Econometrics: A Simple Introduction

Econometrics: A Simple Introduction

By K.H. Erickson

Copyright © 2014 K.H. Erickson

All rights reserved.

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Also by K.H. Erickson

Simple Introductions

Choice Theory

Econometrics

Financial Economics

Game Theory

Game Theory for Business

Investment Appraisal

Microeconomics

Table of Contents

Introduction to Econometrics

Best Linear Unbiased Estimators (BLUE)

Hypothesis Testing

Multiple Regression

Dummy Variables

Chow Tests

Heteroscedasticity

Autocorrelation

Functional Form and Normality Tests

Method of Moments

Introduction to Econometrics

What exactly is econometrics? Like all branches of economics the field is designed to offer greater insight into the world around us, but econometrics is less concerned about theory and what should happen in a perfect world and more about what actually does happen in practice. The goal of econometrics is to understand the relationship between two (or more) variables, or in more simple terms to understand the cause of changes in real world variables. For example, the focus may be an examination of the factors affecting demand for a particular product, which would be of great concern to any business hoping to increase their sales. Or the analysis may look into the relationship between education level and salary, a topic of interest to those considering additional learning and certification.

The field being investigated for its determinants (e.g. product demand and sales, or salary income) is known as the dependent or y variable, and the issue being assessed as a possible cause (e.g. a product’s price, or education and certification level) is the independent or x variable. For every possible level of the independent x variable there will be a corresponding amount for the dependent y variable, as the following diagram example suggests.

The diagram shows different levels of a product’s price and the number of sales that may result, with the various black dots giving the relationship between the two. At price P1 there are S1 sales and every other price level will have its own level of demand and sales too. The information here shows a general negative relationship between price and sales, with higher prices linked with lower numbers of sales.

However, there will never be a definitive answer to the relationship between two variables, and there are always exceptions to any trend or rule. While a lower price may encourage higher product demand and sales there will be consumers who will buy a product no matter what the price. And although greater education and certification may be linked with a higher salary there are exceptions, with some people with little or no education still able to secure a well-paid job. The next diagram shows the overall trend between a hypothetical product’s price and the number of sales, known as a best fit line, with attention also drawn to an outlier that bucks the trend and is noticeably separate from this trend line.

The presence of a single outlier is noteworthy but it doesn’t affect the overall trend here, and the negative relationship between price and number of sales remains the most important feature. The best fit or trend line allows for predictions to be made for other values of price and sales not shown in the diagram, which is helpful for a business wanting to know the sales to expect for a certain price level and prepare their stock supply accordingly. In alternative scenarios with different variables under consideration it could show the likely returns to greater education, and in a more general sense the best fit line supports a greater understanding of cause and effect.

Econometrics essentially revolves around finding the best fit line giving the relationship between two variables, and this requires three pieces of information. First there is the intercept or constant, which is the point where the best fit line cuts the y axis of the y or dependent variable. The value of the intercept is usually symbolized with the Greek letter alpha, α. A second factor determining the best fit line is its slope, which may be positive and upward sloping or negative and downward sloping, and it may range from the horizontal to the vertical. The value of the best fit line’s slope can be symbolized with the Greek letter beta, β. Finally, there is the degree of error linked with the best fit line, which shows how far the actual dependent variable data points are from the best fit line on average, represented by the Greek letter epsilon, ε.

An equation can summarize the relationship between the different factors, known as the linear regression model:

y = α + βx + ε

Y is the dependent variable (e.g. no. of sales here), and it equals the value of the intercept, added to the value of beta multiplied by the level of the independent x variable (e.g. a product’s price), plus the size of the vertical error term. Another diagram can make the model clearer and