Introduction to Econometrics Lecture 01

 

                               Introduction to Econometrics

Introduction to Econometrics

The term “econometrics” comes from the Greek words “econo” and “metrics” and means the measurement of economic relationships. The literal definition of econometrics is that it is primarily concerned with the measurement and analysis of economic variables and phenomena. Ranger Frisch and Jan Tinbergen were involved in the development of mathematical economics theories and coined the term 'econometrics' to describe economic systems through the use of statistical methods. Thus, Ranger Frisch is often considered the father of econometrics. Econometrics is a blend of economics, statistics, and mathematics that employs statistical and mathematical models to represent economic theories, evaluate the current ideas, and estimate future trends based on past data.

Definition:

Econometrics is the science and the art of applying mathematical and statistical techniques to analyze economic data with the objective of measuring the empirical validity of economic theory. Thus, econometrics is a specialized discipline to check that a particular economic theory is valid or not in the real world and very helpful in the economic theory development. It is also very helpful to evaluate the current situation and forecast the future scenario by manipulations.

Economic theory theorized the relationship between economic variables in an economic phenomenon, while econometrics is used to test if those theories are actually valid in an empirical environment. It involves several steps. These steps are given below:

Theoretical economics theorized the relationship between economic variables. (e.g., if the income increases, consumption also increases). Mathematical economics translates the theorized statement into mathematical language or form (called a deterministic model).

Ct = β0 + β1 Yt 

Statistics transformed the deterministic model into a probabilistic model, which is the more realistic form, and attached a term to the right-hand side of the deterministic model.

Ct = β0 + β1 Yt + ϵt

Where:

 ϵt: captures all those variables that can influence the consumption–income phenomenon.

Statistical techniques are used to collect the data, estimate the model parameters, and determine the validity of the economic phenomenon.

Econometrics performs the following three tasks:

i. Verify economic theory/economic hypothesis.

ii. Estimating the parameters of the economic model.

iii. Forecasting economic outcomes.

Types of econometrics

Econometrics as a subject may be divided into two types.

1.      Theoretical Econometrics

2.      Applied Econometrics

Theoretical Econometrics

Theoretical econometrics is concerned with the development of appropriate methods for measuring the economic relationships specified by econometric model, like ordinary least squares method, maximum likely method, etc.

Applied Econometrics

Applied econometrics involves the applications of the tools of theoretical econometrics for the analysis of economic phenomena and forecasting economic behavior. Applied econometrics is used to research government economic policies or an economic issue in any sector of industry or trade.

Methodology of Econometrics

1.      Statement of economic theory or hypothesis

In this step we define an economic theory or hypothesize the relationship between economic variables in phenomena. e.g., we have an economic statement in which Keynes states that “consumers increase their consumption as their income increases but not so much as their income increases.”

MPC: Marginal proficiency cost will lie between 0 and 1.

2.      Specification of the model

In this step translate the relationship between variables in economics into a mathematical model.

 Y = β₀ + β₁X

Where:

0 < β1 < 1

Y is consumption, X is income, and β₀ is the mean consumption when there is no increase in income, called the intercept.

It means that the consumption only depends on income, but this is not true in the case of the econometric model. There are so many other factors (like number of children, residence, …) that influence the consumption. These other influential factors are captured by  called an error term and attached to the right-hand side of the mathematical model.

  Y = β₀ + β1 X + ϵ

Where β₀ and β₁ are called parameters of the model.

3.      Obtaining statistic (data)

To obtain the estimates (numerical values) of  and  represented by  and , collect the data from the past.

e.g., Data on price and consumption are given below:

 

Year	Y	X
2015	55	67
2016	58	70
2017	60	72

4.      Estimation of the econometric model

Using the techniques of basic econometrics and estimating the model parameters.

Here we use the OLS method to estimate β₀ and β₁, represented by β^₀ and β^₁, and collect the data from the past.

From sample data we compute β^0 = 54.00 and β^1 = 0.56.

The estimate of the model is given below:

Y^ = 54.00 + 0.56 X

5.      Hypothesis Testing

We develop certain criteria to check whether the fitted econometric model is according to the expectation of the economic theory or not.

In the above fitted model we test the hypothesis as

HA: β1 < 1

If the above hypothesis is justified, we can say the fitted model supports Keynes; otherwise, not.

6.      Forecasting

If the model has supported the theory, then this model can be used to forecast the values of consumption.

Why econometrics as a separate discipline?

Economic theory is a qualitative statement or hypothesis that provides no numerical measure of the relationship between the variables under study.

Example: Other things remain constant; if price falls, demand rises.

It does not specify how much the price will drop or how much the demand will increase. While econometrics adds empirical content to most economic theory.

Mathematical statistics only transform the relationship between economic variables into mathematical form without regard to empirical verification of the theory.

The demand of a product depends on price.

Demand = Mean demand + β X Price + Error

Economics statistics only collect and process the data on variables and represent them visually. The job of empirical verification is performed by econometrics.

 Following is the timeline to study econometrics:

·          Regression

·         Problems in Regression Analysis

·         Simultaneous Equations & Stochastic Regression

·         Identification

·         Estimation

• Read More: Introduction to Regression
• Read More: Introduction to Statistics
• Read More: Introduction to Time Series