (8.76)(3.52)

where income (INCOME) is in hundreds of dollars and spending (SPEND) is in dollars.

In this case, the two-tail t-statistics for INCOME is 3.52 (= 12.4/3.52).

Hence, spending changes by $12.40 when income change...

Table of contents

• Cover
• Half-title Page
• Title Page
• Copyright
• Contents
• Preface
• Acknowledgments
• Part III Advanced Topics
• Part IV Applied Topics
• Bibliography
• About the Author
• Index
• Backcover